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AD-Alll 511 NAVAL POSTGRADUATE SCHOOL MONTEREY CA F/6 17/7APPLICATION OF THE GLOBAL POSITIONING SYSTEM TO NEARSHORE NYORO--ETC(U)SEP 61 V E NEWELL, 0 0 WINTER
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NAVAL POSTGRADUATE SCHOOL- Monterey, California
DTICS MAR0 l1982
THESIS
I,
APPLICATIOI OF THE GLOBAL POSITIONING SYSTEMTO ;EARSHORE HYDROGRAPHIC SURVEYS "
by
Virginia E. N.1ewellDonald D. Winter
September, 1981
Thesis Advisors: R. W. Garwood, J, Von Schwind
Approved for public release, distribution unlimited
2 1
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,. REPORT NUM691 ".'GOVT ACCESSU ONO, S. RECIPtITS CATAL.OG NUlRSER
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Master's ThesisApplication of the Global Positioning System September, 1981to learshore Hydrographic Surveys . PERFORMNG OXG. REPORT NURA99ER
7. AUTmOtRe) . OW AC ONAuT NMU Rtej
Virginia Elisabeth NewellDonald Dane Winter
S. PIRPORING Oft"MIZAION MAMIE AND A0001666 A ANWR I)_fTwRj[Py TUNSE
::aval Postgraduate School
Monterey, California 939401 ONO6MOjC"U AAOOE2S 'a. REPORT CATE,, CONR~OLNG oC[ NAME .AR -'September, 1981
f!aval Postgraduate School, Monterey, CA 93940 24 NU5ERo9PAEsW I4. NONITORING A4ENCY NAME 6 AOICRSS(It dIt"IfrNI (FOM CR.1 mA4e1 Ofice) t. SWURITY CLASS. 'eei hs roten)
tie. O9CL. ASiIr1CATIONi OOWNGRAINGSCHIOULE
14. DISTNV19UTION STATEMENT NO We. Rep u)
* Approved for public release, distributionunlimited
I?. OISTRIeUTION STAT[MENT (tel t o bagt Erdli1f4 0810 20. IS teene Cm P" s qj
IS. SUPPI-EMENTARY NOTES
to. KEY WO6OS rCapOlu on o"@ eaeo of £Goe9 am aemefr or 61000 N10mb)
Global Positioning System, hydrography, translocation, ARTEMIS, theodolite
20. A66"ACT (COiRHO GR alga if ft....... Ifitly W neaj
Z Translocation of the Global Positioning System has proved to be a highlyaccurate method of position determination for onshore and airborne navigationbut it had not been previously evaluated for nearshore hydrographic surveys.The technique of translocation for hydrographic operations involves thesimultaneous reception of signals from the GPS satellites by two independentreceivers; one receiver onboard the survey vessel and one located at the
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known stationary position. A position correction is obtained at the stationary receiver, which is then applied to the shipboard receiver online orduring postprocessing. An accuracy determination of translocated GPS wasconducted at the Naval Postgraduate School, Monterey, CA, May, 1981. Twomethods of positioning were used for comparison with GPS: '1) a least square!solution of three lines of position observed from three Wild T-2 theodolitesjand 2) a position determined from ARTEMIS, a range-azimuth short rangemicrowave positioning system. Translocated GPS accuracies of 10 meters weredetermined. It is anticipated that greater accuracies will be obtained byusing a more sophisticated receiver and more advanced processing methods.
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Approved for public release, distribution unlimited
Application of the Global Positioning System toNearshore Hydrographic Surveys
by
Virginia Elisabeth lewell Donald Dane Winter
Lieutenant, NOAA Lieutenant Commiander, 1O0AAIB.A., University of Maine, 1971 B.S., University of Michigan,M.S., Virginia Polytechnic Institute 1973
and State University, 1975
Submitted in partial fulfillment of therequirements for the degree of
MASTER OF SCIENCE IN OCEANOGRAPHY (HYDROGRAPHY)
from the
NAVAL POSTGRADUATE SCHOOLSeptember, 1981
Authors:
Approved by:
Co-Advisor
Chai n, t c f O anoqrar'v
Dean of Science and Engineering
3
ABSTRACT
Translocation of the Global Positioning System has proved to be a highly
accurate method of position determination for onshore and airborne navi-
gation, but it had not been previously evaluated for nearshore hydro-
graohic surveys. The technique of translocation for hydrographic opera-
tions involves the simultaneous reception of signals from the GPS
satellites by two independent receivers; one receiver onboard the survey
vessel and one located at a known stationary position. A position
correction is obtained at the stationary receiver, which is then applied
to the shipboard receiver online or during postprocessing. An accuracy
determination of translocated GPS was conducted at the Naval Postgraduate
School, Monterey, CA, May, 1981. Two methods of positioning were used
for comparison with GPS: 1) a least squares solution of three lines of
position observed from three Wild T-2 theodolites, and 2) a position
determined from ARTEMIS, a range-azimuth short range microwave position-
ing system. Translocated GPS accuracies of 10 meters were determined.
It is anticipated that greater accuracies will be obtained by using a
more sophisticated receiver and more advanced processing methods.
4
I. INTRODUCTION ]
II. EQUIPMENT DESCRIPTION AND OPERATIONAL CAPABILITIES..22
1. ARTEMIS POSITIONING SYSTEM .................... 23
B. THEODOLITE NETWORK ............................. 26
C. TRANSIT POSITIONING SYSTEM ..................... 30
III. GPS SYSTEM DESCRIPTION AND OPERATIONALCAPABILITIES ........................ ..... 38
A. SYSTEM DESCRIPTION . .................. . 38
B. MANPACK RECEIVER ............................. 58
C. DIFFERENTIAL GPS * ........... . a .... *...... 7
IV. TEST PROCEDURE ................. ...... . . ... 070
A. POSITIONING NETUORK ...... 70
B. POSITIONING EQUIPMENT .......................... 72
751. Theodolites ...... 0-0. 7
2. GPS and ARTEMIS ............................ 77
C. LOG OF EVENTS ....................... q....0... 083
1 . S t a b i l i t y T s . . . . . . . . . . . . .. . . 8 4
2. Static Test ........................... 84
3. Shipboard Test .......................... 84
V. DATA PROCESSING METHODS ..........................88
A. BASIC SURVEY COMPUTATIONS ...................... 88
Li
B. THEODOLITE AND ARTEHIS SHIP POSITIONDETERMINATION ...........................
C. DIFFERENTIAL GPS SHIP POSITION DETERMINATION ...95
Do STATISTICAL DATA ANALYSIS ...................... 99
VI. ERROR ANALYSIS .......................... 103
A. ARTEMIS POSITIONIN3 SYSTEM ................... *103
1. Microvave System Errors ................... 103
2. ARTEMIS SysteU Errors ..................... 10
B. CONTROL NETWORK ............................... *112 jC. THEODOLITE NETWORK .................. 114
D. TRANSIT POSITIONING SYSTEM .................. 120
E. GPS ERROR SOURCES ........... ... .... *. ... .... 121
7 1 I I . R E S U L T S . . . . . . . . . . . . . . . . . . . . . . . . .] 3
A. STATIONARY GPS EVALUATION .. o................ 135
B. EVALUATION OF NONDIFFERENTIAL GPS ............. 158
C. DIFFERENTIAL GPS EVALUATION WITH STATICCORRECTIONS ...... ........... ..... 174
D. EVALUATION OF DIFFERENTIAL GPS WITHOUT STATICCORRECTIONS ......................... . 181
VIII. CONCLUSIONS ...............................
APPENDIX A ... .... ..... ........ ....... ...... .224
LIST OF REFERENCES .- ........ ... .o.o.-..f.. 228
BIBLIOGRAPHlY ...... . . ... . .. .. .. . . ... . .. .232 I
INITIAL DISTRIBUTION LIST .... .......................... 236
6
I. Ionospheric Group Delay as a Functionof Frequency .............................. 49
II. SANPACK Interface Wiring Code ...................... 66
III. Range Error Budget ............................. 68
IV. Satellite Observation Times ....................... 74_U,
V. Statistical Definitions ............................. 101
VI. Theodolite Instrument Errors ...................... 116
VII. TRANSIT System Errors ............................. 12
VIII. Ephemeris Update Times ........................... 127
7
2.1. TRANSIT Satellite ............................... 32
2.2. TRANSIT Satellite Orbital Network ............... 33
2.3. AN/PER 14 Geoceiver Antenna ..................... 36
- 3.1. The Nonuniform 18 Satellite Constellation ....... 45
3.2. Malker 18/3/0 Constellation Outages ............. 46
3.3. NAVSTAR Satellite ......................... ... 48
3.4. Pseudo-Range Description ........................ 57
3.5. Global Positioning System MVUE Receiver ......... 59
3.6. MVUE Receiver Face ................ .ee... 60
3.7. Cutaway of ,VUE Receiver .............. 61
3.8. NVUE CDU Keyboard/Display Layout ................ 63
3.9. Circuit Diagram of Receiver Interface ........... 65
4.1. Test Area with Traverse Sketch .................. 73
4.2. Antenna Tower on Coast Guard Pier ............... 78
4.3. R/V ACANIA Equipment Layout ..................... 81
4.4. Equipment Installation on the R/V ACANIA ........ 82
4.5. survey Area and Location of Sets by Day ......... 86
5.1. Error Ellipse ...... ....... 93
5.2. Differential GPS Processing ................... 98
6.1. ARTEMIS Range Holes ............................ 106
J8
6.2. ABTEMIS Systeu Error .......................... 109
6.3. Representative Theodolite Intersections for
Error Elipse Computations .............. oo 119
7.1. Stability Test Results 9,10 May ............... 136
7.2. Stability Test Results 9, 10 May ...-............ 137
7.3. Stability Test Results 9, 10 day ................ 138
7o4 Total User Range Error 9 May ...................139
7.5. Total User Range Error 10 May ................. 140
7.6. Static Test Results 11 May *.................... 142
7.7. Static Test Results 11 May ..................... 143
7.8. Static Test Results 11 May ..................... 44
7.9. Satellite Elevation &ngles..................... 1 4 5
7.10. Satellite Azimuth Angles .......... o........... 146
7.11. Total User Range Error 11 May .................. 47
7.12. Geoceiver vs. Gps Position Computation ......... 148
7.13. Distance Between Geoceiver and Stationary GPSPosition 12 ay ....enGe ...r .......d St.o... 150
7.14. Distance Between Geoceiver and Stationary GPSPosition 13 may ................................ 152
7.15. Distance Between Geoceiver and Stationary GPSP o s i t io n 15 M a y . . . . . . . . . . . . . .. . . . . . . 152
7.16. Total User Range Error 13 May o................. 153
7.17. Total User Range Error 15 May .................. 154
7.18. Azimuth Between Geoceiver and Stationary GPSPosition 12 May ........................ 155
I
7.19. Azimuth Between Geoceiver and Stationary GPSPosition 13 May ............................ 156
7.20. Aziauth Between Geoceiver and Stationary GPSPosition 15 May .............. .................. 157
7.21. Distance Between T- $hip Position andUncorrected GPS Position (4 Satellites) Set 1 .. 159
7.22. Distance Between T-? Ship Position andUncorrected GPS Position (4 Satellites) Set 2 .. 160
7.23. Distance Between T-2 Ship Position andUncorrected GPS Position (4 Satellites) Set 3 .. 161
7.24. Distance Between T-2 Ship Position andUncorrected GPS Posit lon (4 Satellites) Set 4 .. 162
7.25. Distance Between T-2 Ship Position andUncorrected GPS Position (4 Satellites) set 5 .. 163
7.26. Distance Between T-?.Ship Position andUncorrected GPS Posit on (4 Satellites) Set 6 .. 16d
7.27. Distance Between T-2 Ship Position andUncorrected GPS Position (4 Satellites) Set 7 .. 165
7.28. Distance Between T-2 Ship Position andUncorrected GPS Position (4 Satellites) Set 8 .. 166
7.29. Distance Between T-? 5hip Position andUncorrected GPS Position (4 Satellites)Sets 9 and 10 .................................. 167
7.30. Distance Between T-2 Ship Position andUncorrected GPS Position (4 Satellites) Set 11.. 168
7.31. Distance Between T-; $hip Position andUncorrected GPS Position (4 Satellites)Sets 12 and 13 ................................. 169
7.32. Total User Range Error 12 May .................. 170
7.33. Distance Between T-2 Ship Position andUncorrected GPS Position (5 Satellites) 12 [ay.. 171
7.34. Distance Between T-2 Ship Position andUncorrected GPS Position (5 Satellites) 13 lay.. 172
7.35. Distance Between T-2 Ship Position andUncorrected GPS Pos t on (5 Satellites) 15 [ay.. 173
10
7.36. Distance Between T-2 Ship Position andDifferential GPS Position With Static Correction1 75Set 1 ......... .............
7.37. Distance Between T-2 Ship Position andDifferential GPS Position With Static CorrectionSet 2 ..... .......... ........................ 176
7.38. Distance Between T-2 .Ship Positioa andDifferential GPS Position With Static CorrectionSet 3 ............... ....................... .. 177
7.39. Distance Between T-2 Ship Position andDifferential GPS Position Without StaticCorrection Set 1 ........................... 78
7.40. Distance petween T-2.Sbip Position andDifferential GPS Position Without StaticCorrection Set 2 ................... .... ...... 179
7.41. Distance Between T-2 Ship Position andDifferential GPS Position Without StaticCorrection Set 3 ........... .. 180
7.42. Azimuth Between T-2 Ship Position andDifferential GPS Position Without StaticCorrection Set 1 .............. ............. . 192
1 7.43. Azimuth Between T-2 Ship Position andDifferential GPS Position Without StaticCorrection Set 2 .. ... .... .............. 83
7.44. Azimuth Between T-2 Ship Position andDifferential GPS Position Without Static* Correction Set 3 ............................... 185
7.45. Distance Between ?-2 Ship Position andDifferential GPS Position Without StaticCorrection Set 4 ....... ..................... . 186
7.46. Azimuth Between T-2 Ship Position andDifferential GPS Position Without StaticCorrection Set 4 ............................... .187
7.47. Distance Between T-2 Ship Position andDifferential GPS Position Without StaticCorrection Set 5 .. .. ... .. ...................... 189
7.48. Azimuth Between T-2 Ship Position andDifferenLtial GPS Position Without StaticCorrection Set 5 ............................ 190
11
7.49. Distance Between T-2 Ship Position andDiffereiotial GPS Position, Without StxtiCcorrection Set 6 ...... .... .. 9.*.... 191
7.50. Azimuth Between T-2 $h'~ Poiion andDifferential GPS Posit ig 11 thloat StaticCorrection Set 6 ** *. ............* ........ 192
7.51. Distance Between T-2 Ship Position andDiffere~itial GPS Position Without StaticCorrection Set 8 ..... ..... ................... 193
7.52. Azimuth Bqtween. T-2 Ship Position andDifferential GPS Position Without StaticCorrection set 8 .................... ........ .194
7.53. Distance Between T-2 Ship Position andDiffereotial GPS Position Without StaticCorrection Sets 9 & 10 .*... ........ *............ 196
7.54. A:;iiiuth Between T-2 h4.p Position andDiffere~tial GPS Position Withouit StaticCorrection Sets 9 & 10.....................19
7.55. Distance Between T-2,Shiip Position and*Differential GPS Position. Without StaticCorrection Set 11 .. ......... ............. 198
7.56. A;imuth Bqtveen T-2 $h~.p Position andDifferential GPS Position. Without StaticCorrection Set 11 ........ .. ... ... .. .. .. . .. . . ... 199
7.57. Di.stance Between ?-2.Ship Position and*Differential GPS Pos-tion Without StaticCorrection Sets 12 & 13 . . . .......................... 201
7.58. A;imuthBptween T-2 ;h~ Position andDi fere tial GPS,3osi.ti n Without StaticCorrection Sets 12& 13 000. . . . . . . .... . . . ... .202
7.59. DitneBetween T-2 Ship Position andDifferential GPStPosition Without StaticCorrection (5 Satellites) 12 M~ay ............... 203
7.60. Distance Between T-2 Ship Position andDifferential GPS ?osition Without StaticCorrection (5 Satellites) 15 day ............... 204
7.61. Latitude Comparison Sets 1, 2 ........... 206
7.62. Longitude Comparison Sets 1, 2 ............. 207
12
7.63. Latitude Comparison Set 3 ...................... 208
7.64. Longitude Comparison Set 3 ..................... 209
7.65. Latitude Comparison Sets 4, 5 .................. 210
7.66. Longitude Comparison Sets 4, 5 ................. 211
7.67. Latitude Comparison Sets 6, 7 .................. 212
7.68. Longitude Comparison Sets 6, 7 ................ 213
7.69. Latitude Comparison Sets 8, 9 .................. 214
7.70. Longitude Comparison Sets 8, 9 ................ 215
7.71. Latitude Comparison Sets 10, 11 ................ 216
7.72. Longitude Comparison Sets 10, 11 .............. 217
7.73. Latitude Comparison Sets 12, 13 ................ 218
7.74. Longitude Comparison Sets 12, 13 ............... 219
1i
gO ABRREVTATIONS
BPS Bits Per Second
C/A Coarse Acquisition Code
CDU Control Data Unit
CHAS Circular Map Accuracy Standard
DNA Defense Mapping Agency
GMT Greenwich Mean Time
GPS Global Positioning System
HTC Hydrographic/Topographic Center at DNA
LMT Local Mean Time
3CS GPS Master Control Station
MIS NVUE Instrumentation System3VUE MANPACK Vehicular User Equipment
NAVSAT Navy Navigational Satellite System
NAVSTAR Global Positioning System
OTES NOAA Office of Ocean Technology and EngineeringSupport
P Precision Code
PVC Polyvinyl Chloride Pipe
SAMSO Space and Missile Systems Organization
UR1 User Range Error
USAF United States Air Force
?JGS 1972 world Geodetic System of 1972
ja4
ACKrIO!ILEDGEMENTS
We would like to thank all the NPS students and other individuals who
contributed their time and expertise during the long nights at the T-2
locations--without their support this thesis would not have been possible.
Thankts go to: Marjorie Amazeen, Bill Anderson, Gene Brown, Bob and Hac
Clar!k, Ron Dickerman, Barry Donovan, Pat Eaton, Mike Ellett, Jerry and
B.J. Mills, Dave tinkel, Roger Parsons and Annette Parsons, Alan Shaffer,
Keith Toepfer, Gerry Wheaton, and Jon Winter.
Special thanks also to Ted Calhoon for his cooperation and to the Captain
of the ACANIA, Woody Reynolds; and the crew members who contributed
their ideas for the equipment installation onboard the ship.
'!e would like to thank Mr. Knute Berstis and Mr. Gary bhitsell from OTES
for their time and efforts in making the thesis possible, and Cdr. A.
Durkee, of the Joint Programs Office, for his interest and bipport in
providing the GPS receivers.
15
I. TO ZO
Shipboard operations for the purpose of oceanographic
research, commercial transport, tactical operations, or
hydrographic surveying require accurate and dependable
positioning systems. The operation of most electronic
positioning systems is hampered by atmospheric effects on
the propagated signal and design limitations which restrict
operating ranges, positional accuracy and dependability. A
universal positioning system that provides accurate
information to the user regardless of atmospheric conditions
and that is free of range limitations is desirable. with
the advent of satellite positioning techniques, such a
system is now available.
The Navy Navigation Satellite System (NAVSAT), or
TRANSIT, has been operational since 1964 and has proved
dependable and sufficiently accurate for certain users.
Although developed for military uses, the application of
TRANSIT in the civilian community has continued to expand at
an exponential rate. The system, however, is limited by the
time interval between fixes, which is 90 minutes on the
average, and the requirement for precise knowledge of the
ship's velocity. Although the system does not provide
16
One method of improving system accuracy is by using two
receivers simultaneously in a technique termed
translocation, or differential mode. The method is based on
the assumption that signal propagation errors to two
proximate receivers are nearly the same. One receiver is
placed over a known position, and the variation of the
observed position with time is determined relative to the
absolute position. This variation is applied to the
observed positions determined by a simultaneously operating
receiver located at another location--on a survey vessel,
for example. The assumption underlying this technique is
that the distance between the two units is not sufficient to
introduce a significant additional propagation error. The
resulting position of the translocated receiver should be
more accurate than the position obtained using a single
receiver.
For hydrographic operations, the translocated Global
Positioning System (GPS) provides an alternative to
presently used positioning systems. The satellites orbit at
20,000 ki, which theoretically would allow receiver
separation of as much as 500 km without causing significant
additional system error. With this flexibility, one
17
sufficient positional accuracy for hydrographic surveying,
it has been used for geodetic application by the Defense
Mapping Agency (DNA) using fixed shore-based receivers to
establish positioning networks in inaccessible areas
worldwide. CRef. 1]
The Global Positioning System, or NAYSTAR, is a more
sophisticated system designed to replace TRANSIT in the
mid-1980s. Six satellites are currently in orbit with
twelve more to be launched before the operational date of
1987. The 18-satellite orbit configuration will provide a
multi-user, passive system with 24-hour availability, global
coverage, and possible fix intervals of less than one
second. The operational network consists of three
elements--the satellites, the ground-based control segment,
operated by the Space and Missile Systems Organization
(SIMSO), and the user's receiver. Prototype receivers have
been tested under optimum conditions by SAMSO at the Yuma
Proving Ground, Arizona, on both mobile and stationary
platforms. Results show excellent system stability and
accuracy when compared to currently used positioning
systems. [Ref. 2]
18
shorebased receiver could be placed at a central location
and a survey of several hundred kilometers of coastline or
offshore area could be completed with only one additional
receiver on the survey vessel. [Ref. 3] The value of this
flexibility would be realized in the significant decrease in
survey planning, cost, and time compared to that spent
presently in conducting hydrographic operations.
The accuracy of the system would be sufficient for all
survey scales. The National Ocean Survey (OS) defines the
required accuracy of a positioning system to be no more than
one-third of the survey accuracy, which is 1.5 millimeters
at the scale of the survey. (Ref. 4] Non-translocated GPS
has been shown to be of sufficient accuracy for 1:80,000
scale surveys and smaller. [Ref. 5]
The object of our research is to determine whether GPS
at the present operational level is adequate for 1:10,000
scale surveys. To do this, a position determined by two GPS
receivers in the translocated mode is compared to the same
position determined by two other methods. If translocated
GPS can be shown to achieve specified inshore survey
accuracies, the system would provide sufficient accuracies
at all smaller scale surveys.
19
L itlr TII
Part of the difficulty in determining this level of
accuracy concerns the reference system used. most geodetic
positions published by the National Geodetic Survey (IGS)
are based on the North American Reference Datum of 1927
(NAD-27) and the Clarke 1866 Ellipsoid, the best
approximation to the shape of the earvk f-- the continental
United States. The satellite syst* ,. ,ever, use a
reference system which is not bast.. rn z portion of the
earth's surface. A mass-centered *#!.- seid referenced to
the earth's center of mass has b.4P. zcoputed using observed
gravity and astronomical data. The best fit to this global
ellipsoid is the World Geodetic System of 1972 (WGS-72),
which is utilized by both ,TRANSIT and GPS. Transformation
equations exist which convert NAD-27 coordinates to WGS-72
coordinates, but uncertainty in the gravity model produces
errors as large as 10 meters due to the transformation
prccess alone. (Ref. 6]
To establish all positions on the same reference
ellipsoid for this research, a TRANSIT receiver was acquired
from DNA and a first order Doppler station was established
at the central location of the test area. A third order
geodetic survey was conducted from the TRANSIT station to
21)!
establish two additional stations on the UGS-72 ellipsoid.
Two single channel aanpack GPS receivers were obtained from
SANSO. Stability testing and a receiver comparison test
were conducted prior to shipboard testing to letermine a
quantitative measure of receiver performance. One of the
receivers was then placed over the TRANSIT station mark and
the other aboard a survey vessel which maneuvered along
j predetermined track lines. Data were recorded via an
interface to an HP-9825 computer and printer at each site.
Simultaneously, two additional independent measurements were
made of ship position--one using a range-azimuth short
range microwave positioning system (ARTEMIS) and the other a
position determined by a least squares solution of three
lines of position observed from three 1-second theodolites
set on the three pre-established VGS-72 locations. The
comparison of the ARTEMIS and theodolite-derived ship
positions with the translocated GPS ship position provided
the test results.
II. SOUIMM DESCRI PTIO ZLP BILITIES
Two positioning systems were chosen for comparison with
the Global Positioning System: a theodolite network and a
microwave positioning system. The theodolite network
consisted of three shore-based units so as to provide three
lines of position. The microwave positioning system
prcvided a range and an azimuth from a known location on
shore. Both systems are accurate at short ranges and
represent two contrasting methods of positioning--visual and
electronic. The theodolite method of positioning at short
range has been and continues to be used for hydrographic
operations as an alternative to electronic systems when
gecmetry and system accuracy limitations impose the need for
a more flexible positioning system. The requirement for
experienced theodolite observers as well as the
communication and logistics difficulties involved limit the
use of this method to special cases.
This chapter describes the ARTEMIS short-range
electronic positioning system, the operation of the
theodolite network as used during the comparison test, and
the TRANSIT satellite system.
22
A. ARTEMIS POSITIONING SYSTEM
The ARTEMIS position fixing system is a short-range
microwave system (to 30 km), built by Christiaan
Huygenslaboratorium B. V., in the Netherlands. It has been
used operationally (primarily in Europe) since 1972, when
the system was introduced at the International Hydrographic
Conference in Monaco. At the present time. fifty systems
are in use. The system is unique in design, is highly
accurate at short ranges, and is particularly useful for
small harbor surveys, river surveys and relative positioning
uses. For this study, the ARTEMIS system, along with
technical assistance, was obtained from the American
distributor, MARINAT Corporation of Houston, TEXAS.
ARTEMIS is a range-azimuth positioning system which
employs a unique tracking method. A stationary or fixed
unit is placed over a known position on shore. Using a
telescope that is mounted on the antenna, the antenna is
sighted onto another known point and the known azimuth
between the two locations Is entered into the system via a
digital display on the fixed unit. The unit is then locked
into place for operation. I mobile unit is placed on the
vessel whose position is desired.
23k4
The mobile and fixed antennas resemble radar antennas
which, while operating, track ,tach other so that the two
antennas are always parallel to each other and perpendicular
to the line of position between them. A microwave link is
established between the two antennas during periods of
measurement and information is relayed between the mobile
and fixed units. (A voice link is also available during
operation.) The fixed unit provides the direction and the
azimuth of the mobile unit with respect to the point sighted
on by the telescope. At the same time, the mobile unit
transmits a coded interruption of the signal to the fixed
unit, which replies with the same interruption. The time
difference between the transmission and reception at the
mobile unit determines the distance between the two
a ntennas.
Distance accuracy is determined by the number of
measurements averaged over time and is available in two
modes--a dynamic mode which averages 1000 measurements or a
static mode which measures 10,000 measurements per displayed
distance. The azimuth and distance information is displayed
by the mobile unit so that personnel are not required at the
stationary unit once operation has begun. The system can be
24
operated in long or short-range modes, which determine the
amount of power output for the system.
The microwave frequencies used are 9.2 and 9.3 GHz.
Problems arising with signal interference, observed with all
microwave positioning systems, therefore can occur with
ARTEMIS. The regions of range holes, or multipath
interference, can be computed for up to 10 ka range by prior
knowledge of the antenna elevations above sea level and the
operating distance from the shore-based antenna. [Ref. 7]
Each antenna is designed with a 22' vertical beam width
and a 20 horizontal beam width. A power source of 22 volts
DC per unit is required, with an average current load of 2.5
amps.
The accuracy of the system depends on both the distance
and the angle measureC. The angle measurement has a 2 a
probability of measuring within 2' of arc (0.0330 . The
distance measurement has a 2 G probability that ..he mean
distance value will vary within + 1.5 meters.
One of the advantages of ARTEMIS over other electronic
systems is that the two lines of position defining the fix
always intersect at 9 0 . A unique advantage is that the
coverage around the fixed unit can be circular, with a
2E4
maximum range of operation to 30 ka, dependent on antenna
heights. The short range applications of the ARTEMIS fill a
need not provided by many currently used positioning
systems.
For this study, the ARTEMIS was used in conjunction with
the positions derived from the theodolite network to
determine the best estimate of the shipis position. The
accuracy of the ARTEHIS was more than adequate for the
ranges encountered during the test, and the ease of use and
operational versatility of the system made its use very
advantageous.
B. THEODOLITE NETWORK
A network of three Wild T-2 theodolites was used as the
control positioning system. The theodolite is widely used
for surveying as a means of measuring angles between two
observational locations--either in a horizontal plane for
traverse or triangulation surveys, or a vertical plane for
astronomical observations.
The use of three theodolites as a short-range
positioning system was an accepted method of positioning
prior to development of electronic distance measuring
systems. There remain disadvantages when using electronic
26
positioning systems for hydrographic operations at short
ranges (1-2 k). Sost short-range electronic systems are
designed for measurement of position at line-of-sight
ranges. This region includes a large portion of inshore
* hydrographic surveys. Inshore positioning involves more
thorough planning to obtain the required accuracy for the
scale of the survey. For example, in a harbor or cove it
may be difficult to place two range-range electronic units
so that the area to be surveyed is not within the region of
positioning system uncertainty, or 300 (radially) on each
side of the baseline between the two units. To reposition
the electronic units as often as is required to obtain
-optimum geometry is time-consuming and requires manpower and
extensive planning, and can result in operational delays.
Interference of the signal due to reflection from a calm sea
surface, or sultipathing, is also a problem at short ranges
for microwave systems.
Theodolites can be set at any intervisible location with
preplanned geometry and can be used for the entire region to
be surveyed. This method requires less expensive equipment
(three theodolites) , more manpower (a recorder- and an
observer at each s.ite), communication between the three
27
locations (via portable radio, for example) and reasonable
weather conditions. The basis of this procedure is that
three angles observed from known locations to a
predetermined point on the vessel constitute three lines of
position. After removing all possible systematic errors and
through a least squares solution of the three lines of
position, the position of the vessel is determined. k major
disadvantage is that observational errors are not determined
in real time because the data cannot be processed
immediately.
The basic procedure for the method requires
predetermined sites which are known relative to each other.
This may be achieved by using published geographic positions
or by conducting a local plane survey to establish new
positions using preestablished stations nearby. Either way,
all three locations must be based on the same datum and
preferably permanently positioned by a disk or a station
mark.
Each theodolite was aligned using a plumb bob or optical
plummet over one of the known station marks or disks. By a
predetermined scheme, each site was marked so as to be
clearly visible to the other sites (lights were used for
28
this study). The telescope of each theodolite was sighted
onto one of the other sites and the horizontal circle set to
read an arbitrary value close to 00. The crosshairs in the
telescope were set to intersect the mark. When the
theodolite was exactly sighted, the horizontal circle was
read and recorded. (At this time the lights were turned
off.) The operation began when all three sites completed
this step, called the "initialling procedure", or "initial
pointing". The instrument was sighted on a point on the
survey vessel that was visible to all operators. The ship
was tracked by the operators by using the micrometer wheels
on the instrument until a "mark" was called over the radio
by the recorder at the control theodolite location. At that
instant, the operator stopped tracking and the horizontal
circle was read and recorded. This observation constituted
a fix. After a series of fixes were recorded, or when the
survey vessel reached a predetermined location, a set of
fixes was completed. The lights were then reactivated at
each site, each observer intersected the original mark, the
horizontal circle was again read and the "final pointing"
was recorded. If necessary, the instrument was relevelled.
The process was then repeated by starting with the
initialling procedure.
29
It was assumed that the theodolites were in good
operating condition. Collimation error had previously been
determined. The observers were kept at the same locations
throughout the test to minimize the error due to individual
observer variations. Since only one portion of the
hcrizontal circle was used, and no reverse readings
observed, a systematic error was introduced. This was
assumed to be minimized during computation of the vessel
position.
The observations were corrected for collimation error
and for pointing error by evenly distributing the difference
between the initial and final pointing values. The
resulting angles were processed using an intersection
computation with a least squares fit applied to optimize the
result. The computations for this study were processed
using an HP-9815 computer and software prepared by Cdr
Ludvig Pfeifer, YOlA. The resulting position was used as
the best estimate of the position of the ship.
C, TRANSIT POSITIONING SYSTEN
The TRANSIT, or Navy Navigation Satellite System, is the
most widely utilized satellite positioning system at the
present time. The network of satellites and ground tracking
30
stations has been in operation since 1964 and is becoming
widely used by both the military and civilian communities.
It is expected to continue operation until at least 1995,
when the Global Positioning System is expected to replace
it.
The system consists of i series of TRANSIT satellites
(fig. 2.1.) in fixed polar orbits of 1095 km elevation,
fcrming a network within which the earth rotates (fig.2.2.).
The orbits are spaced so that satellite passes occur, for a
given ground location, at intervals of between 35 and 100
minutes. Each satellite travels an observable distance of
between 4400 and 7000 km per pass, providing a sufficient
time interval and baseline over which the user can record
data.
The idea of positioning an observer on the earth's
surface by using the satellite as a reference system
originated from observation of Sputnik 1, launched by the
Soviet Union in 1957. By recording the change in frequency
of the satellite signal as the satellite passed overhead, a
Doppler shift could be measured. The Doppler shift gives a
spatial relationship as a function of time between the
observer and the satellite. If the position of the
31i
Fig. 2.1. 7RANS17 Satellite
32
:73
ig. 22. Tar'sit Satellite oroital Nlet'Mor
33
satellite is known at the time of observation, the
observer's position can be determined.
In the TRANSIT system, the satellite positions are
precisely determined by tracking stations located at
Prospect Harbor, Maine; Rosemount, Minnesota; and Wahiawa,
Hawaii. The tracking information (in the form of the
Doppler frequency shift as a function of time) is relayed to
the computing center at the Naval Astronautics Group
Headquarters, Pt. Mugu, California. Here the actual
satellite orbits are computed. This information is used to
predict orbit information. Parameters of this predicted
orbit are relayed to two injection stations at Rosemount and
Pt. Mugu. During the next satellite pass, the information is
relayed to the satellite as part of the navigation message,
with new updates occurring every 12 hours.
The satellites therefore contain predicted orbit
information which is received by the user via a satellite
receiver. Several receivers are available with complexity
and positional accuracy dependent upon the needs of the
user. A computer is normally required to determine the
user's mobile or fixed position in real time from a single
satellite pass.
34
For many users having a dual channel receiver and knowL
velocity, this method of positioning provides sufficient
accuracy with typical error of 27 to 37 meters root sum
square. Optimum accuracy is obtained, however, if the
receiver position is fixed, and several consecutive passes
of the same satellite are recorded. During each pass,
lasting from 10 to 16 minutes as the satellite travels from
one horizon to the other, many Doppler counts (observations
of shift in frequency as a function of time) are recorded.
After a predetermined number of passes are stored, the data
can be forwarded to the Defense Mapping Agency in Brookmont,
Maryland. There the precise ephemeris data from the ground
tracking system is applied to the data from the recorded
passes to provide the optimum solution. The resulting
position has a typical error of 6.3 meters root mean square
for a series of passes, with a 3-dimensional result of 1.5
meters per axis repeatability after 25 precise ephemeris
passes. This method is used to determine positions in
remote areas by DA geodetic survey groups using the
Sagnavox AN/PRR-i Geoceiver (fig.2.3.|. (Ref. 8]
The TRANSIT system uses the World Geodetic System of
1972 (UGS-72) reference ellipsoid which is based on the
35
,AN/IPqR-14 GEocE:'/ERANTENNA
F ig. 2.
~36
Universal Space Rectangular Coordinate System--an earth,
mass-centered coordinate system. The VGS-72 ellipsoid
describes the best fit of the entire earth to a mathematical
model. The satelliie orbits are computed using this
geopotential model, the accuracy of which is based on
4. gravitational and astronomical data.
For the present study, a Magnavox kN/PRR-14 Geoceiver
was acquired from the Department of Satellite Geophysics,
Satellite Tracking Branch, DNA. The receiver was placed
over a fixed point and 4O passes of one satellite were
observed. The procedures described previously for an
optimum solution of point positioning were followed. The
resulting latitude, longitude, and height relative to the
WGS-72 ellipsoid are coordinates of a first order TRANSIT
position as defined by DNA standards. This position was
used as the basis for horizontal control for the study (see
test procedures).
37
III. S SYSTEM DESCRIPTION N OPERATIONAL CAPABILITIES
A. SYSTEM DESCRIPTION
NAVSTAR, or the Global Positioning System, was designed
for maximum operational capability--high accuracy,
twenty-four hour access, passive user, and world-wide
coverage. A brief description of the GPS, and the
satellites (NAVSTARs), will serve as a background for the
more in-depth discussion immediately following.
GPS navigation is based on the measurement of four
ranges, or pseudo-ranges, from each of four satellites with
known, or predicted, positions. Each range determination is
computed using the propagation velocity of the signal
multiplied by the satellite-to-user travel time. Satellite
transmission time is included as part of the navigation
signal message. From the four known ranges, the user
position and user clock error are computed on a three-axis,
orthogonal coordinate system. This computation is then used
to transform the user position onto the WGS-72 ellipsoid.
The remainder of this chapter will provide the
background for GPS development and the three major system
segments of the GPS: the space system segment, the control
38
segment, and the user system segment. Included in the user
system segment will be a discussion of the nanpack receiver
as developed by Texas Instruments Corporation used for this
study.
With the successful operation of the TRANSIT system in
the early 1960's, the Department of Defense (DOD) began to
consider the specifications of, and the technology required
for, the development and implementation of a second
generation system. On 17 April, 1973, the Deputy Secretary
of Defense stated that a Defense Navigation Satellite System
was to be developed. [Ref. 93 Using the new synthetic
oscillator technology, and the Department of Defense surface
and nearsurface navigation objectives and requirements, a
DOD interdepartmental task force developed the GPS as the
second generation satellite navigation system. With the
United States Air Force (USAF) as the managing agency, the
GPS became a joint service program, with representatives
from the DNA, Army, Navy, Maiines, Coast Guard, and the
North Atlantic Treaty Organization. [Ref. 10] The Joint
Programs Office was established within the Air Force Space
and Sissile Systems Organization to design, develop, and
implement the GPS program.
39
GPS was conceived and designed to provide continuous,
real-time, world-wide navigation coverage for subsurface,
surface and nearsurface operational vessels, vehicles, and
aircraft. Accuracy of better than 10 meters was desired
SIl under all conditions, with navigational capabilities to
update and interface with other forms of existing and
,Al projected navigational systems. knother requirement of the
GPS satellites was nearly trouble-free and simple user
operation, even in low signal-to-noise environments. An
encoded signal structure was required for the satellite
system for security reasons. In addition, the signal
transmitted by the NXVSTAR satellites had to include other
operational information in conjunction with the navigational
message. To provide for navigational requirements in event
of hostilities, the GPS was designed to permit the use of
redundant satellites.
To achieve these objectives and requirements, the GPS
program was organized according to three developmental
tasks: concept validation, full-scale engineering
development and systems tests, and production and operation.
Starting in 1974, the concept validation task was initiated
with the merger of the TIMTION series satellite program and
40
the USAF System 21B (a highly accurate three-dimensional
navigation system) program. Tests with the Navigation
Technology Satellite, NTS-1, utilizing two rubidium clocks
(accuracy 5-10 parts per 10 ) and an orbit 7500 nautical
miles (nm) above the surface and three ground based
receivers (called inverted range) provided concept
verification. [Ref. 11] Additional tests were conducted
with an improved NTS-2 satellite positioned at an altitude
of 10,980 nm and containing two cesium clocks (accuracies on
the order of 1 part per 10 ). [Ref. 12] Orbital height of
10,980 nam permitted the evaluation of the effect of the
planned GPS constellation altitude on navigational
accuracies using the improved cesium frequency standards.
In 1980, NTS-3 was launched and the Advanced Developmental
Model (ADR) hydrogen maser frequency standard evaluated for
use on the GPS (providing an expected frequency accuracy of
I part per 1013). [Ref. 13] The results obtained from the
RTS-3 satellite have not yet been released. Since 1978,
additional satellites have been orbited to provide the
six-satellite constellation required to fully evaluate the
first development task--concept validation, Phase I.
41
During Phase I, user requirements were consolidated to
allow the development and construction of four basic types
of test receivers: continuous tracking receivers,
sequential tracking receivers, icw cost receivers, and the
Manpack receivers. [Ref. 14] These receiver types were
then constructed for Phase r testing by various contractors
and their performances evaluated aboard helicopters,
aircraft, ships, vehicles and personnel at the Joint
Programs Office's testing facilities. Phase I, concept
validation, was completed in late 1979 and Phase II testing
was begun in early 1980 with full scale engineering,
developmental, and systems tests.
Phase II tasks, finishing the operational and control
segments of the testing, are scheduled for completion in
aid-1983. The operational control station will be relocated
at a central continental United States site during this
phase. Additionally, all satellite monitor receivers at the
remote monitoring stations will be updated to operational
status. User equipment and receiver selection will be made
in two increments. Four contractors will be asked to
compete for the second increment of the receiver selection
process by providing upgraded and refined user receivers for
42
extensive testing and evaluation. Two of the four
contractors will then be selected to continue the
competition and will provide additional receiver design,
refinement and modificaticn, leading to prototype production
and extensive field testing.
When Phase I is completed in mid-1983, Phase III,
production, will commence with the selection of one of the
two contractors to produce the user receivers. .anufacture
of these receivers will commence shortly after selection,
and commercial availability of recaivers is expected in
1985. (Ref. 15] The GPS should be fully operational with
world-wide coverage using a constellation containing a total
of eighteen satellites in 1988. (Ref. 16, 173
The GPS is considered to be composed of three
inter-related system segments: the space system segment,
the control segment, and the user system sagment. Of these,
the space system segment may be considered the most
important since the other two require the space segment to
be operational at all times. Operationally, the space
system segment consists of 18 satellites placed in orbits at
altitudes of 10,898 na and having orbital periods of about
12 hours. [Ref. 18]
43
The original plan for the satellite constellation
consisted of 24 satellites in three planes of 8 satellites
each. These three planes were to be placed 45 0 of longitude
apart and at an inclination of 63o to the equator.
[Ref. 19] As a result of 1980 budget cutbacks the space
system segment has been reduced to a total of 18 satellites.
(Ref. 20] Several different types of 18 satellite
constellations have been proposed, but all have drawbacks.
One which appears the most promising is the 'Nonuniform 181
constellation containing 6 planes, each of which contains 3
satellites spaced 120 ° apart (fig.3.1.). The areas of user
outages (fig.3.2.) are a disadvantage of this configuration.
The user outages are indicated by the darker areas shown on
Figure 3.2. These outage areas will appear to rotate about
the globe at the indicated latitudes, and positioning with
the GPS will be intermittent, or of decreased accuracy for
users at these latitudes. The final constellation
configuration is to be selected early in 1982. DEef. 21]
Each NAVSTAR satellite has the following
characteristics: weight of 982 pounds, length of 17.5 feet
from tip to tip of the 5 square solar panels, three atomic
44
* Proposed Satellite
o eleted Satellite
Fig. 3I. The Ionuniform 18 Satellite Constellation
45
0 3 L
7.o0U
Vi
apm. ;s
frequency standards (clocks) , and three nickel-cadmiumL
batteries for operations in darkness and during peak load
periods. Stabilization of each NATSTAR is maintained by
four skewed reaction wheels which produce three-axis
stabilization. NAVSTAR station-keeping and momentum damping
capability is provided by a hydrazine propulsion system
within each satellite. Life expectancy of each unit is five
years, and expendables are expected to last for up to 7
years with normal usage.
Figure 3.3. illustrates the parts of each NAVSTAR. k
twelve element shaped-beam helix antenna transmits the
navigation message on two L band frequencies to user system
segments. Simultaneously it receives satellite status,
clock corrections, ionospheric data, and ephemeris constants
from the control segment on two S band frequencies.
(Ref. 22] The two coherent L band frequencies are centered
on 1227.6 MHz (LI), and 1575.4 MHz (L2). [Ref. 23]
[Ref. 24] Both frequencies are necessary to determine the
total ionospheric delay correction for signal propagation
time (Table I ). Zrrors produced by the ionospheric delay
in signal velocity contribute most of the error in the
pseudo-range. By utilizing the Li and L2 frequencies and
47
VA
Fig. 3. 3. 'IAVSTAR Satellite
48
TABLE I. lonospheric Group Delay as a Function of Frequency
R A+ B+ C +ASC f2 -:3 4 ..... C f2
GD(neglecting third order and higher terms which contribute minimalerror)
where A ionospheric delay constant of conditions
R = true range
F: C = speed of lightf = carrier frequency
B K(averaged jarth magnetic field strength alongthe path)
GD = group delay between points G and D
Term rlealected: Range Error atf = 1.5 GHz
B4!5 1 inch
f3
C3 inches
f 4
49_ _ ... __ __ N
the following algorithm, the error is decreased but not
totally eliminated. [Ref. 25]
T -T = A
GDLI GDL2
Where: A-r GDLI f2
L L
where A = ionospheric constant and T GDLI, GL are the
respective ionospheric group delays at frequencies L i and
L L2. Both frequencies are also modulated to transmit the GPS
time codes and the navigation message.
GPS time is transmitted using two pseudo-random noise
chip codes--the Coarse Acquisition (C/&) and the Precision
(P) codes. l3odulat ion on the Li frequency carries both the
C/A and P codes in phase quadrature, while the L2 frequency
carries only the P code. These codes identify each acquired
satellte by matching the unique pseudo-random noise code
pattern generated by each satellite with similar user
generated codes.
50
•~ ~~~~ ~ ~ 1 .. . . . -- ,. .. -.T - - .. - ..
Both codes are required to measure the navigation signal
propagation time. The phase shift is measured and used to
match the user generated signal with the incoming satellite
signal. (Ref. 26] The C/A code has a repetition period of
one millisecond and has a short code stream, transmitting
1.023 million bits per second (bps). This code is easily
acquired and matched with the user generated pseudo-random
noise code but only provides a coarse time signal for
computing the pseudo-range. However, the P code has a long
code stream, repeating only every seven days, and it is
transmitted at the higher rate of 10.23 million bps. With
this higher data transmission rate and long repetition
period, a more accurate time signal is available for
pseudo-range determination. However, the long period and
high data rate makes the P code difficult to match with the
user-generated pseudo-random noise code pattern unless the
receiver has a highly accurate time standard, and the
approximate receiver location is known. In lieu of this,
the usual method of acquiring the P code is by matching the
C/A code of the desired NAVSTAR, then using the Handover
Word (HOW), to locate the correct P code sequence within the
7-day pseudo-random noise code. GPS time is transmitted
51
"Pow- -71
with the HOW every six seconds and provides very accurate
GPS time to the user. Both of these codes provide the
proper time reference for computation of the pseudo-range.
The C/A code provides a less accurate time reference than
the P code. The selection of the code depends only on the
navigational accuracy desired.
The navigation message is also modulated on frequencies
Li and L2 but at a much slower rate (only 50 bps) than
either the C/A or P code. On both frequencies, the
navigation message is identical and consists of 5 subsets of
6 seconds duration each. Bach navigation message begins
with the telemetry message (TLR) and the HOW message, which
are used to transfer from the C/A to P codes. The remainder
of the entire navigation message allocated to each
subsection is transmitted after the TLM and HOW messages.
Information in the navigation message includes approximate
satellite ephemerides, status of other NAVSTAR satellites,
parameters for clock corrections, atmospheric signal delay
corrections, satellite performance status, momentum dump
status since last upload, time since last upload, almanac
and identification codes for all satellites, and provisions
for inclusion of any special or important messages from the
52
L , , .-. .. .. A
control system segment to the user. ERef. 27, 28J
Navigation is thus achievable by combining the information
transmitted by the space system segment in the form of the
C/A and P codes and the navigation message.
Accuracy and proper function of GPS are governed by the
second segment--the control segment. The oontrol segment
monitors and uploads the individual NAVSTAR satellites,
checks operational characteristics, determines the ephemeris
and almanac data and corrections required, computes the time
delay and clock corrections for each satellite atomic
standard, determines the atmospheric delay corrections for
pseudo-range computations and includes special messages in
the body of the navigational message. These functions are
under the command and operational control of the Master
Control Station, currently located at Vandenberg APB,
California. Four unmanned remote monitor stations, located
in Hawaii, Guam, Elmendorf APB, Alaska, and Vandenberg APB,
collect the pseudo-ranges to each satellite, the change in
pseudo-range of each satellite signal, local meteorological
data, and the remote monitor station atomic standard
parameters. Each set of c,.a is transmitted, on request, to
the Haster Control Station, where all the data is combined
53
and the satellite upload corrections and parameters are
computed. These corrections and parameters are then relayed
to the Upload Station, Vandenberg AFB, for transmittal to
the respective NAVSTAR satellites. The uploads occur when
the satellites are first visible to the Upload Station and
,. when the User Range Error exceeds 4 meters, as computed by
the Master Control Station. [Ref. 29, 30, 313
The last segment, the user system segment, combines the
information provided to the space system segment (by the
control segment) with the information received from the
sp.ce system segment to obtain the pseudo-ranges from four
NAVSTAR satellites. These ranges are computed using the
following algorithms:
a i = C(tR-tti) - CAtAi
where =i = true slant range to satellite i, c = speed of
light in a vacuum, tR = time of received GPS signal by user
receiver (assumed to be simultaneous from all satellites),
tt time of transmission at satellite i, and
LtA- =atmospheric propagation delay time from satellite i
54
(fig.3.4.). Assuming a user clock error, the true range can
be expressed in terms of a pseudo-range:
RP. R + CtA. + c(A. AtS .1 1
where Rp. = pseudo-range including clock error, AtR = time
delay in the user receiver cf the received signal, and
At5 time delay in satellite transmission from satellite
i.
To determine the slant ranges:
i- i Ji-) 2 + (Ys -Y) 2 +(Zs_Z) 2
s i- =_X) 2 (YS iY) 2 (Zs i_ Z) +a Ac+tA C(AtRAtsi
The following quantities are known: x , y , z obtained
from navigation ephemeris data; A tAi computed using the
ionospheric delay correction obtained from observing
frequencies Li and L2 (tropospheric delay neglected); A tSi
obtained from the navigation message as the satellite clock
error. Thus, there are four unknowns: x, y, z (user
position coordinates) and AtR ( user clock error or bias).
To solve this set of equations, four satellites must be
observed simultaneously. [Ref. 32]
55
Should only three satellites be observable, the altitude
may be assumed and the solutions can be computed for the
other two location variables and the user clock error.
Solutions of this type (altitude hold) significantly degrade
position accuracy.
The above description is over-simplified since the
relativistic effects of N&VSTAR satellite velocity, as
observed by the user, are neglected in terms of the
satellite time delay correction and the atmospheric
propagation delay correction. The actual user velocity, in
terms of velocity in the x, y, and z directions, is
calculated using the Doppler shifts of the two frequencies
Li and L2 and the estimated satellite position taken from
the ephemeris data. With the relativistic effects as an
integral part of the data set, solution of the navigation
position problem becomes more complex. Phase I receiver
manufacturers have included them in the solution of the
problem by several different methods. Sethods of solution
depend on the usage of the receiver (whether static, high or
low dynamic) and the expected cost/benefit ratio for the
receiver (in terms of the total cost, weight and size).
Current state-of-the-art design technology and navigational
56
0
I -
u 4~
,, - .4Jt4-
.4.J J- -
U,-l
0 -
0
•- -.
I CC
(00
C-C'
Fi.34 suoPag ecito
I57
algorithms, developed since Phase I, will be included in the
Phase Il receivers and will significantly improve accuracy
of future receivers.
B. IANPACK RECEIVER
The Phase I receiver used for this research was the
Texas Instruments GPS Manpack, also known as the Manpack
Vehicular User Equipment (MVUE). MVUE is a single channel
low dynamic receiver, usable for receiver velocities from 0
to 25 meters per second. [Ref. 33] System configuration is
illustrated by figure 3.5. Composing the system are the
Manpack control data unit (CDU), antenna and vehicle mount,
and vehicle power converter. The Manpack is the receiver
unit (fig. 3.6.) with provisions to connect an external data
output, through the NVUE Instrumentation System ("IS)
interface, figure 3.7. Facilities for an internal
preamplified antenna mount, or an external preamplified
antenna, and an attachment for either an external power
source or the integral battery pack are also shown (figure
3.7). Together, the NVUE and the SSP/9900 microprocessor
data processing unit have storage capacity for 47,360
sixteen bit words. This storage capacity allows
[interrogation of NAVSTAR satellites sequentially, with the
58
~77
-V
1c
LJi
C ILU X-
It tj
59.
20 0 04 4w
Z0 C i z
w ai
LL.
J w CD'
w z oL4c Z W
60
LIMITE
-C-
611
receiver computing a position fix every 24 seconds. The
relativistic velocity effects on the received signals are
determined by matching the incoming frequencies with the
expected frequencies. The user velocity relative to the
satellite is determined from the cbserved frequency shifts.
The nominal frequency shift for each satellite transmission
is computed using the simultaneously transmitted ephemeris
data. Total weight of this receiver unit is 33.5 pounds,
and it has a volume of 17,958 cubic centimeters.
The second element of the NVUE, the CDU (fig. 3.8.), is
the input/output device for the non-automated Hanpack user.
Inputs are entered by keying the pressure pads set in six
rows of four pads per row. To obtain a navigational
position, the approximate user latitude, longitude, and
Greenwich Mean Time (GMT) are keyed. After the warmup
period of 3 to 5 minutes, the satellite signals are
received, and the CDU will display the actual position.
Additional input may include NAVST&R satellite selection,
user altitude, and other position datums. Output options
include position, GMT time, and system error messages.
Other inputs and outputs are listed in the NTUE manual.
CRef. 34]
62
Li
-- I I T-- 4 -+
I Ii 1i II I I
! *I I IL I
S I I I I It( 1) =(12) 1 (13) 14) 1 (15) l(161) (17) 1 (18) 1019) 1 (20) 1
L . .L _.L . .L .J _ I _... J. . . _ _ AJ
ON AUTO
ENT RAO SEL GRDSTSY- MAN
j.. I CLRLA
AS EE
23 TIM
(9) (10) (1') (12)
GJH 10(7L~.L~
4' 5 6' RNG
MIN OP QR
Fig. 3.3. MVIJE CDU Keyboard/Display Liyout
63
Automated users may elect output either to a radio
interface or through the MIS interface. For this research,
a special interface unit, designed and constructed at the
Office of Testing and Evaluation of Systems, NOAA, was used
to link the HIS interface board within the receiver with a
Hewlett Packard 9825T computer. With this interface, user
latitude, longitude and GPS time were logged onto magnetic
tape for future processing. Figure 3.9. and Table II are
the engineering documents used in construction of the MVUE
interface unit.
Other NVUE elements are the antenna and the antenna
external preamplifier vehicle mount. Located within the
antenna are two antenna subassemblies associated with
frequencies Li and L2. Both of the subassemblies are
connected to the external preamplifier with two lengths of
coaxial cable, enclosed in a flexible conduit. The entire
unit, antenna and preamplifier, is connected to the Manpack
receiver with a power cable and a coaxial antenna cable.
Cable length is determined by the location of the external
antenna but is limited by the minimum strength required by
the ,anpack receiver. The combined antenna and preamplifier
unit is 36 inches long, and it weighs 1.9 pounds.
64
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TABLE H. MANPACK Interface Wiring Code
Wire Color OUT IN Wire Color
Code BIT BIT Code
90 1 1 26 1 0
91 2 2 27 2 1
92 3 3 28 3 2
93 4 4 29 4 394 5 5 30 5 4
95 6 6 31 6 596 7 7 32 7 6
97 8 8 33 8 7934 9 9 34 9 912935 10 10 35 10 913
936 11 11 36 11 914937 12 12 37 12 915945 13 13 38 13 923946 14 14 39 14 924
947 15 15 40 15 925948 16 16 41 16 926
98 PCTL 17 42 PFLG a927 CTLO 18 43 PSTS 908
928 CTLI 19 44 STIO 916
901 1 BIT 1/0 20 45 STII 917
902 PRESET 21 46 EIR 91822 4723 4824 49
GNO 25 50 GNO
6o
The power converter must supply 24 volts DC to the
Manpack receiver. During this research, a power supply
which converted 120 volts AC to 24 volts DC was used. This
power supply was considered more stable than the power
converter provided with the MVUE, and the voltage output and
power were controlled and monitored during the testing
period.
C. DIFFERENTIAL GPS
As mentioned earlier in this chapter, atmospheric
propagation delays are the major source of error in the
navigational equations because ionospheric propagation is
poorly understood. The tropospheric propagation delays are
neglected in the navigation equations, and the resultant
error is dependent on local tencerature, pressure, humidity,
and MAVSTAR elevation and azimuth. Tropospheric corrections
are usually neglected if the observed satellite is more than
50 above the local horizon. (Ref. 35]
Additional error sources are receiver and satellite
clock perturbations, lengths of signal paths from different
satellites, multipathing delays, satellite ephemeris errors,
and receiver noise. Combined, these factors lead to errors
of 3.6 to 6.3 meters, as table III illustrates. CRef. 36]
67
TABLE III.RANGE ERROR BUDGET
Uncorrected Error Source User Equivalent Range Error,
feet meters
SV Clock Errors *
Ephemeris Errors 5.0 1.5
Atmospheric Delays 8.0 - 17.0 2.4 - 5.2
Group Delay (SV Equipment) 3.3 1 .0
Multipath 4.0 - 9.0 1.2 - 2.7
Receiver "laise and Resolution 0 0 1.5Vehicle Dynamics
Root Sum Square 11.8 - 20.7 3.6 - 6.3
*Two hours after update
58
One method used to reduce the magnitude of this error is
that cf differential, or translocated, positioning. To use
this method, one receiver is positioned over a known
geographic position. Pseudo-ranges to each satellite are
determined, and a differential correction is obtained for
each pseudo-range. These corrections are then applied to
the satellite pseudo-range observed at a second mobile
receiver. With the differential corrections applied, the
net error of the mobile GPS receiver is significantly
reduced. (Ref. 37]
I
69
iv. gz&1
A. POSITIONING NETWORK
One of the considerations in planning this test was to
examine the various methods of positioning the shore-based
equipment. It was desirable to use closely spaced (1-2 kin)
locations within the immediate surroundings of Monterey
harbor for reasons of ready access by personnel during
installation of equipment and for optimum accuracy of the
positioning systems chosen for control. As mentioned
previously, the positioning systems chosen for the
comparison (the three theodolites and the ARTEMIS) give best
results at relatively short ranges.
Two predetermined station marks were selected for the
test--I) USE LON 1978, a bronze disk set by the Army Corps
of Engineers, located on a sand dune on the Naval
Postgraduate School property 400 meters from the ocean at an
elevation of 40 meters above sea level and 2) MUSSEL 1932, a
bronze disk set by the Coast and Geodetic Survey in a rock
outcrop 7 meters above sea level at the shoreline on the
property of the Hopkins Marine Laboratory of Stanford
University. The third station mark was set in the center of
70
A
the Monterey Coast Guard Pier for purposes of the test.
This was a DMA bronze disk stamped GEOCEIVER ST& 31370.
This location was chosen for access to power facilities
available at the pier and because of central location to the
test area.
The position of the Geoceiver station was established
using a Magnavox Geoceiver (Model AN/PRR 14) obtained from
the Department of Satellite Geophysics, Satellite Tracking
Branch, DNA/Hydrographic Topographic Center. The equipment
was operated in accordance with DMA requirements to obtain a
documented first order station. The data were submitted to,
and processed by, DNA/HTC in Brookmont, Maryland, using
precise ephemeris information to provide the WGS-72
position. Michael Ellett of DMA provided the technical
expertise for acquisition of the data and maintenance of the
geoceiver during the test period.
A third order, Class I, closed traverse was conducted
following the standards of the National Geodetic Survey
(NGS), using a Wild T-2 theodolite to measure angles and a
Motorola MRA V Tellurometer to measure distances. The
TRANSIT position computed by DMA/ETC was used for the
initial position of the survey, and a Polaris observation
71
using the theodolite provided the initial azimuth (fig.
1.1.). A total closure error in distance of 0.061 meters
and angle of 5.4" was achieved. The positions determined
from the traverse and used for the control network are as
follows:
USE RON 36 36'08.424"N 1210 52'140.301"W
MUSSEL 360 37'21.882"N 1210 54' 16.048"V
GEOC-IVER STA 31370 360 36136.246"N 1210 53' 29.693"W
B. POSITIONING EQUIPMENT
As previously described, three positioning systems were
used during the test-the three theodolites, the GPS, and
the ARTEMIS. In addition, the geoceiver was set to acquire
data during the shipboard portion of the test. During the
time of day that the GPS satellites were available (Table
IT) only one or two observations per day of the same
TRINSIT satellite were possible. The geoceiver data were
recorded but were not used for this study.
72
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74
1. Thoitll~
This section describes the placement and operation
of the equipment during the test. One theodolite was set on
a tripod at each of the three stations, and each was
occupied by an observer and a recorder. Communication
between stations was maintained via portable radios.
Because tests could be conducted only between 10 PH
and 2 AM local mean time (LET) due to GPS availability
times, it was necessary to plan a systems of lights for the
stations. The three theodolite sites were made visible by
placing battery powered lights directly over the station
marks. In addition, battery operated light packs for the
theodolites were used. All shorebased lights and light
packs for the test were provided by the Pacific Marine
Center, NOAA.
The ship system was designed with an omnidirectional
pair of lights anchored around the support pipe for the GPS
antenna. Also, the equipment shelter on the boat deck of
the ship was lighted by spotlights so that the GPS antenna
was easily seen by the shorebased theodolite operators.
During the test, each theodolite observer initialled
on one of the other stations and recorded the reading on a
log sheet. The theodolite operators then intersected the
75
lights on the ship GPS antenna using the theodolite
telescope and tracked the ship until a 'mark' was called
over the radio from the personnel aboard the ship. The
angle measured at this time was recorded on the log sheet as
a fix. The time interval between fixes was approximatoly
one minute. Each series of approximately twenty fixes
constituted a set. At the end of each set, a final reading
was made of the angle to the reference station. The fixes
were numbered consecutively throughout the test, and the
Greenwich Mean Time (GMT) of each fix was recorded on the
ship log sheets. The length of the sets depended on the
ship position and heading.
To correct the observed theodolite angles, the mean
of the final pointing and the initial pointing was
determined for each set and for each station. This value
was assumed to be a constant throughout the set and was
removed from each angle. A collimation error for each
theodclite was also removed from each theodolite
observation. The same observers and theodolites were used
nightly at all stations except &USSEL, where two different
individuals observed over the test week. This continuity of
personnel and equipment was designed to reduce operator and
instrument error to a minimum.
76
2. ARTEM
To colocate the different pieces of equipment at the
GEOCEIVER STA 31370, a wooden tower was built as shown in
figure 4.2. This tower was set over the station for the
period of the test. An YPS equipment vehicle was parked as
close as possible to the tower. Electrical power was
obtained from the Monterey Coast Guard facility.
Prior to the ship test, both GPS antennas were
placed on the tower and centered over the station mark. For
the first two nights, 9 and 10 Hay, equipment problems
allowed the use of only one system each night and data were
acquired only to determine the stability of each system.
During the next night, 11 May, position outputs for the two
simultaneously operating GPS receivers were recorded. This
static test gave a determination of any difference between
the two receivers under almost identical conditions.
For the ship test, the GPS antenna was centered over
the mark and was anchored at the top of the tower; the
geoceiver antenna was centered over the mark and anchored at
the middle level; and the theodolite on the tripod was set
over the mark at ground level. This arrangement provided
colocation of all three systems. It was assumed that no
77
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780
error was introduced by the presence of the wooden
structure. The shorebased ARTEMIS antenna unit was offset
from the theodolite to eliminate interference in the signal
due to the tower. An offset position was computed relative
to the station mark and was used in postprocessing of the
ARTEMIS data.
Except for the antennas for the GPS, the ARTEMIS,
and the geoceiver systems, all other equipment was installed
in the equipment vehicle, where an operator was stationed
throughout the test to monitor the data quality.
The GPS Manpack is a manually operated system. As
mentioned previously, it was decided that manual operation
of GPS was detrimental to the goal of the test, and that an
interface that would provide an automated printout of
positions from the anpack as well as a printout of GPS time
would be desirable. Knute Serstis and Gary Whitsell of the
Office of Testing and Evaluation of Systems (OTES), NOAA,
assembled two interfaces that provided data storage on
cassette tapes as well as the desired printout. Each system
operated in conjunction with a HP-9825 computer and a
HP-7845 printer/plotter. Software was provided by OTES,
NOAh. This arrangement permitted storage of the satellite
79
messages for further processing and provided an automated
printout of the ARTEMIS data. A GPS Manpack had been sent
to OTES for testing during the construction of the
interface. Technical expertise and operation of the
interface during the test were provided by OTES.
The data from the GPS receiver were printed at an
interval of 214 seconds, and consecutive data were
continually recorded on tape and printed during the test
periods. In addition, a manual recorl of the GPS position
from the CDU was logged as the 'marks' were called via the
radios.
The ship positioning systems were installed as shown
in figures 4.3. and 4.4. An equipment shelter was secured
to the boat deck of the R/V ACAIIA. A length of six-inch
diameter polyvinyl chloride (PVC) pipe was attached to the
aft wall of the building on the centerline of the ship. The
GPS antenna and the system of lights previously mentioned
were set on top of the pipe.
The ARTENIS mobile antenna unit was set on a
platform located on the centerline of the ship and at the
top of the building high enough to not interfere with the
signal from the ship radar beam. For the period of the
80
oC i00
03 0
C0 a
0L
a -
____ ___ ___ ____ ___ ___ ____ ___ ___ 9.205 m
4 __ ____ ___ ____ ____ ___ 7.935 m
_________6.6m
I r~y 11 71 r-3.6m
00 0
Mean HigherHigh WaterLevel
Fig. 4.4. Equipment Installationon the R/'1 ACANIA
82
test, the weather conditions allowed ship operations without
use of the radar, thus there was no possibility of damage to
the ARTEMIS unit.
All other equipment--the ARTEMIS receiver unit, the
GPS receiver, control data unit, power filter, and
interface, the HP-9825, the HP-7845 plotter/ printer, and
the real time clock--was placed inside the building. An
operator monitored the equipment during the ship tests and
another individual radioed the 'mark', or fix, to the
theodolite operators on shore. The equipment used at the
shore location was installed in a vehicle and consisted of
the same components as on the ship. Operation of equipment
duri.; the ship tests was monitored by an individual located
in the vehicle.
C. LOG OF EVENTS
The test was divided into two portions--i) a shorebased
test which consisted of two nights of stability testing, and
one night of receiver comparison tests, and 2) the ship test
consisting of three nights of shipboard operation. The R/V
ACANIA from the Naval Postgraduate School was the platform
used for the shipboard tests.
83
1. Stablit
Operations began on 9 May, 1981, GMT. One of the
GPS systems was placed over the station mark, and continuous
data was recorded during the satellite availability periods.
In this manner, system 1 was tested on 9 May, and system 2
was tested on 10 May. A position was defined as a quality
observation if four or more satellites were used by the
receiver to obtain the output.
2. Static Tes
:1 Both GPS antennas were centered over GEOCEIVER STA
31370, and data from simultaneous operation of both
4 receivers were recorded at the equipment vehicle. One
" antenna was placed on top of the wooden structure and the
* other immediately below it on the middle level. The
' vertical displacement was assumed to cause negligible error
in the horizontal positions. Data ware acquired on 11 May
frcm both receivers with a quality observation defined as a
position determined from four or more satellites.
3. Z=
For the entire period of shipboard testing, the wind
speeds were less than 5 knots and the seas were calm with 1-
2 feet or less of swell. Visibility was excellent throughout
84
the test week. The ship track for each set is shown in
figure 4.5. A log of subsequent operations follows:
12 May---The GPS Manpack receiver was installed on the R/V
ACANIA and jPS and theodolite operations were conducted.
The ship was allowed to drift during sets 1-3 (fix 1-69)
with 23 fixes per set, in a east-northeasterly direction.
13 May---The ship cruised at 4 knots on track lines from
south to north for sets 4 and 6, and lines from north to
south for sets 5 and 7. During fixes 139 through 157 the
radio at the Coast Guard pier was disabled, and no data were
acquired by either the theodolite observer or the operator
in the equipment vehicle.
14 May---The shipboard GPS system was inoperable. The
trouble was traced to a faulty antenna cable, requiring
replacement. No data were acquired.
15 May---The ARTESIS, the GPS and the theodolite network
were all used for this test period. Data from sets 9
through 13 were acquired (fixes 165-262)
16 May---The control data unit on the shore based GPS system
failed before the start of ship operation and could not be
repaired without factory maintenance.
85
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I total of 252 fixes were recorded by the theodolite
network and all GPS positions corresponding to the
theodolite fixes were manually logged. The ARTZMIS azimuth
and distance information and consecutive GPS positions on
the ship and in the vehicle were stored on cassette tapes
and printed by the RP-7845 printer/plotter.
87
V. a&ZRA METHOD
Processing of the thesis data was divided into four
interrelated, but separate, tasks. These tasks were the
basic geodetic survey, theodolite and ARTEMIS ship position
determination, differential GPS ship position determination,
and the statistical analysis of the ship position
comparisons. Each task will be discussed separately.
A. BASIC SURVEY COMPUTATIONS
As described earlier in the Test Procedures, a basic
geodetic survey of the test area was conducted to place the
theodolite control stations on the world Geodetic System of
1972, or VGS-72. To begin the survey, a Magnavox AN/PR 14
Geoceiver was placed over the center survey disk, GEOCEIVER
STA 31370 1981, and the digital Doppler data, from TRANSIT
satellite 68, were recorded onto paper tape. Thirty-three
passes, over a period of two and one half weeks, were
recorded, but analysis of the equipment maintenance
diagnostics indicated a possible error in the records.
These data were therefore discarded.
A second set of forty satellite passes of TRANSIT
satellite 68 were recorded over a ten day period and were
determined to be of acceptable quality according to the
88
standards of the DNA Department of Geodesy. This second set
of data was then submitted to DR&, Department of Geodesy,
Computation Section, for analysis. Also submitted were
meteorological data taken during the passes and additional
information required for documentation of a first order
TRANSIT position. Satellite 68 Doppler data for the survey
was then processed in conjunction with the tracked satellite
position by DNA computer facilities. A final geodetic
position on the WGS-72 ellipsoid was obtained for GEOCEIVER
STA 31370. Coordinates of the station are listed in the
Test Procedures section. The computed height relative to
the ellipsoidal surface is -33.39 meters. Computation of
the geographic position utilized a minimum of 38 individual
TRANSIT satellite passes recorded for GEOCEIVER STA 31370.
This provided for an accuracy of one part in 105 (first
order accuracy standard) . [Ref. 38]
To orient the positioning network, an initial azimuth
from GEOCEIVER STI 31370 to station MUSSEL 1932 was computed
from two sets of observations of POLARIS. All observations
and computations of the star sighting utilized procedures
outlined in the National Ocean Surve? Photogrammetric
Instructions Number 4, Revision 1, 4/24/73, the .ydrographic
89
Manual, and the Manual of Geodetic Triangulation, SP-247.
[Ref. 39, 403
Having the initial azimuth, distances were measured
* between all three control stations using a Tellarometer aRA
5 microwave distance measuring unit. Twenty observations of
distance were made for each of the three lines measured:
GEOCEIVER STA 31370 to MUSSEL, GROCEIVER STA 31370 to USE
MON, and MUSSEL to USE MON. The average of the distance for
each line was then corrected for instrument error and
meteorological conditions following the instructions
contained in the Operators Manual and the Tellurometer
Manual. [Ref. 41] Resulting slope distances were then
reduced to geodetic distances using the respective
corrections for slope to horizontal distance, reduction of
elevation to sea level, and the chord to arc distance.
These corrections were computed using the WGS 1972
ellipsoidal parameters and the methods outlined in the
Hydrographic Manual, the Manual of Geodetic Triangulation,
and Introduction to Surveying. (Ref. 42] The resulting
geodetic distances meet third-order, class I specifications
for traverse accuracy, 1:20,000. In addition, angles to the
other stations were observed at each control station, giving
90
a total of three sets of angles. Each set was comprised of
four direct and four reverse plate observations with a wild
T-2 theodolite. Each pair of direct and reverse
observations was corrected for initial pointing errors.
Observations and computations were made using the methods
detailed in the Hydrographic Manual, the Manual of Geodetic
Triangulation, and the Manual of Second and Third-Order
Triangulation and Traverse. [Ref. 43] The resulting
closure meets the specifications for traverse accuracy of
three seconds per traverse station or a closure of 6
seconds.
With the geodetic position of GEOCEITER STA 31370 known,
as well as the azimuth from GEOCEIVER STA 31370 to MUSSEL
and the distance from GEOCEIVER STA 31370 to MUSSEL, the
geographic position of MUSSEL was computed on the WGS 1972
ellipsoid using the direct geodetic computation. This
computation used the Rainsford's method modified by T.
Vincenty and including the Helzert's elliptical terms.
[Ref. 44]
Next, using the azimuth from MUSSEL to USE 30N, the
geodetic distance, and the results of the direct geodetic
computations, the geographic position of USE MON was
91!A
determined. Also, the ARTENIS geographic position was
calculated as an offset using an azimuth and distance from
GEOCEIVER STA 31370. With these computations, the geodetic
survey was completed.
Positioning of the ship, f/V ACANIA, required one
azimuth, or line- of-position, from each of the control
stations MUSSEL, GEOCEIVER SZA 31370, and USE MON. These
lines of position were used to triangulate the vessel
position. Angles from each of the three theodolite
locations were observed as described in the Test Procedures.
Each of the three angular measurements were then corrected
for mean pointing errors and the individual theodolite
collimation errors. Each corrected angle was then adjusted,
by control station, to obtain an azimuth from south, as
required to triangulate the vessel position. The three
resulting azimuths and the corresponding control station
latitude and longitude were then used in a least squares
three line of position intersection computation. Results of
the computation were a vessel position in latitude and
longitude, error ellipse semi-major radius, error ellipse
semi-minor radius, azimuth from south of semi-major radius,
and circular standard error. (Ref. 45] Figure 5.1
illustrates these error ellipse parameters.
92
THE ERROR ELLIPSE
The mean displacement of a point to be expected in the direction ofthe two coordinate axes, X and Y, due to measuring errors, can be ex-
* pressed by the quantitiesvrx and oy.
When the north-south axes are rotated, two axes (X and Y) perpendicularto one another are obtained, corresponding to the maximum and minimumvalues of u and a- The maximum and minimum values of w, and theclockwise rofation angle (cK) of the major axes of the error ellipse areincluded as part of the output of the Geodetic Package and can be usedas input if desired.
The circular standard error (CSE) is also included in the output with theerror ellipse parameters. The value of CES is the radius of a circlewhose area is equal to the area of the error ellipse. That is:
max min
EXAMPLE: Error Ellipse
Az-Max 144.90
Max 0.235 mMin 0.211 m
CSE 0.223 m
S
Fiq. 5.1.
93
For this study, 262 vessel positions, or fixes, were
observed and recorded. On examination during processing, 51
fixes were found to contain errors and data omissions which
rendered the vessel positioning computation invalid or
indeterminate. The remaining 211 fixes comprised the data
set which was then broken down into smaller sets for
analysis and comparison. These sets were numbered 1 through
13 and categorized according to vessel track. All sets were
then processed using several different methods to determine
the most accurate approach.
B. THEODOLITE AND ARTEMIS SHIP POSITION DETERMINATION
Before processing the GPS Manpack data, the ARTEMIS data
were processed to ensure the vessel positions, as obtained
by theodolite, were correlated with the correct automated
and hand recorded GPS data. ARTEMIS data consisted of an
angle, SUSSEL-ARTEMIS OFFSET-vessel, and distance from the
ARTEHIS OFFSET to the vessel. The angular measurement was
first converted to an azimuth from south usins the azimuth
of ARTEMIS OFFSET to MUSSEL as the correction and adding the
measured angle. Vessel position based on ARTEMIS was then
computed using the direct geodetic program (also used for
the basic survey). Comparisons of the resulting geographic
94
positions and the theodolite derived geographic positions,
were made for corresponding fix numbers using the inverse
geodetic computation on the UGS-72 ellipsoid. The inverse
computation utilizes two geographic positions as inputs for
calculating the forward and back azimuths and the distance
between the positions. [Ref. 46] For comparison, if the
two positions differed by more than 20 meters, the ARTEMIS
positions on either side of the suspect ARTEMIS fix were
then used to compute the inverse computation to the
theodolite ship position. In seven fixes, the fix position
values were changed in the May 15 GPS data to give more
accurate results.I
C. DIFFERENTIAL GPS SHIP POSITION DETERMINATION
With the check and adjustment of the GPS data and the
theodolite determined vessel position complete, the first
GPS data processing was the comparison of the uncorrected,
non-differential ship GPS Manpack receiver data to the
theodolite computed ship position. Using the inverse
*geodetic computation, the forward azimuth and the distance
between the theodolite computed ship position and the
ncn-differential GPS ship position were completed. These
results were then used in the analysis of the differential
495
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MICROCOPY RESOLUTION TEST CHART
processing to examine the stability of the shipboard Nanpack
receiver compared to the GPS Manpack receiver located over
GEOCEIVER STk 31370.
There were two methods of analysis of the differential
GPS. The first of these was the determination of a static
correction to be applied to all the GPS data. This static
correction in the differential GPS computations was to
account for a suspected bias between the two similar, but
not identical, Manpack receivers. A mean static correction
was computed for the most stable reception period during the
static tests on 11 May. With the two receivers colocated
over the GEOCEIVER STA 31370, a mean correction of -0.954
seconds of latitude and -0.3 07 seconds of longitude was
found between GPS Manpack System 1 and System 2 during times
07:16:00 GMT and 07:25:12 GMT. This static correction was
then added to the latitude and longitude of GPS Manpack
System 1 (located over GEOCEIVER STA 31370) data.
The second method of analysis or processing in the
differential mode used the latitude and longitude obtained
directly from the GPS Man pack receivers. In either
processing method, the computation of the differential
corrector to the shipboard 3PS Manpack receiver data was the
96
same. An explanation of the computations and processing of
the differential correction for both methods follows.
Computation of the differential corrector for each GPS
fix position was accomplished by using the geographic
position obtained with the stationary Hanpack receiver,
located over GEOCEIVER STA 31370, and the geographic
7 position of GEOCEIVER STA 31370. These two positions were
then used in the inverse geodetic computation to obtain a
differential correction vector (forward azimuth, and
distance) from the stationary GPS reqeiver to GEOCEIVER STA
31370. In figure 5.2, the differential correction vector is
labelled "A". Using the direct geodetic computation, the
differential correction vector was applied to the
corresponding shipboard GPS Manpack receiver position, and
the differential GPS position was obtained. These .sulting
positions were computed on i one-to-one basis using the fiz-
numbers as identifiers. Vector "B", the differential
corrector vector which is identical to the vector "A" in
figure 5.2, is applied to the shipboard GPS Manpack receiver
and results in the differential GPS ship position.
Comparison of the differential GPS ship position with
the theodolite-computed ship position was accomplished using
97
T-2 COMPUTEDSHIP POSITION
DIFFERENTIAL GPS SHIP
POSITION:! GPS SHIP
DIFFERENTIAL POSITION
CORRECTOR VECTORAPPLIED.
GEOCEIVER STA 31370
DIFFERENTIAL STATIONARY GPS POSITION
CORRECTOR VECTORCOMPUTED, A
Fig. 5.2.DIFFERENTIAL GPS PROCESSING
98
EIthe inverse geodetic computation for both methods of
differential GPS processing. The resulting forward azimuth
and distances for both processing methods were used in the
statistical analysis.
D. STATISTICAL DATA ANALYSIS
Statistical analysis was done on data separated into
sets according to the method of data processing. The static
data and stability data were graphed as functions of
latitude and longitude versus time. User range error,
furnished by the Space Division, GPS/OL-AQ, Vandenburg, AFB,
was plotted as a function of time for each day of the test
(see Results). Other graphed relationships are the
gecgraphic positions of the stationary GPS Manpack receiver
data versus the GEOCEIVER STA 31370 and the theodolite
semi-major radius as a function of fix number (see Results).
Other statistical data analyses were represented by
histograms. Plotted on these histograms are the relative
frequency on the left margin, variable bar increments scaled
on the bottom, number of variable observations in each bar
increment on the top, and the total sample size on the top
margin. Within the histogram the frequency bars are denoted
by asterisks, the mean by a capital M, the quartiles by
99
periods and the empirical density function by the capital
curve. The empirical density function was computed using:
- U'(Z)14(3I1)) i=1 W 314
CRef. 47] where: ?(z) = the empirical density function, z
the frequency of observation, x = individual observation,
N = the total number of observations, V = weight function, B
bandwidth,
1=17 -z
B(N) = range of all observations / 4W
The statistf.cal values listed below the histogram are
defined in Table V. Computed histograms show the distances
between: 1) the theodolite-computed ship position and the
differential GPS ship position, both with and without the
static correction, by set; 2| the theodolite-computed ship
position and the differential GPS ship position, without
static correction, for five satellite observation periods on
each of the three ship test days; 3) the theodolite-computed
ship position and the non-differential GPS ship position for
the five satellite-observation periods on each of the three
100
TABLE V. STATISTICAL DEFINITIONS
The definitions of the basic statistics computed by the program are
listed below:.
MEAN: Average of the sample
- MEDIAN: Mid-Value of the sample, if there are an odd number ofsample points, or the average of the two middle valuesfor an even number of points
TRIMEAN: 0.25 * (Q1 + 2Q2 + Q3), where Q are the quartiles
MIDMEAN: The average of all sample values lying between the upperand lower quartiles
MIDRANGE: Average of the maximum and minimum
GEOMETRIC MEAN: GM nx * x
HARMONIC MEAN: HM = n /x
VARIANCE: Unbiased estimators for variance and standard deviationare used - the square of the standard deviationIn 2 -2
STANDARD DEVIATION: S = 'x - n x-
COEFFICIENT OF VARIATION: Standard deviation / IMeani when themean is less than 10. ** -30, the coeffic-ient of variation is set to zero.
MEAN DEVIATION: The average of the sum of the absolute differencesbetween the sample values and the median
RANGE: Maximum - minimum
MIDSPREAD: Q3" Ql' also called the interquartile distance
M3: Third central moment. Unbiased estimator is used
144: Fourth central moment. Unbiased estimator is used
COEFFICIENT OF SKEWNESS: M3 / (Standard Deviation) ** 3
COEFFICIENT OF KURTOSIS: (M4 / (Standard Deviation) ** 4) - 3
BETAl: Biased estimate of third central moment; can be used intesting for normality
BETA2: Biased estimate of fourth central moment
MAXIMUM: Largest sample value
MINIMUM: Smallest sample value
QUANTILES: The alpha-quantile, x(alpha), is the solution to theequation:
Probability (x .le. x(alpha) ) alpha
101
ship test days; and 4) the GOCEIVER ST& 31370 position and
the uncorrected stationary GPS position for the three days
of ship ests. In addition, the azimuths between the
theodolite-computed static corrections, for each subset,
were graphed as a series of histograms. To illustrate the
difference between the GEOCzITER STA 31370 position and the
stationary GPS position, the azimuths between the two
positions are graphed on histograms for each of the three
test days.
102
I
The error sources contributed by each positioning system
are described. Estimates of the effect of each on the final
results are determined where possible.
1. ARTEMIS POSITIONING SYSTEM
The sources of error in the ARTEMIS ship position can be
divided into tvo categories--those sources of error inherent
in all microwave positioning systems and those unique to the
AREMIS system. kll are investigated and the contribution
of each to the total error is determined.
1. Mioav Ss erroL=
Sources of system error include range holes,
inaccuracies in calibration, non-ideal geometry of the lines
of position describing the fix, and interference with
reflections of the signal from nearby objects.
Range holes are a cause of unreliability in
microwave positioning systems. The problem exists when the
sea surface is calm enough to reflect part of the
transmitted -signal. The reflected siignal will arrive at the
receiving antenna at a later time than the signal which
travels directly, causing a phase difference between the two
signals. A zone or region of destructive interference of
103
the directly transmitted signal and the reflected signal
will occur within which the vessel will receive an
attenuated signal. When the phase difference of the two
paths is exactly 180 ', no signal will be received provided
the reflected signal is as strong as the direct-path signal.
Prediction of the range holes, therefore, is useful in
survey planning so as to avoid this problem.
The range hole is a function of shore unit and ship
unit antenna heights, the wavelength of the system, and the
distance from the shorebased unit. If the operating area is
known, antenna heights can be determined and equipment can
be installed so that no range holes exist in the survey
area. If fixed antenna heights are known, the region of
uncertainty can be determined from the equation: [Ref. 48]
The following equation is used for this computation:
Dn = 2(hl)(h2)/nX,
where A is the wavelength (constant for AIRTHIS at .032 i),
hl and h2 are antenna heights, and an is the distance from
the shore based unit to the nth range hole. For this study,
the antenna height of the fixed unit above mean sea level at
the GEOC-IVER STI 31370 was 3.8 meters. The mobile antenna
was installed on top of the equipment shelter on the boat
104
deck of the R/V ACANIA at a height of 7.9 meters above the
the waterline. Two range holes within the survey area were
determined to be located at ranges of 1876 meters for n - 1
and 938 meters at n = 2 (fig. 6.1). These two ranges were
computed for the case of mean lower low tide. The change in
width of the range hole due to a tidal fluctuation of 1.5
meters during the test is shown in figure 6.1. (During the
night of 15 May the sea surface was sufficiently disturbed
by a two-foot swell and a surface wind of 2-4 knots such
that surface reflection was minimal and no loss of signal
was observed at the computed ranges).
Calibration of the ARTEMIS system was accomplished
in two stages. As part of the study, the ARTE.MIS was
obtained for a one week test of the system from 13 to 17
April. During this time it was calibrated for azimuth and
range over the baseline between the GEOCEIVER ST& 31370 and
MOSSEL. The azimuth readings required no adjustment but the
range was reduced by two meters. The equipment was returned
to Harinav Corporation to fulfill prior commitments and then
was returned to Monterey for the ship test on 15 May.
Before the evening operation, the ARTEMIS was used to
measure the same baseline as previously. A plus two meter
105
UU,C~i V)
L60
L6..
r % LL.
C..'J.
0 vi
106
bias was observed at this time, but no immediate
compensation was made. This error was assumed constant
throughout the test and was included in. the calculation of
,he ship-determined ARTEMIS position lurin4. postprocessing.
One of the advantages of the ARTEMIS system, unlike
other microwave positioning systems, is that the geometry is
always ideal for the lines of position that determine the
fix. The range-azimuth technique of determining the vessel
position defines an uncertainty ellipse having axes that are
always mutually perpendicular. This allows prediction of
errors as a function of range only, independent of the
angle.
The manufacturer's specified error in range
measurement of the ARTEMIS is + 1.5 meters for all line of
sight ranges. One axis of the uncertainty ellipse is
therefore constant. The other axis, that describes the
error introduced by the system azimuth uncertainty, is 60 cm
per 1000 m range. (This is determined from an angular error
of 0.0330 or 2' of arc). Both system error values represent
an accuracy of twice the standard deviation value, or a 95%
probability of the true value occurring within the margin
allowed by these parameters.
107
The positional uncertainty can be expressed In terms
of the radius of a circle of equivalent probability within
which the true fix is expected to occur. The method of
computation of this radius is described in Appendix A. The
technique allows the conversion of uncertainty ellipses to
radii of circles of equivalent probability. Values from
this computation for the radii of circles of 90% probability
at different ranges used in the survey area for 15 May are
displayed in figure 6.2 along with the circles of 90%
probability, the magnitude of the radii at the ranges used
for the study do not exceed 5.4 meters. One goal of this
study was to measure the difference in positional accuracy
between ARTEMIS and GPS. A maximum error of 1.0 meters, an
order of magnitude smaller that the tested system accuracy,
is desirable. At the present time, however, there are few
systems that can provide the order of accuracy system for
the position of a moving vessel, so the 5.4 meter error
observed at 4000 meters had to suffice.
Error caused by reflection of the signal from nearby
objects is difficult to measure. To minimize this problem.
the offset position for the ARTEMIS unit was planned so as
to be clear of possible interference from the wooden
108
0 CCM
V I-
Cj
0V
109
structure and the eluipsent vehicle. No signal interference
was observed despite the ship's notion. This source of data
unreliability was therefore not considered to be
significant.
2. AREI System Errors
Errors unique to the ARTEMIS system include a
pointing error source and the lack of resolution of the
azimuth measurement in the dynamic mode of operation.
The operation of the ARTEMIS system requires a
manual alignment of the fixed antenna so that it is
perpendicular to a known object. This is necessary to
establish an original reference direction upon which all
angular measurements are based. It is possible that a
pointing error couli be produced by the operator if the
crosshairs of the telescope used to align the antenna are
not exactly sighted. This would introduce a systematic
error into all subsequent angle measurements. To minimize
this source of error, the alignment of the antenna was
checked before and after the period of operation. The
original azimuth displayed on the antenna unit display
agreed exactly with the final azimuth value. Any
contribution to ship position error was considered minimal.
11.0
The ARTEMIS was operated using the dynamic mode
option (see Equipment Description--kRTEMIS). The resolution
of the system in this mode is 1 meter for displayed range
and 0.10 for azimuth values. This resolution limit
introduces an uncertainty of +0.5 meters in range and 0.05.
in angle measurements. The computed uncertainty ellipse as
expressed by radii of circles of equivalent probability, is
shown in figure 6.2. The system error and all other errors
mentioned above are assumed to occur within the scope of
this resolution uncertainty.
Another source of system error has been proposed in
a study conducted in June, 1980, by NOAA. (Ref. 49] The
test compared the ARTEMIS system with tvo ranges measured by
two Del Morte Trisponders (a short range microwave
range/range positioning system) and two lines of direction
measured by two shore-based theodolites. The results
described an underway bias of -0.050 of unknown origin in
the angle measurements. This discrepancy has not been
resolved. The preliminary test conducted in Monterey in
April, 1981 compared the ARTEMIS system with three lines of
direction determined by three theodolites. The purpose of
the test was to resolve the underway bias problem. Results
are enclosed in a separate report. [Ref. 50]
111
B. CONTROL NETWORK
The entire survey was oriented relative to the TRANSIT
position on the Coast Guard Pier (GEOCEIVER ST& 31370).
Therefore, errors inherent ia the position of this station
mark affected all results. Assuming that the geographic
coordinates published by D[ A/RTC represented the best
estimate available of the GEOCEIVER STA 31370, the remaining
significant sources of error affecting all results were
survey errors. The control network for the study was
* idetermined from the traverse and it was assumed that all
positions used in the study were oriented relative to each
other on the UGS-72 ellipsoid. A change in the ellipsoidal
surface within the area encompassed by the traverse was
assumed to be insignificant.
Survey errors stem from the methods used for obtaining
the initial azimuth for orientation of the survey, the type
of traverse chosen, and the geometry of the traversed
triangle.
To obtain a starting azimuth for the traverse, two sets
of observations on Polaris were recorded at the GEOCEIVER
STA 31370. A striding level attachment to the theodolite
was not used. The instrument level bubble was observed
112
repeatedly during the observations to ensure constant
instrument alignment with the vertical. Failure to keep the
instrument level could have introduced a + 30" uncertainty
into the starting azimuth of the survey. (Ref. 51] To
consider the significance of such an errt-', all stations
were recomputed using a deviation of + 15" from the computed
azimuth. The resulting shift in the positions of MUSSEL and
US! SON are listed:
USE SON 0.133 m distance at 230036847.1611 azimuth
IUSSEL 0.132 m distance at 230033, 4.08" azimuth
The change is considered insignificant relative to the other
errors described above.
The survey was a closed loop traverse using GEOCEIVER
STA 31370 as the origin and closing position. The weakness
in this method involves the measured distances. m ethod of
checking the observed angles in the triangle exists via the
angular closure if a significant deviation in one of the
angles can be detected. The distance measurement, however,
can produce an undetected bias in the survey if the distance
measuring instrument contains a systematic error. This
error would shift all the surveyed positions. Correct
113
A
measurement of distance by the dRA V Tellurometer,
therefore, was important. The equipment was calibrated over
a known baseline and the errors were within the centimeter
range. This error was therefore negligible.
- IThe geometry of the triangle was not optimum. Ideally,
the triangle would have been equilateral to minimize the
source of observing error. The choice of traversed points
was based on the location of preexisting station marks and
the desired geometry of the theodolite fixes to the ship.
The closures computed for the traverse met third order
specifications for accuracy, and the survey was not adjusted
to remove the closure error. (Ref. 52, 53J
The survey errors were considered to be within the
uncertainty of the TRANSIT station location and were
therefore not considered significant for the study.
C. THEODOLITE NETWORK
The errors generated by the theodolite network are
divided into equipment errors, operator related errors and
system errors, of which the litter is the most significant.
The equipment used for the theodolite network were three
1-second theodolites which have a measurement resolution of
+0.5". All theodolites were in good condition.
114
Instrumental errors of a theodolite are listed in rable VI.
[Ref. 54]
The major source of equipment error was introduced by
not changing face, the process of observing angles a second
time with the telescope reversed. Due to the nature of the
test coupled with 1-minute fix intervals, it vas not
possible to observe all the fixes in both the direct and
reversed modes. ks an example of the magnitude of this
error, the horizontal collimation errors were determined for
' e each theodolite prior to the study. The results are listed
below:
Zheodoliti CliaonError
# 14405 - 1.0"
# 14482 + 2.7"
# 14452 - 0.7"
All the measured angles were adjusted for this error as
described in the processing section. The largest influence
on the remaining instrumental errors was the non-verticality
of the main axis. If the non-verticality were large (for
example, one division off-level in the lower spirit level
bubbles, the angle measured could be in error by 7".
CRef. 55] To minimize this error, each theodolite was
115
TABLE VI. Theodolite Instrument Errors
ERROR ELIMINATED BY:
Eccentricity, misplaced indices Reading both sides of circleand changing face
Graduation of circles Changing zeros
Micrometer run and vernier error Selection of suitable zerosetting
Non-verticality of main axis Error is not can.r-*4 ,. lAny
observing proced..r.
Bad setting of the upper spirit Correct setti;t): rvi -
level tion of correct ic,
Verticality of cross wires Changing faca . q samepart of wire
Horizontal collimation Changing face
Vertical collimation and index Changing facesetting error
116
relevelled if necessary between sets of observations. The
magnitude of this and the collimation errors were considered
to be insignificant relative to the system errors discussed
later in this section.
The operator-related errors are a function of the
individual performance of the observers. The experience and
personal comfort of the observer, for example, are two major
factors which can influence the observed angles. An
observer's performance and resultant impact on the quality
of the results depend on the judgment and reaction time of
the observer and are influenced by variables such as fatigue
and age. The subjective nature of the problem makes an
estimate of the error difficult, therefore, for this study
the error was considered random.
The major source of error in the theodolite positioning
system dealt with the timing of the fix. A delay existed
between the time the 'mark' was called over the radio and
the actual time the angle was observed. The timing problem
was most critical when the ship was close to one of the
three observer locations because the rate of change of the
bearing of the ship was greatest at this time. Hence a
small delay generated a large amount of error in the angle
117
recorded. To indicate the effect this error source may have
had on the position of the ship, two fixes were chosen
arbitrarily--one at close range to each of MUSSEL and
GEOCEIVER STk 31370. A one minute value was added to the
angle which was most affected by the timing error and the
fixes were recomputed. The same process was repeated for
the three fixes with the one minute value subtracted from
the critical angle in each fix. The results follow:
Number Original Fix + 1 minute - 1 Ninute
210 36 0379 20.6228211 360 37120.61468" 36037120.63081"
0* 0121 53#41.97184" 121 53141.96933" 121 53141.97426"
259 360360I45.88048" 360 36'15.87574" 36036 145. 89082"
121 52'54.0506211 121 52054.04635" 121 52'54.05459"
No significant error was generated from this source.
Another source of system error was associated with the
geometry of the fix. Ideally, the three theodolite angles
would describe two equilateral triangles to the ship;
however, within the operating area, the geometry varied. As
an indication of the size of this error, representative
fixes were chosen and the circular map accuracy standards
(CHAS) of each of the combinations was determined. Figure
6.3 illustrates the approximate error caused by variations
1ills
'7I
S.
Ln m
L61.
C~j CA
000
C~C
L613
V) 0
Ila,
in the geometry. Vithin the area outlined in the figure the
geometry creates a CHAS of not more than 10.4 meters. This
is therefore the source of the largest probable error in the
theodolite method of positioning. Nevertheless, this method
in combination with the ARTEMIS system provided the best
estimate of the ship location.
D. TRANSIT POSITIONING SYSTEM
The method used to determine the TRANSIT position
(GEOCEIVER STA 31370) is the most accurate satellite
positioning technique presently available. Error sources
are reduced both during data collection and during
postprocessing of the recorded values.
inA places requirements on the collection of data that
will minimize error. For this study, only satellite passes
whose maximum altitude ranged between 10° and 80 0 were
recorded. 3eteorological data (temperature, pressure, and
humidity) were collected for each pass, and a determination
of the receiver clock drift was computed after each pass.
The amount of clock drift as a function of time gave a
real-time indication of receiver performance. Equipment
checks were conducted routinely, and the results were
included with the data package submitted to DNA.
120
An error budget of the TRANSIT system for point
positioning is listed in Table VII. [Ref. 56] The precise
ephemeris method of postprocessing accounts for all of these
errors: 1) for each pass the tropospheric correction is
computed from the meteorological data; 2) the ionospheric
correction is determined by observing the shift in frequency
between the two transmitted frequencies; 3) the receiver
clock error is known; 4) the satellite orbits are observed
by the tracking stations so that precise satellite positions
are known; 5) errors due to uncertainties in the
geopotential model and surface drag forces are accounted for
during computation; and 6) the receiver altitude relative to
the ellipsoidal surface is computed approximately from the
given HSL elevation.
The accuracy of the computed TRANSIT position is stated
as 1.5 meters per axis within a 90% confidence interval.
This is assumed to provide the best estimate possible of the
GEOCEIVER STA 31370 relative to the WGS-72 coordinata
system.
E. GPS ERROR SOURCES
Global Positioning System error sources are separated
into two main categories, the space vehicle system errors
121
TABLE VII.TRANSIT System Errors
SOURCE ERROR (m)
Uncorrected propagation effects(ionospheric and tropospheric effects) 1-5
Instrumentation and measurement noise(local and satellite oscillator phasejitter, navigator's clock error) 3-6
Uncertainties in the geopotential modelused in generating the orbit 10-20
Incorrectly modelled surface forces(drag and radiation pressure acting onthe satellites during the extrapolationinterval) 10-25
Uncertainties in navigator's altitude(results in a bias in longitude) 10
Ephemeris rounding error 5
122l
and the GPS user receiver errors. There are seven possible
sources of error in the space vehicle system--errors
associated with satellite equipment, satellite clock,
ephemeris, atmospheric delays, signal multipath effect,
satellite update, and satellite propulsion firing. Table
III lists these error sources and the approximate user
equivalent range error for each. [Ref. 571
The satellite equipment error, also termed the group
lelay, is caused by differences and uncertainties in
processing and transmission of the message through the
individual satellite's circuitry. Each satellite has the
group delay calibrated prior to launch and this known group
delay is included in the satellite time corrector within the
navigation message. However, unknown delays in signal
processing and circuitry not accounted for by the corrector
contributes an estimated one meter to the error budget.
Satellite clock error is caused by variations in each
satellite clock. Satellite clock time may depart by up to
976 microseconds from the correct GPS time. Corrections for
the predicted clock variations are included in the
navigation message. Residual clock variations contribute to
the error budget and are included in ephemeris errors since
123
the clock errors are small and have the same effect as
ephemeris errors.
Ephemeris errors are the result of satellite clock
variations, drift by the monitor station clocks, monitor
*0 station signal processing delays, lack of precise monitor
station geodetic positions, solar wind and pressure
parameter variations, and earth gravity model error. These
sources all contribute to the ephemeris error budget. The
ephemeris error budget is monitored over long time periods
and translated by the master Control Station into an
User-Equivalent Range Error (URE). When the URE exceeds the
prescribed value of 4 meters the satellite ephemeris data is
uploaded to reduce the URE. (Ref. 58] Most of the URE is
included into the user clock corrector obtained in the GPS
position computation. However, not all of the ephemeris
error is removed during the position computation, and the
residual error has been estimated to be approximately 1.5
meters. See Table IiI.
Atmospheric delays in signal propagation are the result
of two effects, ionospheric delay and tropospheric delay.
Of these, the ionospheric delay, which depends on the
frequency of the transmitted signal, is greater. With the
124
two frequencies, Li and L2, transmitted by each satellite to
the user receiver, the ionospheric propagation delay can be
modelled. Using this model, the majority of the propagation
delay is accounted for, but a residual delay results in an
error. The other part of the atmospheric delay error
depends on the tropospheric propagation delay. Propagation
delay in the troposphere is a function of signal path length
through the layer, the receiver air temperature, and air
pressure and humidity. Since the tropospheric delay is not
a function of frequency and is highly localized, the
tropospheric delay corrector has not been incorporated into
the atmospheric correction computation and is therefore an
additional source of error. These two error sources combine
to yield an atmospheric delay error estimated to have a
magnitude of between 2.4 to 5.2 meters.
Ionospheric scintillation of the GPS signal, in addition
to the ionospheric propagation delay, cause errors in
positioning. scintillation has the effect of random
interference with the propagated signal as the signal is
transmitted through the upper ionosphere. [Ref. 591
Interference caused by scintillation combines with the GPS
user receiver processing noise to cause a random ranging
125
error and, if the interference is severe, interruption of
the pseudo-random number binary code causes loss of signal.
Errors and signal losses caused by scintillation cannot be
predicted or estimated.
Signal multipath errors result from the reception of a
satellite's signal transmitted via different propagation
paths. Received signals thus may have been distorted or
reduced in strength to a sufficient degree so as to affect
the range determination from the satellite. Error due to
multipathing is highly localized and cannot be modelled.
Estimates of the error magnitude are between 1.2 and 2.7
meters.
The last two space vehicle system error sources are
attributable to the Raster Control Station (MCS) satellite
accuracy and maintenance functions. Usually the MCS uploads
each satellite at a given time each day and the ephemeris
data is changed(Table VIII). Should the user not be aware of
occurrence of upload and if the receiver therefore does not
obtain the new ephemeris data, ranging to the satellite in
question will contain a possibly very large error. In
addition, if the MCS, through the Remote Stations,
determines that the four skewed reaction wheels cannot
126
kn CDO OL 0 0U) (mC 0 0 ULA Layl -' (" o- 0 - q ~
00c~ k 00 00o 0)%0 0 V)0
to ulA O 00 CDL 00C DU. )C LAO0 LA'O L -C 0 C LA D LCDO qwO aA en 4wmA%0~ Q %0- 1 00- %00% 00 0 U
Ln LA 0 0 LA
OX - LA LA LA LA c
LA 00 00 00 L LLA(n CD 0 00 00( D '
LA L L % LA CO LA co mrf0D 00 00 00 D 0 0
0 ~ - LAO L 0 00 DL OLn Ln O Ln ALL LA LALA
ua- D0 m nm a. -( - - -c
--cc
ccKK
127
maintain satellite antenna alignment with earth, the
hydrazine propulsion system is activated and the satellite
is rotated. Once the propulsion system has used, the
satellite orbit cannot stabilize immediately, and the
ephemeris data will be inaccurate. A period of up to
several hours may be required for orbit stabilization and
for the new ephemeris data to be computed and uploaded.
During that period, the ranging computations to the
satellite will have large errors. The magnitude of these
two error sources cannot be estimated but is assumed to be
several orders of magnitude larger than the previously
stated errors.
The second error category is that related to the GPS
user receivers. These sources of error associated with the
user GPS receiver, the fanpack, are receiver signal noise,
receiver vessel velocity, signal resolution, method of
signal processing, ephemeris update capability, and, for the
differential GPS computations, system accuracy comparison.
Received signal noise errors result from interference
introduced into the receiver GPS signals through processing
and internal receiver circuitry. Additionally, quality of
signal resolution is dependent upon receiver type and can be
128
a source of error. The combined errors from these two
sources are estimated to be 1.5 meters. [Ref. 60]
Estimates of these error sources for the TUE have not been
made but are estimated to be of the sane magnitude.
Velocity of the receiver vessel results in GPS errors of
varying magnitude. The higher the velocity, the larger the
error. This error is due to the time lag required to obtain
and process each H&VSTAR satellite range with the VTUE
single channel receiver, to compute the average vessel
velocity and to use the average velocity for positional
computations. The Manpack requires a six second time
interval to obtain and process the pseudo-range from each
satellite used. Thus the fix position is an extrapolation
of the four satellite ranges to obtain a convergent fix
position. at one knot, the vessel travels 0.51 meters in
one second. During the full twenty-four seconds required to
obtain four satellite ranges, the vessel would have
travelled 12.24 meters. With the vessel travelling at four
kncts, the distance travelled during the total time interval
required for a GPS fix position would be 48.96 meters.
Processing the pseudo-ranges from four satellites requires
the solution including the average vessel velocity during
129
the 2:-second ranging period. Use of this average neglects
the relative velocity of the receiver antenna which is
mounted on the mast. During this test, the GPS antenna was
mounted 9.06 meters above the waterline of the R/V ACANIA.
Assuming five degrees of pitch and roll and a vessel roll
period of 15 seconds, relative average antenna velocity was
0.16 meters per second. The antenna velocity error
translates into a random error of 0.16 meters. The other
velocity errors have not been estimated but are assumed to
be less than one meter for the low vessel velocities used in
the test.
One error source mentioned previously requires further
clarification: error due to the relative position at the
time of the fix. The Manpack requires up to twenty-four
seconds to obtain and process the satellite ranges. The
position of the fix and the associated time of fix are then
recorded. However, the time of the fix may not have been
the same time the computational results were printed. Thus
the output position may not have been correlated with the
correct theodolite computed ship position since the
theodolite lines of position were observed when the GPS
position was printed. Errors from this bias source may
130
range from 12.24 meters at one knot of vessel velocity to
48.96 meters at four knots. This error varied with the
processing time required to obtain a convergent position.
An estimate of this error magnitude was not made because of
its wide variability.
The type of receiver and the method of signal processing
also contributed to the error. Multichannel receivers
designed for Phase I testing have a lower magnitude error
for satellite signal reception and processing than do the
single channel receivers, such as the Manpack. In the
multichannel receivers, four or more satellite pseudo-range
data are taken simultaneously. The single channel receiver
sequentially receives each satellite and computes the
pseudo-range data. Simultaneous data reception reduces the
user velocity error and therefore has less position aliasing
than that found in the single channel receivers.
The method of signal processing may induce positional
errors through the use of non-optimal weighting functions in
the position computation. Should the ephemeris or ranging
data change significantly, as happens during uploaoing,
signal processing using Kalman filters as used in the
Manpack do not change the computed position rapidly enough
131
-, I, .. .... ... .. ... .. .. . . .. .. ....... . . .. .. .
to reflect the large changes in ranges and result in a slow
change drift of the GPS position. Estimated time
requirements for user receivers to stabilize after an upload
are up to two hours. [Ref. 1J]
The capability of the user GPS receiver to receive
ephemeris data immediately after upload reduces the
ephemeris errors caused by using an outdated ephemeris. The
ephemeris data is repeated every thirty seconds and its
length requires sections of two message subframes.
[Ref. 62, 633. The use of current ephemeris data in
the computations reduces the error for the ephemeris to the
value shown in table III. The Manpack has the capability to
accept new ephemeris data immediately, but during the test
large errors were introduced into the computation on
satellite ephemeris upload because this selected optional
function either did not operate properly or was neglected by
the operators.
For the differential GPS user, an additional error
source is introduced into the error budget: the assumption
that both GPS receivers will observe, obtain the
pseudo-ranges, and compute the position solution in exactly
the same manner. If this were true then both receivers
132
should be able to compute the identical position if placed
at the same position at the same time. With the Manpacks,
the assumption that the units were identical and the
position solutions were identical was not made because prior
testing established that the receivers differed in position
*i computations by as much as 3 08 meters. [Ref. 64]
For the static testing on 11 May, one error source not
previously discussed was the vertical separation of the two
Manpack antennas, colcated over the GEOCEIVER STA 31370
* control station, and the possible interference of the
uppermost antenna, System 1, with the GPS signals received
by the lower System 2 antenna. Separation of the two
antennas was 2.1 meters. Calculations using the speed of
propagation in a vacuum and the two GPS frequencies produce
wave lengths of 0.19 meters and 0.24 meters. Since
separation of the antennas was much greater than either
wavelength theoretically there should have been no
positional errors due to antenna interaction or
interference. Differing elevations of the antennas above
the ellipsoidal surface also may have induced errors in the
position computation. Estimated errors for the elevation
differences are less than 0.1 meters. Total errors for the
133
antenna vertical elevation separation and antenna
interference or interaction have not been estimated.
Thus, the error budget for the Global Positioning System
suggests a combined error of up to 57.35 meters. Using the
differential technique, the bias errors can be reduced in
magnitude or eliminated. These bias errors include
ionospheric propagation delays, tropospheric propagation
delays, variations from predicted ephemerides, and satellite
clock perturbations. Teasley, Hoover, and Johnson (1980),
evaluated the error budget for a more idvanced GPS receiver
and found the predicted filtered solution error was reduced
from approximately 11 meters to approximately 3 meters with
differential GPS processing. (Ref. 65] Error budgets for
the Nlanpack and the differential correction vector
processing method used in this test did not attain the four
meter accuracy but were not expected to because the
receivers used were less accurate, and of different types.
k134
Results of the GPS tests have been separated into four
sections: stationary GPS evaluation, evaluation of non-
differential GPS, differential GPS evaluation with static
correction, and evaluation of differential GPS without
static correction. Tables TV and VIII list the optimum
satellite observation periods and the, NAVSTAR upload times
for each day of the testing period.
A. STATIONARY GPS EVALUATION
Stationary GPS receiver evaluation was separated into
the stability tests, the static tests and the tests of the
stationary GPS receiver used during differential testing.
Figures 7.1, 7.2, and 7.3 illustrate the results for the
stability test conducted on 9 and 10 May. The receiver was
less stable than expected and depended to a great extent on.
the NAVSTAR uploading times and the URE of NAVSTAR 1 (fig.
7.4 and 7.5). Correlation between times for the NAVST&R
upload and changes in the stability can be observed at 0620
on 9 May (fig. 7.1), 0655 on 9 May (fig. 7.2), 0815 on 10
May (fig. 7.3), and 0845 *n 10 May (fig. 7.3). The
relationship between stability and URE is illustrated by
comparison of the UBE for NAVSTAR 1 at 0640 on 9 May (fig.
135
61
STABILITY TEST RESULTS36 37 15 9/10 MAY 1981
00
Lu~ EA x Axc x
a (10 MAY tIAVSTAR 1)
36 36 30 (10 MAY A
4AVSTAR 3,5,6) (9 MAYNAVSTAR 5,6)
121 53 45
i&ILl IL Xr
30 - , , le x L ji
121 53 15 x 9 MAY - SYSTEM I
lO MAY - SYSTEM 2
( 3 SATELLITE JPOATESSI I
0545 0600 0615 0630 06A15 0700
GREENWICH MEAN TIME
Fig. 7.1.
136
36 37 15STABILITY TEST RESULTS9/10 MAY 1981
*007
-j45
x xE
36 36 30- A 3-
121 53 45-
11-I
121 53 1SF9 MAY - SYSTEM 1
.10 MAY - SYSTEM 2
SATELLITE UPDATES
0645 0700 0715 0730 0745 0800
GREVMIICH MEAN TIME
Fig. 7.2.
1137
36 37 15 STABILITY TEST RESULTS
9/10 MAY 1981
x 9 MAY - SYSTEM 1
00 olO MAY - SYSTEM 2
( ) SATELLITE UPDATES
i--
45 (10 MAY NAVSTAR 1)(9 MAY NAVSTAR 510 MAY NAVSTAR 6)
36 36 30
121 53 45
30 x l AX x xA
0w
121 53 15
l I I I I
0800 0815 0830 0845 0900 0930
GREENWICH MEAN TIME
Fig. 7.3.
138
~u1
LA- OA00
LLai
Ld.O
>. >. >.I-
If: -<Q CC
2t Zz
I% LJ.)
139 C.
o
L6.
onto
'Ir-
140'
7.1 ) with the stability plot on figure 7.1 for the same time
period. On figure 7.2 the stability plot variation at 0745
on 10 Say remains unexplained but may have been due to a
receiver malf unction.
Results for tests on 11 May (fig. 7.6, 7.7, and 7.8),
exhibited less stability than expected. Also, system 2 was
less stable than system 1. The largest difference in
reading between the two receivers occurred at 0750 (fig.
7.7). This difference may have been caused by the location
of the antenna of system 2 under the antenna of system 1.
At approximately 0800, the satellite constellation elevation
angles were the largest, between 56 0 to 800 above the
horizon (fig. 7.9), and antenna interference may have led to
the large differences. Neither the satellite constellation
azimuth angles (fig. 7.10) nor the user range errors (fig.
7.11) appeared to have any effect on the stability.
Comparison of the stationary GPS receiver positions with
the position obtained with the geoceiver is depicted in
figure 7.12 for the stability and static tests. The
comparison indicates, that there is a nearly constant offset
of the two positions with the GPS position almost due south
of the geoceiver position. Further comparisons between the
141
mf
STATIC TEST RESULTS
11 MAY 1981
SSYSTEM 1
a SYSTEM 2
( ) SATELLITE UPDATES
36 36 35-
uJ
I - -4
36 36 30
121 53 35-
_ 30
121 53 251 I0705 0710 0715 0720 0725 0730
GREENJWICH MEAN TIME
Fig. 7.6..
142
STATIC TEST RESULTS
*SYSTEM 1 11 MAY 1981
*SYSTEM 2
)SATELLITE UPDATES
3636 35
3636 30
121 53 30
lpl
143
STATIC TEST RESULTS
V £SYSTEM 1 11 MAY 1981
aSYSTEM 2()SATELLITE UPDATES
36 36 35
36 36 30
121 53 40
uLj
35
121 53 30
0755 0800 0805 0810 0815 0820
GREENWICH4 MEAN TIME
Fig. 7.8.
144
SATELLITE
100 ELEVATION ANGLES
VISIBLE GPS SATELLITES
90 MONTEREY, CALIFORNIA90 MAY 1, 1981
80 - .5.NAVSTAR I (SV 4).4NAVSTAR 3 (Sv 6)-'NAVSTAR A SV 8)
t70 - -NAVSTAR 5 RSV 5)-qNAVSTAR 6 (SV 9)
20
10
2 4 6 8 10 12 14 i6
GREENWICH MEAN TIME (HOURS)Fig. 7.9.
145
e - SATELLITE
200 AZIMUTH ANGLESVISIBLE GPS SATELLITES
160 MONTEREY, CALIFORNIAMAY 1, 1981
120
80
S40
k NAVSTAR 1 (SV 4)uj -I- NAVSTAR 3 (sV 6)
-i-NAVSTAR 4 (SV 8)4AVSTAR 3' (SV 5)NIAVSTAR 6 (wY 9)
-40
-80
K -120[ -160
-200 I
2 4 6 8 10 12 14 16GREENWICH MEAN 71ME (HOURS)
Fig. 7.10.
Ia
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U- -j
-~ Z3I
-' n c IL
ul VI V)V V
IC -c cc -
147
GEOCEIVER VS. GPS POSITIO.1 cOrlPUTATION
GEOCEIVER POSITION VS. GPS SHORE-BASED POSITIONFROM DATA COLLECTED
i 9, 10, 1I MAY STATIC ANDSTABILITY TESTING
d. ]36 37 1
00
, - 50
GEOCEIVER 40
GPS 30
20
_[ io
I I 36 36 0
T21 54 1Zl 5310 30 50 40 30 20 10 00
Fig. 7.12.
148
stationary GPS receiver position and the geoceiver position
reinforce this conclusion. In figures 7.13, 7.14, and 7.15,
the mean distances between the two positions are 127, 173
and 143 meters, respectively. The higher means for the data
shown in figures 7.14 and 7.15 are due to the URE (fig. 7.16
and 7.17) for those dates and the NAYSTAR upload frequency.
If the data from 13 May is deleted because of the high URE
for that date (fig. 7.16), and the median distance used for
15 May is taken to be a representative value (130 meters on
fig. 7.15), The difference is approximately 128 meters
Between the two positions. The azimuth was also nearly
constant with the observed median values of 181 , 2070 and
1780 from south as shown in figures 7.18, 7.19, and 7.20
respectively. Neglecting the data on 13 May because of URE
values (fig. 7.16), the remaining two values are nearly
identical and have a mean of 179.5 from south. Thus the
data indicates a nearly constant offset between the position
obtained with the geoceiver and the position obtained with
GPS. This difference is about 130 meters and has an almost
north-south orientation.
149
Figure 7.13.
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Figure 7.14.
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Figure 7.15.
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Figure 7.18.
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Figure 7.20.
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B. ERULUATION O NONDIPYENETIAL GPS
Evaluation of the non-differential GPS positions was
done on a set by set basis. Figures 7.21 through 7.31 depict
the distance in meters between the theodolite-computed ship
position and the shipboard GPS receiver position. Sets 1, 2
and 3 have the smallest distance difference, as shown in
figures 7.21, 7.22, and 7.23, with mean values between 118
and 133 meters and standard deviations ranging from 7.45 to
16 meters. These smaller mean distances are a result of the
low user range errors for 12 Say as shown on figure 7.32.
The highest mean distances occurred during sets 4, 9, 10,
12, and 13 when the ORE values were high and the NAVSTkR
uploads occurred (fig. 7.16 and 7.17). The remaining
distances vary between 144 and 278 meters.
The results during the best satellite observation
periods are depicted in figures 7.33, 7.34, and 7.35, where
the non-differential GPS ship position was compared to the
theodolite-computed ship position, the distance between the
two being plotted as a histogram. Mean distances on figures
7.33 and 7.35 are representative of the five satellites
obseVed and the improved accuracy of the system, with mean
distances of 134 and 149 meters and standard deviations of
158
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Figure 7.21.
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Figure 7.34.
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173
--
10 and 52 meters. The large standard deviation for 15 May
is apparent in the bimodal empirical frequency curve (fig.
7.35) and is caused by the YAVSTAR upload (fig. 7.17). In
this case, the GPS receiver did not obtain the new ephemeris
until halfway through the time period of the observations.
The data for 13 May (fig. 7.34) reflects frequent 3AYSTAR 1
uploads and the resulting high VRE values (fig. 7.16) for
that date.
C. DIFFERENTIAL GPS EVALU&TION WITH STATIC CORRECTION
The results of the evaluation of the data of 12 May
(sets 1, 2, and 3), computed using the differential GPS
positions and the static corrections, are shown in figures
7.36, 7.37, and 7.38. Mean difference between positions for
the theodolite ship position and the GPS position are 29.1,
27.4, and 64.8 meters, with standard deviations of 7.7, 7.5,
and 22.7 meters. These distances are larger than those
determined for the theodolite ship position and the
differential GPS position (fig. 7.39, 7.40 and 7.41). This
higher mean distance indicates that the static correction,
as applied, results in a larger error in the differential
GPS position. Therefore, further evaluation of differential
GPS with static corrections were not conducted.
174
Figure 7.3f.N
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Figure 7.37.
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D. EVALUATION OF DIFFERENTIAL GPS WITHOUT STATIC
CORRECTIONS
Evaluation of differential GPS without the static
corrections were computed by sets for the five satellite
constellations for each day of testing. Set 1 (fig. 7.39)
shows a mean distance of 10.1 meters between the two
positions and a standard deviation of 5.0 meters. The
median azimuth between the two was 2570 from south (fig.
7.42), which also was the approximate course of the vessel
during the test. These values indicate that the error is
caused by the bias, or alias, in GPS position due to the
Sanpack 24-second fixing interval and positioning algorithm.
For this set, the GPS position was obtained after the
theodolite position.
During set 2 the mean distance difference between the
two positions was 11.7 meters, and the standard deviation
was 6.8 meters (fig. 7.40) ; the median azimuth was 710
(fig. 7.43). These values were slightly greater than those
of set I due to the increased URE for NAVSTkR I during the
set (see 0700 on fig. 7.32) Additionally, the azimuth was0
nearly 180 from that computed in set 1, with the vessel on
the same track as set 1. Unlike the error obtained from the
181
Figure 7.42.
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Figure 7.43.
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Sanpack bias on set 1, the error in set 2 was due to a
similar time delay bias because the theodolite position was
obtained after the GPS position.
Set 3 values on figures 7.41 and 7.44 are similar to
those of set 2, except the mean distance values were
greater--4.7 meters for set 3 versus 11.7 meters for set 2.
Mean distance increases for set 3 were due to the upload of
SAYSTAR 1 (fig. 7.32) and the availability of only a four
satellite constellation. Set 2 had a five satellite
constellation available.
For set 4, figures 7.45 and 7.46 show the distances and
azimuths for the set. These histograms fail to illustrate
the constantly increasing distances between the two
positions. These increasing distances result from the
uploads of NAVSTARls 5 and 6 and the large URE for NAVSTAR 1
(fig. 7.16). Onboard the vessel the new ephemeris data
uploaded for NAVSTAR's 5 and 6 was not obtained until late
in the set. Also near the end of the set, NAVSTAR 1 was
uploaded with the result that the last several distances
were very large, as shown in figure 7.16.
In set 5, a very high URE value for NAVSTAR 1
contributed to the extremely large position difference
184
Figure 7.44.
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Figure 7.46.
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between that determined by the theodolites and that for the
differential GPS position (fig. 7.47). The azimuth remained
nearly constant between the two positions with a median
azimuth of 43 (fig. 7.48). These values for set 5 show
that the large URE for NATSTAR 1 was the most important
contributing error source (fig. 7.16). The large tTRE may
have been caused by activation of the hydrazine
stabilization jets to dampen momentum on NAVSTAR 1.
For set 6, the mean distance difference between the two
0positions was 60.0 meters and a median azimuth of 93 (fig.
7.49 and 7.50). These values indicate that the upload of
NAVSTAR 1 near the beginning of the set (0715 on fig. 7.16)
was received and utilized in the Manpack position algorithm,
but the higher distance between the positions also indicates
a large (RE (also shown on fig. 7.16).
Data from set 7 were not evaluated because the
stationary 1fanpack receiver did not record the GPS position
for each fix due to radio failure. The mean distance
between the two positions for set 8 was 121 meters with a
mean azimuth of 68 0 (fig. 7.51 and 7.52). Both the
distances and azimuths show that the URE for MAVSTAR 1 at
0530 (fig. 7.17) was increasing in magnitude and thus
188
Figure 7.47.
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Figure 7.48.
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Figure 7.50.
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resulting in a greater positional difference. Another
factor was the bias introduced by the Manpack 24-second
reception period. This is evident in the azimuth for the
theodolite ship position obtained from the GPS shipboard
receiver.
The data for sets 9 and 10 were combined for evaluation
and the results were a mean distance between positions of0
241 meters and an azimuth of 267 (fig. 7.53 and 7.54).
Values of that magnitude show that the URE for NAYSTAH I was
the error source. Data were sampled from 0600 to 0640 (fig.
7.17). Thus the correlation between the high NATSTAR 1 URE
and the high mean distance difference between positions.
Again, receiver bias also introduced an error into the
evaluation.
Analysis of set 11 shows a bimodal distribution in both
the two position differences and azimuths (fig. 7.55 and
7.56). The peaks on the distance histogram are
approximately 133 and 160 meters; the peaks on the azimuth
histogram, approximately 220 0 and 2360. Both peaks are
caused by the upload of NAVSTIR 3 halfway through the set
and the increasing magnitude of the NAVSTIR I ORE just after
the upload as shown by figure 7.17. The total positional
difference for set 11 was approximately 151 meoters.
195
Figure 7.53.
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1 l
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. .b . .... R .. t4.. w
* to. 4 NN NNme6 *4 u # 4 * 4 4 E *4 4 * 4 4 4 4w*44 4 4 4 4 4 *
No W6a 4054. .4
*6 *-V
C lb I ONtI'
lb *4b 0 f -- co* lbC a *
06 lb0C0N00-00000
4p I *--W W i lt
*11. w 21 mCI
- 0 66 lb--wsC
I *Ia
06 lb
Cy lb C93 4 O r
09 lbCWIJMUUlb s 2 ~ Ndat
010 lb N tn 0IS~
C Ilb VIX . 6-SItitflt4m 9b 1 4,
-s a*.....4*....a. a wN c.*~~~~~Uf lb* 44444 * *44 . V
ab *O *4 * *4to44 11*6 lb 4-4 C0.
lb*I4 4 44 * 4 4 a gt.Uw
C lb4***4444***444 mlWf UW Io a .. 4* 44** 4.*. * a 2lCJ.-
*.. ... ... ... ... ... ... O 10 a
Evaluation of the combined sets 12 and 13 (fig. 7.57 and
7.58) result in a mean distance between the two positions of
172 meters and a mean azimuth of 2620. The mean distance
was large because of the large magnitude of the NAVSTAR I
OURE (fig. 7.17). & contributing source of error was the
bias introduced by the Manpack receiver.
Overall, the data using a five-satellite constellation
were as good or better than the data using only four
satellites. The results for 12 May using five satellites
(fig. 7.59) show a mean distance of 11.4 meters and a median
of 10.6 meters. This compares favorably with the results
from sets 1 and 2 (fig. 7.39 and 7.40), which had mean
distances of 10.1 and 11.7 meters, respectively. The five
satellite data from 13 May showed a very large variance due
to the large NAYSTAR 1 ORE. Therefore, data were not
compared to remaining 13 day data. Data on 15 May for the
five satellite constellation had a bimodal distribution
because NAVSTAR 1 was uploaded. Once the uploading
occurred, the peak distance was 137 meters (fig. 7.60) which
compares favorably with 121, 241, 154, and 172 meters for
sets 8, 9 and 10, 11, 12 and 13. Thus with a five-satellite
constellation, positioning results were as good or better
than the four-satellite constellation.
200
kWL
Figure 7.57.
I IL =CC a-I U P*WeQN.SfI
41 4-4
0I04 4 S
IL 1 6I
Ww L II 14-~Nt 4 444.IL*44*4 444*444*44*44*444*4 @444404*4 NI O34
I 4 I . 4 4 4. 4 * 4 4 4*04 4 * 4 4 *4 4 * 4 4 4
du *0*444*4 4*t4*4**4*444 4 4 *4 4 4
0n IL .IN .00IttI ttt ...... . 'I 91* w #P 'r O f q
OS.~~z I I %0 I
j IL 4.t UJCIL a.m leIu= 400000lcvldd
q9 U..aS IL S N
*~4 IL4 C 4W50.0$ ILS - NCOO.
4* a .IL %A -&G.~~I
It IL Im IJ 3 .
WOL M. Ico -zNA co ILh IL " 4i
45 4 I 4N II~l L *444*44444*44444444 ONIL QL
IL .4 * * * 4 ** 4 4 * 4 4 .~ . ....... ......IL *4*464****44444**44* N' 1~ UjII
40 1~ W6 0,0 m~2LUL4.464 4 4 44 4 4 * ** ,. : z~~
4 I L **.***44*45*444*0442 M,45 IIL **~*44***4~444444444NU6
4 IL@1 IL -U.
* IL S o fl iN
42 IL: '"UM~o~9 IL 4 41- 44444
00 *4 'o JUL.4444 4 @* 4 444 zoo::::W ,I I *4*444*4*4*44444W4 N us o14 4
* IL444e44444*4444444404 . 10 NO7
Figure 7.58.
* IL 4 MWWWIL
. . ........ . . .
IIL . . ..... IAO'vO
I *& IL
I I
IL xIU
01 1L 4 r m w aI LI N 0 0-0
W6 IL 4y 40-UWI
IL 4**440 N 04..-.JM6*~~~V U&.I .. . . .. . . . . . . .
I IL ***,*4 I-NNN.4 IL 4 ~ ZZZZ
W.I IL- aas WL*.. 44 4 ** .** * ZL*
0iL IL L
U4 7u; 4-04014
I~~~ ILW, 4 4 4IL~W- 4 I - 00. .*
M6 -I- N 6O4~~o * I 4c*.~jm l0I a
IL I N ~~wz4UNUIww I IL V K C.
of AL ~C 1 O4 IL 4 OZE I
U IIL6 + 1 3-Am
of I. W"* -Vr
-L q 0000Pf
wU. 4, U. U14 .9
-V UI0Ctl
I20.2A1A0.
Figure 7.59.
0 *46
a ***444444* L*44 *-.444
S Sb S sa . a Sn -b
* Sb *L
G a SI a a~ .r~ p ,O.AN
*** a.a
W. ! at UAs as.z z".4
I uW.
O. 0400N50
a 1s. N16a~4~v u.a * r0O@
4 O.f a05 u. 'l6S~A
wtu as a
OS Sb S N 0000000
* S6 4 mI 4SSPOOS Sb a
A0 I Cb5aS 0 ud-
*L -14 i..4 4 3 -A 0 Z "SM~~I 41 1S. ** 4 * 4* 4 * 4 4 .JN ~ ~ ~ ~ ~ ~ ~ ~ 0 5 b **44044*. 0 . f
* S 1. * 4044.04.4*4. * a2035
Figure 7.60.
6..
. ..... * .. . . . .. 4. .. . . .cR. . . .. e . N
o f 44 4 4 . * O 4 4 * * ~ * * 4 4 4 - f
0 Im Ijw
ILV IL or
IL11 IL~~ @ 4*4.4 N
Of U...
*. I IWWP
IL .
04 3
IL ow S lC*I LbS
*I IL % .
IL S
us U. S-a IZ
W. I
01 ~IIL
r~~~~ z rnrz a aaw.
* IL ~ 1.'~I.,%96%
-W W I I E23 1 *
05 5 -. MAU. -4p ..d W&
t* ILL w 01A. .
4IM I ; 4Z .- @*I-32 -.1
fA6 S L I A wUj -
~~.9S"4 ILl a,
05 IL% S -c--S IL S UJIL m
* IL I14 l~204
Figures 7.61 to 7.74 show the difference by fix between
the latitude and longitude plots of the theodolite ship
position, the differential GPS position, and the uncorrected
GPS position. During most of the testing, the longitude of
both methods of GPS positioning was in closer agreement with
the theodolite ship position than was the latitude. Shown
on figure 7.9 and 7.10 are the satellite elevation and
azimuth data for the testing period. This data indicates
that the satellite constellation had a larger effect on
latitude than longitude because the predominant ranging was
computed from one quadrant.
The large differences between the GPS position relative
to the theodolite ship position were easily identified
during the shipboard testing period. Latitude and longitude
plots (fig. 7.65, 7.66, 7.69 through 7.74) for sets 4, 5, 9,
10, and 12 show the deviations of the GPS receiver positions
from the predicted positions that were obvious to the GPS
operators during the shipboard testing. For sets 4 and 5,
the stationary GPS receiver positions began to deviate
greatly from the geoceiver position, resulting in a large
differential correction to the GPS ship position. These
large differential corrections caused the differential GPS
205
LATITUDE COM1PARISON SETS 1 ,2
SHIP TEST RESULTS
I 12 MAY 1981I ~ T-2 POSITION
36 3800 LUNCORRECTED GPS POSITION
I * TRANSLOCATED GPS POSITION
50
SET 1
40
~30
2OF SET 2
10
3637 0010 20 30 40 50
FIX NUMBER
Figure 7.61.
206
L0flGITUDE COMPARISONi SETS 1, 2
SHIP TEST RESULTS
121 53 20 12 M4AY 1981
10
53 00-
SESE \1
50
40k
30[1 T-2 POSITION
aUNCORRECTED GPS POSITION
I eTRANSLOCATED GPS POSITION
121 52 2 1 -II III10 20 30 40 50
FIX NUMBER
Figure 7.62.
207
LATITUDE COMPARISON SET 3
SHIP TEST RESULTS
12 MAY 1981
AT-2 POSITION
aUNCORRECTED GPS POSITION36 37 50
TRANSLOCATED GPS POSITION
40 - ET 3
30
20
10
36 37001so5 60 70 80 90
FIX "JUMBER
Figure 7.63.
208
LONIGITUDE COMPARISON SET 3
SHIP TEST RESULTS
12 MAY 1981
121 52 40 T-2 POSITION
SUNCORRECTED GPS POSITION
TRANSLOCATED GPS POSITION
30-
20-
x
- SET 3o 10-
5001
121 51 50~50 60 70 80 90
FIX 4IUMBER
Figure 7.64.
209
LATITUDE C0MPARISO."l SETS 1,5V
36 38 40 SHIP TEST RESULTS13 MAY 1981
20
SET 4
38 00
SETS5
40
20x
4x
37 00
ST-2 POSITION
40 a UNCORRECTED GPS POSITION
TRANSLOCATED GPS POSITION
36 36 2070 80 90 100 110 120
FIX I48MER
Figure 7.65.
210
LON!GITUDE COM1PARISON' SETS 4, 5
121 53 50 -SHIP TEST RESULTS
13 MAY 1981
30
10
5250oX.
xc~x
3 0 X J R x x V * bS E
SET 4
10
ST-2 POSITION51 50 - UNCORRECTED GPS
POSITIONrRANSLOCATED "UPS
POSITION
72 5 0 80 90 100 110 120
FIX 4UMBER
Figure 7.66.
211
LATITUDE 'COMPARISOM SETS 6, 7
SHIP TEST RESULTS
13 MAY 1981
3638 20~T-2 POSITION
aUNCORRECTED GPS POSITION
*TRANSLOCATED GPS PrX ,1.38 00
40
20 SET 6cc SET 7
37 00
40
36 36 20110 120 130 140 150 160
FIX NUMBER
Figure 7.67.
21 2
LOr'GITUDE COMIPARISONi SETS 6, 7
SHIP TEST RESULTS
K ~ ~~121 53 50K13AY98
30
53 10
xx SET 750-
30
'T-2 POSITION
a UNCORRECTED GPS POSITION
52 10 o TRANSLOCATED GPS POSITION
121 51 50o110 120 130 140 150 160
FIX NUMBER
Figure 7.58.
213
36 38 20LATITUDE COMPARISON SETS 8, 9
363820SHIP TEST RESULTS
15 MAY 1981
38 00
40 SET 8
20
SET 9
S37 00
40
I.20 m T-2 POSITIONUNCORRECTED GPS POSITIONj
TRANSLOCATED GPS POSITION
36 36 00 I160 170 180 190 200 210
FIX NUMBERFigure 7.69.
214
LONGITUDE C0MPARISOM SETS 8, 9
121 3 40SHIP TEST RESULTS
15 MAY 1981
400
20
52300SE 9
* - 40 TRNLCAE *
POITO
-0- OSTO
2 01718192020
52006
]$
LATITUDE COMPARISON SETS 10, 11
1 SHIP TEST RESULTS15 MAY 1981
36 38 30
10' SET 1
37 50
LiJ
SET 10* 30
10
x
36 50 - T-2 POSITION
UNCORRECTED GPS POSITION
TRANSLOCATED GPS POSITION
3636 30I I2O220 230 240 250
FIX NUMBER
Figure 7.71.
216&
LONGITUDE COMPARISON: SETS 10, 11
SHIP TEST RESULTS
15 MAY 1981
121 54 10
SET 7053 50K
30
SET 71lo-
52 50
30~ T-2 POSITION
aUNCORRECTED GPS POSITION
TRANSLOCATED GPS POSITION
121 52 10 20 21 220 I3 4
FIX NUMBER
4 Figure 7.72.
217
LATITUDE COM1PARISON SETS 12, 13
SHIP TEST RESULTS
36 38 30 -15 MAY 1981
38 10
50
30 SET 12
6 T-2 POSITION
37 10 *UNCORRECTED GPS POSITION
*TRANSLOCATED GPS POSITION
aSET 13
3636 30240 250 260 270 280
FIX lUMBER
Figure 7.73.
218
LOM!GITUDE COMPARISON SETS 12, 13
SHIP TEST RESULTS
15 MAY 1981121 53 10
A
52 5SET 13•52 50
30
I-,
10 SET 11
51 50
A v T-2 POSITION
a UNCORRECTED GPS POSITION30 -SET 12 " TRANSLOCATED GPS POSITION
121 51 10 1240 2O 260 270 280
FIX IUMBERFigure 7.74.
219
position shown on figures 7.65 and 7.66 to deviate a large
amcunt from the theodolite position and the uncorrected GPS
position.
220F
The objective of the study was to determine whether the
application of GPS in a translocated or differential mode
provides sufficient position accuracy for near-shore
hydrographic surveys. Several assumptions were made prior
to the test: (1) two GPS receivers required for the
differential mode performed the computations similarly, so
that in the worst case a constant bias would be displayed if
both receivers were colocated; (2) the process of updating
the ephemeris information would not contribute a significant
positional error to GPS in the differential mode; (3)
reasonable accuracy could be obtained by using the output
from the receiver control display unit, that is,
sophisticated processing methods were not required; and (4)
the Manpack receiver results would not differ when used in
stationary or low-dynamic environments (shipboard at 4
knots).
None of these assumptions proved to be valid. It was
originally expected that the two receivers would produce
similar positions if both sets were operating at the same
tine over the same location. One limitation of these
receivers, however, is that current ephemeris information is
221
not received unless the receiver has been activated prior to
the update. (Ref. 66] For a period of time after the
receiver is activated, the portion of the satellite message
that contains the updated ephemeris is not acknowledged.
Therefore, position degrades rapidly when a VAVSTkR is
updated and the current ephemeris information is not
utilized by the receiver. For this study, unfortunately,
the initial times of activation of the two receivers were
not recorded. Hence, the effect on position caused by this
receiver parameter was not defined.
The URE plots illustrate that the ephemeris updates did
contribute significantly to the range error and,
consequently, the resulting position error. The position
determined by the Manpack receivers was not affected as
seriously by the clock error in NAVSTAR 1 when a
five-satellite constellation was used. The inaccuracy of
pseudo-ranges received from this satellite required frequent
updates from Vandenburg, especially on 13 May. A receiver
that had the option of totally eliminating the erroneous
pseudo-range would have given the best results for the
study. Since the receivers operated independently, and the
ephemeris information was not concurrent, the differential
mode was effective for only a few cases.
222
k simple correction was applied to the values output on
the control display unit of the Manpack receiver. This did
not permit application of tropospheric or refraction error
corrections, other than that applied by the receiver during
computation of the position. & more sophisticated
prccessing method, resulting in greater accuracy, would
require acquisition of the pseudo-ranges and subsequent
postprocessing to determine the receiver positions.
The best results during the onboard portion of the study
were obtained when the ship was allowed to drift at
approximately I knot on 12 Bay.
In conclusion, use of two Phase I Hanpack receivers in
the differential node meets the required accuracy of 10
meters only if the ship speed is less than 1 knot and other
parameters such as ephemeris information and the number of
satellites used for the position computation introduce a
minimum amount of error. Further testing using differential
GPS should incorporate more sophisticated processing methods
and more advanced receivers to achieve the survey accuracy
required for nearshore hydrographic surveys.
223
UDESCRIPTION QZ ERRO TBEZ23
From application of error theory in the evaluation of
positional information, it is possible to establish a
meaningful accuracy statement subject to uniform
interpretation. To provide a logical and acceptable basis
FOR COMPUTATION AND COMPARISON, POSITIONAL ERRORS ARE
assumed to follow a normal distribution. The assumption is
valid because positional error components generally follow a
normal distribution pattern when sufficient data is
available.
The statistical treatment of errors utilizes measurable
errors obtained in the sources of positioning information.
Analysis of the linear components provides a two-dimensional
expression of the accuracy of the positioning system in the
form of an error ellipse. The use of an error ellipse is
complicated by the problem of axes orientation and
propagation of elliptical errors. Therefore, the ellipse is
commonly replaced by circular form which is easier to use
and understand. The linear standard errors are combined and
converted to a circular distribution and the final accuracy
statement is expressed in terms of circular errors.
224
The circular form assumes the circular probability
distribution function. This function expresses the
probability that the radial error will be equal to or less
than the radius of the probability circle. The dispersion
of errors within the distribution is measured in terms of
precision indexes, each of which represents the error which
is unlikely to be exceeded for a given probability. The
preferred circular precision indexes are the circular
standard error (a , the circular probable error (CPE or
CEP), the circular map accuracy standard (CHAS), and the
circular near-certainty error, or 3.5 sigma (3.5 a ). For
each precision index, the given probability is 39.35%, 50%,
90%, and 99.78%, respectively.
Each of the precision indexes can be converted to one of
the others by using the following table:
Circular Error Conversion Factors
39.35% 50% 90% 99.78%
39.35% 1.0000 1.1774 2.1460 3.5000
50% 0.8493 1.0000 1.8227 2.9726
90% 0.4660 0.5186 1.0000 1.6309
99.78%. 0.2857 0.3364 0.6131 1.0000
225
The rapid approximation for determining the circular
standard error is
CSE - 0.5000 (ax + ay)
wherea x and ay are linear standard errors obtained from the
sources of positioning information, and therefore are the
axes of the error ellipse. For a truly circular
distribution, where ac is identical to the circular standard
error, a x and a y are equal and the angle of intersection
between the two is 900. In all other cases, a normal
circular error distribution is substituted for the
elliptical distribution. The substitution is satisfactory
for an analysis within specifiedasin/amax ratios, wherea sin
is the minor or smaller linear standard error of the two.
Distortion in the error distribution between elliptical and
circular forms at lower Gain/ amax ratios limits the use of
the circular concept to ratios greater than 0.2 .
The CHAS is the precision index used as the U.S.
National Map Accuracy Standard. It is interpreted as
limiting the size of error which 90% of the positions will
not exceed. CHAS is computed from circular standard error
as follows:
CRAS 2.1460ac
226
The two-dimensional error distributions for positions
determined by the ARTEMIS system and the theodolite network
are described by CHAS. The accuracy of the specific
positions is expressed by a statement of probability and
error magnitude. The accuracy statement does not mean thatthe error in position is exactly the value shown in figure
5.1, rather it expresses the probability that the error in
position will not be larger than the error given.
2I
227
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3. Personal communication, Lt. T. Rialon, NOAA, 2February, 1981.
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5. DUnaP. and Rees, J. yraao-cA
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Canadi.an Hydrographic Conference, Halifax, N.S., 1980.
8. Q2 i±.Stansell, 1978.
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Alaa.1.n, V. 5;No. 1, Summer, 198.~ tnad"
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14l. Dew, 1979.
1. Personal communication W.Hovr TeaIntuns1. Corporation, 3 March 1§81.Hoer TxaInrmnt
228
16. Jorfelsen, P.S., "Combined Pseudo-Range and DopplerPos t oning for.the Stationary NAVS AR User", IE!!Pjans 80. Position Location and Nay catlo SvmgOlreod1980.
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26. 2R ci±, Milliken and Zoller, 1978.
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229
33. Global pgsiioninu ystem ma npack/ahicular "SarBRU3-Ient LAYU nual, Texas Instruments Inc., 1979.
3. ibid-
35. O c Spilker, 1980.
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IEEE Plans 8o 0 poition TLocation and Navigatigon- VDOsiUa Record, 1980.
38. OM ci%, Munson, 1977.
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40. Gossett, F.R., Manual of Geodetic Triangulation, NOS,1950.
01. Poling, A.C., Tellurometer Manual, NOS, 1961.
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48. U 1A Van der Ree, 1981.
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230
50. Nevell V. LT, NOAk and Winter, D., LCDR, NOAA,ARTEMIS Test Results, NPS, 1981.
51. Personal communication, R. Helby, PMC, NOAh, 5 April,1981.
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61. IJlj.
62. QU gjt, Spilker, 1980.
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231
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Jac bqon, L. gser Eonipment fo; the NAI;TAR gIlobajlitini - stem paper presented a h
WeIecomunIcations Conference, Dallas, Texas, 1 December,1976.
Jacobson L. and Huffman L., "Satellite Navigation withGPS," Saiellite Communicati.ons, July, 1979.
Jor ensen, P. S. BAYSTAR/Global poSionj. fl Systemi8-a.Rtefl &.3JLZ.l2as, paper p resented am Tneinstitute orav gatIon Conference, Monterey, California,25-29 June, 1980.
Joseph, K. H,, *tand others, NAVSTLAR GP eceiver forSAtelli.te 1D lctlojg,, paper pree ER aXAG T3-Guidance anq Control Pa9 symposium, London, UnitedKingdom, 141-17 October, 1980.
the A piition o eas aa es asters Tesis, naa
Logistics Review Group Report, NlkYSTA&, Global PositioninoSystem IGPSI Audit Summary, 2b April, 197.
Mainavox Technical, Report SX-TH-33241-80
Rd .Q&r..QQ 2 rnU UL y %. 1. aenpa, Agust, VU
Magnavox Report 140413, Global Positioning S9stea Phase IUser Satz Descrigtions, October, 1915 u.
R~asters es6 N aval Postgraduate Scco, 3oncey,
233
Juh nnual 5yposiurn on Frequency control, Atlantic City,New Jersey, 2-4 June, 1976.
e #' eme erng o erence, H att House Hotel, Los Angeles,Califrna. 18-20 October, 1 77.
Nambeional3 Aeronautics and Space Administration ContractItudy and Analysis, by . Goad, 12 j y, 94
Naval Ocean Systems Center Field 'Test *Operations PlanFTOP-PF-1052. ATSI& Goa Positionind system on.rigate/FFI102 , July, 1978.lb
Naval Ocean Systems Center Field Test 0operationis PlanContract Number N00123-77-C-OO&6, NAVSTkR global politioziingqgl~aoL.kU, by SAI C01ISYSTENS corporation, I N ovestker,
Naval Ocean Systems Center TechnicaL Regort Number 417,
RocVSl neraina eor,1 ASA Global positioningSse hRarAtnaTss
Ranae-zi t Colln Gernicet Avonica stison papebrrese ,e
Space and Mlissile S stems Organization CS/ E DefinitionContract Nlumber P04170 -73- -029
y General Dynamics, g ectronicsl i son, 2 e ruary,1974
Space and Missile Sistems Organization CS/TIE ContractDefjtn til ? 04701-73-,,-0298, nl Rqr :o aoh
1ynamics, iec ronics iv sion.e ra-ry, j97 4 Y eer
Space and Missile Systems Or aization NAVSTAR GlobalPositionn.pe C~tatNme I-DE10 ra mpaodjj t tan r te -UhL22tinn Sr:@
234
Space and missile Systems Or~ani; ation Finai~ Field TestReport for Major Fie]4 Test Ob ective Number 1 01SiporOgrtos 1 June, 1979.
Sgace and Missile systems Organization Major Field Test
S ace 0 and Missile S S s Orianization Re r
Sequent 0YTI 05~~a Ps ong 5stem nase i
University of Texas at Atstin Bid Invitation Yumber 0088gloal ~giignng ecev n Slttmlg= Field Portable,
235
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