the design of a celestial navigation microcomputer with
TRANSCRIPT
L POSTGRADUATE SOU
Monterey, California
u
TH oeoTHE DESIGN' OF A CELESTIAL NAVIGATION
MICROCOMPUTER WITH THOUGHTS ON AN INTEGRATED
INFORMATION DISTRIBUTION SYSTEM
by
Jon Prichet Moore
David Br andt Rainsberger
June 1975
Thesis Advisor: V. M. Powers
Approved for public release; distribution unlimited.
NAVAL POSTGRADUATE SCHOOL
onterey, California
THESISTHE DESIGN OF A CELESTIAL NAVIGATION
MICROCOMPUTER WITH THOUGHTS ON AN INTEGRATED
INFORMATION DISTRIBUTION SYSTEM
by
Jon Prichet Moore
David Brandt Rainsberger
June 19 7 5
Thesis Advisor: V. M. Powers
Approved for public release; distribution unlimited.
UNCLASSIFIED
Jl-.CUHlTY CLASSIFICATION OF THIS P«&Ef»'»i.r f>>(. Ertfr* }
of this nature brings to light the need for an informationdistribution system. Thoughts on a system of this
purpose are presented.
DD Form 14 73, 1 Jan 7;^
S/N 0102-014-6601UNCLASS IFIED
SECURITY CLASSIFICATION OF THIS PACtC*^*" £>•'• Enffd)
The Design of a Celestial Navigation
Microcomputer with Thoughts on an Integrated
Information Distribution System
by
Jon Prichet MooreLieutenant, United States Navy
B.S., Oklahoma State University, 1968
and
David Brandt RainsbergerLieutenant, United States NavyB.S., Miami University, 1968
Submitted in partial fulfillment of therequirements for the degree of
MASTER OF SCIENCE IN COMPUTER SCIENCE
DUDLEY KNOX LIBRARYNAVAL POSTGRADUATE SCHOOL.MO^gEY^CAJJEORNIA 9394Q
ABSTRACT
This report lays the groundwork for further development
of a microcomputer that provides full celestial navigation
capability. The physical design specifications and design
philosophy are investigated. The fix algorithm which
allows determination of position without the use of H.O.
Publications is implemented in the BASIC language.
The application of microcomputer technology to devices
of this nature brings to light the need for an information
distribution system. Thoughts on a system of this purpose
are presented.
TABLE OF CONTENTS
I. INTRODUCTION - - - - 6
II. NEED FOR A CELESTIAL MICROCOMPUTER PERIPHERAL- - - 8
III. DESIGN PHILOSOPHY- - - - 11
A. OBJECTIVES ------ 11
B. PHYSICAL DESIGN SPECIFICS - 12
IV. THE CELESTIAL FIX ALGORITHM- 14
V. PROGRAM THEORY AND IMPLEMENTATION- -------- 22
A. THEORY -------- - 22
B. IMPLEMENTATION - - - - - - 31
VI. THE INFORMATION DISTRIBUTION SYSTEM- ------- 36
A. INFORMATION DISTRIBUTION ----------- 36
B. DESIGN PHILOSOPHY- ----- 38
VII. LANGUAGE SELECTION ---------------- 43
VIII. CONCLUSIONS ----- 48
APPENDIX A: CELESTIAL FIX PROGRAM LISTING- ------- 51
APPENDIX B: SAMPLE PROGRAM RUN - 70
BIBLIOGRAPHY- ---------------------- 72
INITIAL DISTRIBUTION LIST ---------------- 74
FORM DD 1473- ----------------------
LIST OF FIGURES
Figure Title Page
1 Celestial Navigation Microcomputer ------ 13
2 Geographic Position (GP) of a Star 15
3 Navigational Fix from Altitudes ofTwo Celestial Bodies ---- ___18
4 Triangles Used for Navigational Fix- ----- 19
5 Overall Celestial Situation with SixIntersection Points Depicted - ---21
6 Information Distribution System- -------41
I. INTRODUCTION
This paper deals with two interleaved subjects. The
two subjects will be discussed with varying levels of
detail and scope. The more specific subject of the two is
the conceptual design of a celestial navigation computer.
A general approach toward a digital information distribu-
tion system is the second subject. The celestial navigation
computer is discussed first, as it is an element of the
entire system, and the design specifics of this device
relate better to the entire system than vice versa.
The celestial navigation computer provides for manual
input of information as well as documentation of the out-
put for legal records. The main reason why a computer is
beneficial for celestial positioning is that it eliminates
errors made in recording, computing and plotting of celes-
tial information. The design efforts attempt to eliminate
manual recording of substantive information and manual
plotting of lines of position (LOP's) for use in determining
position. Automatic information recording is provided.
This paper provides an analysis of the programming
language, program I/O requirements and physiological require
ments of the device. The initial purpose of this paper was
to design the device, then to see how this philosophy and
design process could be applied to other building block
devices applicable to the information distribution system.
Comments to this point will be made in Section VI.
II. NEED FOR A CELESTIAL MICROCOMPUTER PERIPHERAL
It would seem that with all of the fancy new gadgetry
on the market today, the age-old method of navigating by
the stars might just start to fade away. It is conceivable
that this could happen in the civilian world; however, the
military is often more demanding in the constraints placed
upon its ships. The electronic devices which use electro-
magnetic radiation in the position determination loop are
subject to deception, jamming and detection (as in the
case of radar), and support failure, e.g., destruction of
navigational satellites or LORAN stations, etc. The only
other navigation device not subject to standoff disabling
is the ship's inertial navigation system. It must be
pointed out that an inertial navigation system is only as
good as its platform's stability and the stability only
as good as its positional estimates. Thus the longer the
platform goes without being updated, the worse the platform
stability becomes - -truly a spiraling decline in accuracy.
With all of the electronic fixing devices out of the
picture, visual sighting or sonar positioning is all that
is left. Visual sighting is passive and includes celestial
position determination, and this is the reason for main-
taining excellence in position determination by the stars.
The microcomputer is a newcomer to this field. This
technology properly applied allows for increased speed and
accuracy and the reduction of human errors. A need to
determine position faster simply goes along with the increase
in ship speed, e.g., new hydrofoil ships can conceivably
reach speeds in excess of 60 knots. The need for increased
accuracy is an economic as well as operational benefit.
Accurate positioning is needed for proper and efficient
deployment of weapons, efficient navigation and maneuvering.
The submarine force has implemented a celestial naviga-
tion system in the most complete terms. Completely computer
controlled, several "spot shots" are obtained in a moment
and the submarine's navigation systems can then be updated.
The Air Force has used the ASTRO-TRACKER to aid in celestial
navigation.
In January, 1975, Carl Nuese and Dr. Alan Schneider
provided the algorithms necessary to create a celestial
navigation calculator using the Hewlett Packard Model 65
programmable microcomputer [Ref . 8] . The peripheral device
under design in this paper was intended to hit the mark
somewhere between the HP-65 calculator and the submarine
celestial navigation computer- -much closer to the HP-65
side of the spectrum.
The HP-65 calculator solution to navigation problem
lacks the same sort of smoothness that placing a square
block into a round hole does; with a lot of effort it works
but it leaves a lot to be desired. The HP-65 general purpose
calculator uses programmable magnetic cards to hold prestored
programs that are executable on the machine. Though the
device is relatively inexpensive the following drawbacks
are noted:
1. Storage and maintenance of the program cards are
cumbersome
.
2. I/O is nonexistent.
3. Data format is not "conventional."
4. Record keeping must still be done manually.
5. The device is subject to pilferage.
6. Expansion of programs is difficult in its 100-
instruction memory.
The advantages are the following:
1. Self contained (excluding the magnetic cards).
2. Easier to operate than most terminals.
3. Inexpensive.
4. Good supporting vendor.
5. Applicable to many other mathematical problems.
10
III. DESIGN PHILOSOPHY
A. OBJECTIVES
The objectives of the design of the device are simple:
1. Implement Nuese and Schneider's algorithms in a
device that does not have the disadvantages of the HP-65.
2. Maintain the advantages of the HP-65 without appre-
ciably increasing the cost/performance factor.
3. Provide for integration into the overall information
distribution system.
4. Provide the fail safe/soft features and hardcopy
printout capabilities.
Two definitions will be stated at this time.
Microcomputer: A small general purpose computer. Itcontains a microprocessor and a small number of (sup-port) LSI circuits. Usually mounted on one or twoprinted circuit boards. May or may not be programmable.
Minicomputer: A computer with larger word sizes andfaster execution times than a microcomputer.
The proposal to specify a microcomputer for the celestial
computer was based on the further observations that the micro
computer can be exactly specified as to the I/O structure,
memory structure and contents, power supply designs, etc.,
whereas the minicomputer requires adjusting of all of the
above mentioned properties to "fit" the minicomputer. The
cost for a microcomputer is also much less than that of the
minicomputer
.
An eight-bit-wide microcomputer consisting of a micro-
processor, a 128 x 8 bit RAM, a 1024 x 8 ROM and peripheral
11
adapter cost around $473 in 1974, and by 1976 is estimated
to cost under $100 [Ref . 6] . Though larger than the HP-65
it is still less than ten times as large. An examination
of data equipment suppliers will show that a small mini-
computer will cost around $5,000 and higher.
The device must be self-contained (except for power)
,
easy to operate and relatively inexpensive. The I/O struc-
ture must allow for keyboard entry, and the formats for data
must be naturalized (36° 15' 33" vice 36.1533°) to the prob-
lem. Note that the algorithm expressed in Appendix A uses
the latter form due to limitations of the BASIC language
I/O structure. As the device would be a small production
lot, vendor support would be minimal or nonexistent; yet
the simplicity of the device should allow for easy onboard
maintenance
.
B. PHYSICAL DESIGN SPECIFICS
The device must be housed in one unit. The unit must
allow for connection to power and to the data distribution
system. The unit will have a simple ten-digit keyboard with
a N/E (north or east) and S/W (south or west) key. A 16
element five-by-seven dot LED must be placed above the key-
board for verification of entries as the line printer prints
a completed entry.
A 30 character wide line printer (for printing instruc-
tion, entries and calculation results) must be placed in
the unit. The unit is illustrated in Figure 1, and a
sample output strip is displayed in Appendix B.
12
Data Verification Readout (LED)
Program Selectors
Data Entry Keyboard
Figure 1-Celestial Navigation Microcomputer
13
IV. THE CELESTIAL FIX ALGORITHM
The purpose of the proposed navigational computer is
to enhance the speed, accuracy and ease with which calcula-
tions such as those used in celestial navigation can be made.
The program presented in Appendix A removes the need for the
user to depend on the Nautical Almanac [Ref. 13] and other
required H.O. publications by computing the values supplied
by these tables.
When taking a fix several phases of sight reduction are
considered: insertion of user values, correction of the
sextant altitude, establishment of the position of the
observed celestial body, solution of the navigational
triangle and displaying the results.
User values include Greenwich date, day, month and year,
the observer's assumed position, the name of the body ob-
served, the time (Greenwich Mean Time), the sextant altitude,
the observer's height of eye or dip and the sextant's index
of correction.
Correction of the sextant's altitude includes changes
in altitude due to refraction, semi-diameter of the sun and
moon and parallax for the moon.
Establishment of the position of the observed celestial
body on the earth (GP) involves the calculation of the
Greenwich Hour Angle (GHA) and declination (Dec) of the body
(see Figure 2) . Associated \\rith each star are eight
14
intermediate constants which are calculated and combined
with universal constants (rate of precession of the equinox,
rotation of the earth on its axis and aberration) to produce
the GHA and declination.
Constants which apply to all stars are the following:
1. Rate of rotation of the earth with respect to the
vernal equinox [Ref . 11]
.
2. The longitude rate of the sun based on the time
between successive crossings by the sun of the vernal
equinox [Ref. 10]
.
3. The obliquity for epoch 1975 [Ref. 10].
4. The annual precession rates for epoch 1975 in right
ascension and declination [Ref. 10]
.
With these common constants, particular intermediate
constants associated with each star are developed. Utiliz-
ing the apparent right ascension and declination as found
in Apparent P l aces of the Fundamental Stars [Ref. 14]
,
right ascension and declination can be computed to a
reference time through the effects of precession and
aberration. Other constants include the rate of increase
of the mean sun longitude in degrees per day, precession
in right ascension and declination in degrees per day, true
right ascension and declination in degrees, and the time
behavior of the corrections for aberration [Ref. 8]
.
When the intermediate constants are developed and
applied to the algorithms, the computed GHA and declination
of a star will result. Discussion of the computation of
16
the constants, GHA and declination is presented in the
next section. With the algorithm for computing GHA and
declination of a star implemented it now becomes a matter
of selecting those stars necessary to perform a sight
reduction yielding a navigational fix.
Considering a three-star fix, the GHA and declination
for each star is obtained as discussed above. Working with
pairs of stars the solution of the associated navigational
triangles will produce intersection points on the circles
of equal altitudes (see Figure 3)
.
Three triangles are used to calculate a possible position
as shown in Figure 4. The first triangle has vertices N
(north pole), A and B. The angle A is either G1-G2 or
360°- (G1-G2) . This angle represents the difference in the
GHA's. Given the angle A and cosides dl and d2 (the
declinations) , the law of cosines is applied to solve the
third side t. Given the three cosides the angle B opposite
coside dl is calculated. Given three cosides in the second
triangle, HI, H2 and t, the angle B3 opposite HI is found.
Letting m be the sign of the sin(Gl-G2) , the angles
B(l)=mB-B3 and B(2)=mB+B3 are found. Given angle B(l) and
cosides d2 and H2, the third coside L(l) is found. Given
the three cosides d2, H2 and L(l) the angle A(l) opposite
H2 is found. In the same manner L(2) and A(2) are found.
L(i) is equivalent to the latitude and A(i) is equivalent
to the longitude of an intersection of the circles of equal
altitude
.
17
Repeating the algorithm considering the third celestial
body and one of the previously used bodies, a second pair
of positions will be found. A third repetition yields two
more positions totaling six (the maximum) possible positions,
as shown in Figure 5.
These six positions are then investigated to determine
the closest three by determining the shortest distance
connecting these three points. With this resulting triangle
the location of the two endpoints of a line which is one-
third away from any side of the triangle is computed. The
center of this line containing the two endpoints is the
center of mass of the triangle and therefore is considered
the celestial fix.
The program will provide for accuracy in mathematical
manipulation of numbers to one part in four billion using
the BASIC interpreter at the Naval Postgraduate School and
implementing the program on the INTEL 8080. This will pro-
vide for the accuracies of .1 or .2 miles as presented in
Ref. 8.
20
V . PROGRAM THEORY AND IMPLEMENTATION
A. THEORY
When computing the constants needed for the program
a common reference time is necessary to provide for the
accuracy of results. If the data is referenced to the mean
equinox and equator of date, or to a fixed epoch then
no error is introduced. The reference time employed in
the algorithms is 0000 29 Nov 1971 as suggested by Ref. 8.
Any data known at some other time is retarded to this
reference time.
Note that the GHA of the star is related to the
Greenwich Hour Angle of Aries (GHA ) and the sidereal hour
angle of the star (SHA) , the latter being 360° minus the
right ascension a. Thus for any time t,
GHA = GHA + SHA (1)Y
GHA = GHA + (360 - a) (2)
GHA = GHA - a (3)Y
The GHA increases at a constant rate, namely, the rate
of rotation, a, of the earth with respect to the vernal
equinox. Knowing GHA at some time t, , then
GHA = a(t - t1
) + GHA±
- a(t) (4)
22
where t is the present time measured in days and decimal
parts of a day from the time t, , a time in the recent past.
Because it will later prove efficient to refer all events
to an earlier time (t = 0000 29 Nov 1971) this leads to
GHA = a(t - t ) - a(t - t^) + GHA - cx(t) (5)
= a(t - t ) + GHA - a(t) (6)s o yo
where GHA = GHA , - a(t, - t ) (7)yo yl 1 o J K J
The apparent right ascension a at time t is related to
its known true value a ! at some previous time t, through
the effect of precession and aberration.
Therefore (see "Supplement," [Ref. 11, pp. 39-49])
a(t) = a'ftj) + a(t - t^) + Aa(t) (8)
where
a'(t-,) = the true right ascension at time t,
a = precession in right ascension (degrees
per day)
Aa = correction in right ascension at time t
for aberration (as defined on p. 47,
"Supplement")
In order to refer all data to the common reference time
t , it is convenient to rewrite (8) as follows:
23
a(t) = a'(t1
) + a(t - tQ
) - a(t1
- tQ
) + Aa(t) (9)
= ct'(to
) + a(t - tQ
) + Aa(t) (10)
where
cx'(t ) = a'(t1
) - a(tx
- tQ ) (11)
Inserting (10) into (6)
,
GHA = GHAyo
+ a(t - tQ
) - ct'(tQ
) - a(t - tQ
) - Aa(t) (12)
= [GHAyo
- a'(to)] + (a - a) (t - t
Q) - Aa(t) (13)
Or,
where
GHA = alg
+ al9
(t - tQ
) - Aa(t) (14)
a nQ = GHA - a' (t ) (15)18 yo v o J v J
and
GHA ,- a(t, - t )yl 1 o
a'Ctj) + a(tx
- tQ ) (16)
a19
= a - a (17)
Now Aa must be developed into a usable form. The equation
on pages 47 and 48 in "Supplement" [Ref. 8] shows that aber-
ration at time t is given by
= -k sec 6 ' [cos a' cos X cos e + sin a' sin A] (18)
where X is the longitude of the mean sun measured along the
24
ecliptic from y , e is the obliquity (angle between the mean
planes of the ecliptic and equator) , k is the constant of
aberration defined on page 48 in "Supplement," having a
value of 20.47", and a' and 6' are the true right ascension
and declination, all values being at time t. Selecting t-,
as a convenient time for determining the mean place of the
star and the obliquity, and regarding a', 6' and e as
constants over the interval from t, to t, equation (18)
becomes
:
Aa = - ( ?fiA n se c "5-J cos a
]cos e -i) cos X
- (-r^kn— se c <${ sin aj) sin X (19)
= a incos X + a,., sin X (20
where
a 10=
"^fioo
sec^i
cos a\
cos cl
ill)
an =" loW1 sec 6
isin a
i(22)
The factor 3600 enters because Aa will be computed as
fractions of a degree whereas k was given in arc seconds.
Equation (20) can be rewritten as
Aa = a1 7
sin (A + a, .,) (23)
25
where
12 \l 10 "11
and
a i9= J am 2
+ a ni2
(24)
-1 ama13
= tan C^ ^ 25 )
The longitude of the mean sun increases linearly with
time according to the equation
X(t) = X(t - t1
) + X (26)
where X- is the known longitude at some convenient reference
time t-. . As has previously been done, it is best to refer
to a common reference time t by rewriting (26) as follows:
X(t) = X(t - tQ
) - X(t1
- tQ
) + X1
(27)
= X(t - tQ
) + XQ
(28)
where X is defined as follows:o
X = X. - X(t, - t ) (29)o 1 v 1 J
Substituting (28) into (23) , the results are
Aa = a, sin [X(t - t ) + X + a n ,] (30)12 L v o o 13 J
a12
sin [X(t - tQ
) + a14 ] (31)
26
where a, . is defined as follows :
a14
" XQ
a13 (32)
Using (31) in (14) the substitution yields
GHA = alg
+ a19
(t - tQ ) - a
±2sin [X(-t
Q ) + a14 ] (33)
Because a, q includes earth rate, roughly 360° per day, and
that t - t may be on the order of 30,000 days, to preserve
accuracy in the computation it is worthwhile to separate
a-, q into two parts, one of which, a?
, , is 360° and the
other a ?7 , is the remainder. Let
al9
= a21
+ a22 C34)
where
a21
= 360 (35)
and
a22
= a19 " 360, ^ 36 ^
In similar fashion, denote the number of days from the
reference t to the time t to be D.d where D is a wholeo
number of days since 0000 Nov 29, 1971, and d a fractional
part. That is
t - tQ
= D.d (37)
Then it is obvious that the product of the angular rate times
the time yields an angle modulo 360° which can be expressed
27
as follows
:
al9
(t - tQ
) = (360 + a22
)(D + d) (38)
= 360D + a22
(D + d) + 360d (39)
= a22
(D + d) + 360d (40)
= a22
(D.d) + 360d (41)
Substituting this result and (37) into (33) yields
GHA = alg
+ a22
(D.d) + 360d - a12
[X(D.d) + a14 ] (42)
The constants a and 6, precession in right ascension and
declination, for a particular star are obtained using the
formulas on page 39 in "Supplement," except that the values
of the constants have been taken for epoch 1975 from the
American Ephemeris and Nautical Almanac [Ref. 10]. Conver-
sion to degrees per day is
" =3600 x 36S. 24219418 [ 4 6.1060 20.0404 sin a' tan «•] (43)
«=
3600 x 36 5.24219 418 [20.0404 cos «] (44)
This now completes the derivation for the Greenwich
Hour Angle of a star at time t.
Turning attention to the derivation of declination, it
is noted that the derivation is similar to those just
carried out. Declination of a star changes because of
precession and parallax. Letting <5 be the apparent
28
declination at time t, 6' be the true declination at some
specified time, 6 be the rate of precession of this star
in declination, A6 be the correction to declination for
aberration, the result is
6(t) 6'(t1
) + 5(t - tx
) + A6(t) (45)
where t-. is the reference time of which the true right
ascension and declination are known. The numerical value
of 6 is given in (44) . This form is converted to the
standard reference time t by the same method which haso
been used above. The result is
«(t) = <5'(t ) + <5(t - tQ
) * A6(t) (46)
where
<5'(t) = 6'(tx
) - 6(t1
- tQ ) (47)
From pages 47 and 48 in "Supplement" the time behavior of
the correction for aberration is
A6 = -k(sin e. cos 6' - cos e, sin a' sin <5,') cos A
-k cos a,' sin 6,' sin A (48)
= a n c cos A + a, , sin A (49)lb lo
where
a, j-=
vft'nQ (sin £,' cos 61 - cos a' sin al sin 61) (50)
20.47i ' • * i /r-na
16=
3TDT"C0S a
l31n 6
1(5i)
29
The constants a..5
and a _, are in degrees. Simplifying further
A6 = a, 7 sin (A + tan"1 -^) (52)
17 al6
where
a1?
= yla16
2+ a
152
(53)
Substituting (52) and (28) into (46),
6(t) - 6'(t ) + 6(D.d) + a1?
sin[X(t - tQ
) + a2Q ] (54)
where
a20 = X
o+ tan_1
^ft55 ^
and
t - t = D.d (56)o
The final equations of importance which lead to GHA and
declination are (42) and (54) . Note that eight star-
particular constants are involved in these two equations,
plus A, a constant which appears in all calculations of
GHA and declination of the stars.
The equations involving reference times have been set
up in such a way as to maximize freedom in their selection.
Reference time t was selected to be 0000 Nov 29, 1971, too
facilitate the calculation of time in days with a minimum
number of entries as suggested by Ref. 8.
30
The reference time t, is any convenient time, presumably
in the recent past, at which the GHA of Aries is precisely
given in some reference tabulation. The time t-. is referenced
to true right ascension and declination as listed in some
reference almanac. The true right ascension and declination
at cx'(t,) and 6 ' (t, ) can be obtained from the apparent
values a(t,) and 6(t,) by setting t = t.. in equations (8)
and (45) and solving for a' and 6'.
The reference time t, is also the time, again in the
recent past, at which obliquity e, , a' 6' and A, are
accurately known. The reference time for A, is such that
the accuracy of the sun's mean longitude is known from some
almanac data. It will minimize the errors due to (a) eccen-
tricity of the earth's orbit, and (b) the leap year cycle,
if t-, is chosen at or near the time of earth perihelion,
in the midpoint of a leap year cycle.
It should be noted that t.. for the known value of GHA
of Aries may be different from the t-. for the known values
of true right ascension and declination. Likewise t-, may
be yet another time for the known sun's mean longitude.
Since all the values (constants) associated with t-, are
retarded to t no difference in t, is objectionable,o 1 J
B. IMPLEMENTATION
The program presented in Appendix A is the result of
several conversions. The first conversion consisted of
taking algorithms expressed in Ref. 8 with the HP-65
31
programs to produce a debugged FORTRAN IV program. The
HP-65 programs deal with degrees as a unit of angular measure
vice radians. A conversion of all data from degrees to
radians was made for use in the FORTRAN IV and BASIC pro-
grams. General routines 0010 and 0020 provide for I/O
conversion of radians to degrees, and hours, minutes, and
seconds to hours (and vice versa) . These conversions were
needed for ease of data entry and data output.
The HP-65 programs are compact due to the limited
number of registers used for intermediate storage. This
efficiency of memory was carried through to the FORTRAN IV
programs and then to the BASIC programs for the routines
that determine the GHA and declination of the star and the
subroutine that determines the azimuth (Zn) and distance
(subroutine 0300 and 0400, respectively). It was felt that
this level of efficiency need not be continued in the
remainder of the program due to the need for self-documentation
FORTRAN IV was selected as the intermediate step in the
conversion due to the amount of core memory allocated to
the FORTRAN compiler. The BASIC interpreter is limited in
memory on the IBM 360 installation and would not hold the
completed BASIC program.
The reduced precision of the FORTRAN IV version of the
program (as it was not programmed in double precision) was
attributable to the internal formatting of the variables.
High precision was not of great concern at this stage of
development.
32
As the goal of this process was to provide a program
that would implement the algorithms necessary to complete
a celestial fix on a microprocessor, the FORTRAN IV version
was converted to BASIC. The BASIC program allows for much
greater precision in computation as the values are expressed
in 32 bit floating point, when interpreted by the available
BASIC interpreter in the Microcomputer Laboratory at the
Naval Postgraduate School. The BASIC interpreter at the
W. C. Church Center was not of sufficient size to run the
entire program. Therefore, the main subroutines and all
required support routines were run and debugged separately,
and required information was transferred manually from rou-
tine to routine. Because the BASIC language does not pro-
vide for scopal variables and due to the limited types of
identifiers available much of the self-documentation of the
FORTRAN IV program was lost. Table I correlates variables
in subroutine 0100 in the program listing (Appendix A) to
those variables previously discussed during the theory
presentation.
Subroutine 0100 computes the eight constants associated
with a star and places them in array C (elements C(2)-C(9)).
Element C(l) is the rate of increase of the mean sun longi-
tude (common to all stars)
.
In order to organize the variables as much as possible
a scheme was invoked as explained below. Since there were
a number of subroutines in the program, a method of passing
variables was constructed. The variables R1-R9 and P1-P9
33
TABLE I
Identifier Correlation of Variables in Subroutine
0100 and Equation Variables
Subroutine Variable
C(l
C(2
C(3
C(4
C(5
C(6
C(7
C(8
C(9
13
14
15
16
17
19
JO
Jl
C5
Equation Variable
20
17
<5'(t )^ o y
22
12
L
18
14
9
a
19
10
11
15
a16
34
are passing variables. Variables used in three or more
non-general routines were considered as global and were
selected to be as self-documenting as possible. For example,
the two constants for each star are placed in the array
S(X,X) . The constants used by routine 0300 to determine
GHA and declination which are created from the S array are
placed in the C vector. All other constants were repre-
sented by the format C1-C9.
Several routines use intermediate variables while calcu-
lating the object variables. These variables are repre-
sented by 11-19, J1-J9 and M1-M9. All logical values are
represented by L1-L9. Note that this scheme was invoked
to eliminate problems created by not having scopal varia-
bles. This must be considered in the selection of a
language for other peripherals used in the system. Points
to be considered in selecting a final programming language
for such a system and the peripherals attached to it are
discussed in Section VII.
35
VI. THE INFORMATION DISTRIBUTION SYSTEM
A. OBJECTIVES
This subject will primarily be concerned with the
integration of a general purpose computer into the existing
shipboard information flow. The "system" in the spotlight
is the navigation suite aboard U.S. Navy ships. The phil-
osophy for this approach is simple and is best stated by
Joseph Weir [Ref . 1]
:
"Good systems can be designed only in the presence ofpotential users and applications. By using the systemin numerous applications and assiduously watching itsperformance, it gradually can be adopted to the (actual)needs of the application and the user. Ingenious ivorytower solutions frequently do not work or they solveproblems that don't exist."
A close examination of this statement while relating
it to the navigation suites will show that in fact the
"system" has been designed both as far as it need and can
be with the existing equipment. Note that the "system"
comprises geographically dispersed equipment and telephones
for communication links.
The application and needs of the navigation system have
been defined as will be discussed later in this section. If
all this is true then why rock the boat by imposing a
system, apparently complex, on an existing "system"?
Discussion with crewmen aboard the USS Hancock indi-
cated that tiie existing system is cumbersome, subject to
human frailties and is not timely enough for the devices
36
on board. OMEGA radio navigation sets are capable of
providing information for navigational fixes every few
seconds, yet this information is only used hourly. In
this case the communication link is the "weak" link, and
to eliminate this weak link an information distribution
system must be imposed. The distribution system must
appear translucent and straightforward to the user, for as
Weir mentions
,
"The more complex the system, the more likely it isthat it won't get used or will be misunderstood ormisused." [Ref. 1]
All systems have sensors and effectors, and some
communication constraints placed on them. Although most
of these sensors for the navigation system in fact exist,
there are always new devices being created.
For example, ten years ago operational OMEGA navigation
sets did not exist. If a system had been created and imple-
mented on the ships at that time without forethought with
regard to new devices, then the information system would
not have been able to integrate the new device into the
network.
In order to fully utilize an information distribution
system there must be "terminals" with which to input informa-
tion and query the system. For example, suppose the bridge
wants to know the average RPM of the four propulsion shafts.
Engineering would have a terminal (either automated or manual)
that would accept certain required data, e.g., tachometer
inputs, transform it into its varied forms and relay the
37
data to the central processor. The processor would then
transfer the required information to the terminal at the
bridge
.
B. DESIGN PHILOSOPHY
The question might be asked, "Why try to integrate an
information distribution system with the existing periph-
erals?" The answer should be obvious- -cost of implementa-
tion. Existing equipment must be fully exploited until
it is not wise to continue using it.
By integrating existing equipment into a network instead
of creating all of the component parts of the system anew,
the cost of research and development of all the new sensors
and effectors in the system can be elided [Ref. 2]. Of
course, the use of current equipment will demand the design
of interfacing equipment such as analog to digital converters,
digital to analog converters, fault sensing networks, etc.
However, the cost of these units should be relatively inex-
pensive when compared to the redesign of any one sensor or
effector in the system. The application of the same item
(A/D or D/A, etc.) to many peripherals is a cost savings
when design efforts are considered.
As distribution of existing data is the concern of the
central system and since there is a multiplicity of like
data, the question of which source's information should be
distributed must be handled. A rather trite answer is
"the best." Again a question, "Which sensor is providing
'the best' information?"
38
A definition of the term "best" is recursive and must
include words like timeliness, accuracy and statistical
validity. As each sensor in the system is operating at
pre-system design rates, some periodic (auto track LORAN C)
and others at non-periodic rates (celestial sightings)
,
timeliness takes on a meaning associated with the quality
of the source. For example, if the only peripheral capable
of input to the system is the celestial navigation unit,
an output of ship's position would only be considered timely
if the last celestial position had been updated with inputs
from the "best" heading and speed information to provide an
estimate of the current position.
The word "accuracy" when associated with "best" means
most accurate on a timely basis. A position based on a
ten-hour old OMEGA position is usually not as accurate as
a five-minute old celestial position.
This is all well and good, yet how are these descriptors
compiled? A central machine is obviously the device that
will have to provide the software to meet problems based
on statistical properties.
Statistical properties of each measuring device must
be taken into account. The proper error probabilities must
be applied to each input; then based on the result of the
combined statistics, the "best" source is selected to repre-
sent that class of input. It is this source's information
(corrected for time) that must be distributed.
39
Along with statistical constraints imposed on the data,
a status check must also be imposed on the device. If
the data is apparently correct yet the device has failed,
then the data is obviously of no use. The status determina-
tion system must be as nearly fail-safe as possible. Since
this paper is proposing a centralized star network vice a
fully connected or ring network [Ref . 2] , all the status
checks must be initiated at the central computer (see
Figure 6). In order to design a fail _ safe status monitor,
the following considerations must be employed:
1. Notice of failure of the central computer must be
distributed to all peripheral stations.
2. Failure of each peripheral must affect only that
peripheral and, at worst, place the system in a degraded
mode
.
3. Status of selected peripherals might have to be
recorded for legal records.
4. Failure of the peripheral must not cause failure
of the status check mechanism.
There are several reasons for designing an information
distribution system. Many operations aboard a ship are
dependent on the same source of information. For example,
the Combat Information Center and radar stations need true
course and speed information. These are parallel operations
and their information must be based on the same source. A
distribution system would be the answer to this problem.
40
All of the discussion thus far has been about distribution
of information gathered from sensors, so where is all this
fine information used? An example may best describe the
answer. Suppose the navigator updates the current ship's
position with the celestial navigation computer. If the
Captain desires to proceed to a desired point, the point
could be placed into the system and the system would pro-
vide proper steering information (great circle steering)
to the Helmsman, or this data could be transmitted to an
auto-pilot upon request.
42
VII. LANGUAGE SELECTION
The subject of language selection is placed at this
point in the paper due to its applicability to both the
celestial navigation microcomputer and an information
distribution system as described within. The considerations
in selecting a programming language for these two devices
have much in common, the most important of which is the
microprocessor
.
There are two main considerations in selecting a pro-
gramming language for a microcomputer. The first and most
important consideration is that of efficiency; efficiency of
both memory utilization and program execution speed. The
second point concerns the cosmetics of the language (i.e.,
is the language easy to read and is it self -documenting?)
.
In consideration of the first property, that of
efficiency, the language must be chosen in the light of
cost/availability of volatile memory. Even though the
addressing schemes of some microprocessors provide for
large memories there may be physical and/or cost limita-
tions placed on the microcomputer design that make very
efficient use of the available memory imperative. For
peripherals operating with unmodifiable code the number of
memory locations can be optimized and placed with a high
degree of efficiency. For processors using programs which
have subroutines with arrays of data created during the
43
execution of the program, the placing of these arrays
on a metal mask chip or fixing and reserving the addresses
of these arrays is an inefficient use of memory.
The best way to program in an efficient manner is to
use block structured programming techniques utilizing
"scopal" variables. Block structured languages like Algol
60 and PLM [Ref. 12] allow for scopal variables to include
arrays which provide for efficient use of random access
memory and reduce the amount of programmable/read only
memory. By creating arrays as needed, common random
access memory may be used very efficiently allowing for
lower investment in space and cost.
The second area of concern, that of cosmetics, is a
growing concern with all languages. It may be a seemingly
unimportant aspect until the prospects of non-volatile
runtime modifiable LSI memories (e.g., ferroelectric
memories [Ref. 15]), multiplicity of similarly constructed
peripherals and common maintenance support are considered.
The celestial navigation microcomputer program bases
all of the calculations for geographical positioning
of the body constants which vary from year to year.
In order for the device to enjoy extended longevity,
the constants must be alterable. The language must
allow for the documentation to help provide this support.
An assembler program is not a self-documenting
program no matter how efficient it is. Its logic and
44
meaning are often forgotten with the loss of the programmer.
Indeed, the programmer may lose the logic to his own program
if he has been away from it for a length of time. For
example, the statement below is obvious in its intent:
NO$YEARS = NO$DAYS / 365.
Yet even though the next statement provides for the same
efficiency of calculation it does not connote as clear a
meaning
:
LIT DAYS; LIT 365; DIV; LIT YRS ; STO; .....
The assembler language form of this statement loses the
easily conceived meaning of the first statement.
Though the celestial fix program in Appendix A was
written in the BASIC language due to the precision attainable
through its use, the program itself would not be under-
standable without the comment statements and extra
documentation.
Specifically, there are primarily two high level
languages available to the microprocessor programmer;
BASIC as implemented at the Naval Postgraduate School and
PLM. BASIC, as the name implies, provides for the basic
needs of a programmer. BASIC has subroutines, iterative
and logical capability, the full range of mathematical
manipulators and limited I/O. A quick glance at the program
in Appendix A provides the evidence of a major drawback:
lack of variable scope and identifiers. There are no local
45
variables; all variables are global. This property coupled
with the limited identifier schemes causes a programmer of
a large program to run out of variables quickly. His atten-
tion is turned to efficient use of identifiers instead
of efficient programming techniques.
PLM, on the other hand, provides for scopal variables
and identifiers that allow for self-documentation. The
following statements are equivalent; however, the second
connotes more meaning:
LET Jl = G(Q) - G(R)
DIFF = GHA1 - GHA2.
The array used in the determination of the three
intersections used to calculate the fix (subroutine 0600 . .
.
ARRAY V(6,6)) is a temporary array. In BASIC the array is
permanently allocated space. Using PLM and scopal variables
the array would be created by the program during execution
(indeed, could be of variable size) and be destroyed or
written over upon exit from the subroutine. There are a
few drawbacks with the use of PLM. The primary drawback
in the execution of the program in Appendix A is the word
size. Sixteen bits do not provide the accuracy needed for
the celestial navigation problem. Though this problem can
be solved, it is not easily solved.
Special mathematical routines like trigonometric func-
tions are not available in PLM, yet they can be programmed.
The point is that PLM can be tailored to the needs of the
46
programmer with a little extra work while the BASIC language
cannot be tailored to the user at all. PLM provides a
much more versatile language yet the detail required in
programming is greater than that of BASIC.
A final comment on the selection of a language deals
with the multiplicity of processors on an information
distribution system. If each processor were programmed at
a different level with a different language the maintenance
and design problems would be horrible. For example, suppose
one processor is to provide a second processor information.
If the first processor is programmed in BASIC then it would
probably transmit its data in 32 bit floating point form.
The second processor (programmed in PLM) would have to have
an I/O routine to convert that processed data to a local
format. If there were a third language then the PLM-
programmed processor may need yet another I/O processing
routine. This situation is the grounds for selection of a
single programming language for a system of microprocessors.
47
VIII. CONCLUSIONS
Currently, the proposed computer is capable of developing
a navigational fix (without use of the Nautical Almanac and
H.O. Publications) utilizing only the 57 navigational stars.
Because of this limitation it is obvious that numerous and
known applications are yet to be incorporated. Among these
include methods which employ the attributes of the sun, moon
and planets so that positioning with these bodies can be
performed. Considering functional aspects for future
development of programs, suggested programs are closest
point of approach (CPA),great circle calculations, star
location utilizing estimated altitude and azimuth and fix
triangulation routines.
The sun, moon and planets present special problems
because of their proximity to earth. They do not appear
fixed in the sky as do stars. Stars do move across the
sky due to the earth's rotation but their great distances
impart a constant relationship to their neighboring stars.
The planets and moon, being closer to earth, possess no
fixed relation in the evening sky with the stars.
The size of the sun and moon requires a special con-
sideration termed semi-diameter. More accurate sight reduc-
tions can be performed by aiming the sextant at the upper
and lower limb of these bodies; corrections for the radius
of the body can be programmed.
48
For lunar observations horizontal parallax is a
parameter required to be considered. It is the apparent
difference in the position of a body when viewed from two
different locations. Horizontal parallax is significant
for the moon because it is the closest body to earth.
The celestial lines of position are included to give
the navigator the option of plotting LOP ' s . This method
should provide the navigator with an azimuth, a distance
and a toward/away indication in reference to the assumed
position of the observer with which the LOP should be
plotted. This is the backup routine to the fix calculation
algorithm.
The proposed celestial navigation computer was used as
a vehicle for the approach to a design of a dedicated micro-
computer. Other devices of similar construction used as
peripherals in the information distribution system would be
approached in the same manner. Approaching the design of
each device on its own merits will allow for the system to
grow in a manner that "fits'* the situation, i.e., a single
"ivory tower" system would not result.
Indeed, the development of the central processor
(assuming enough ports are planned for) would grow with the
system as each new unit would simply add length to the polling
routines and interrupt structures. Following along with
Weir's natural growth concept, each processor's programs
would be designed and built (or at least the algorithms be
provided for) as needed by cognizant individuals, from
49
current literature, as done in the case of the celestial
navigation computer. The only restraint placed on the
design/designer would be that of language and interface
specifications. As delineated earlier, the authors believe
that of the two languages examined PLM would be the most
efficient language and would provide for much needed
self- documentation.
The central processor in the information distribution
system may very well be a minicomputer or a microcomputer
depending on its functions. It need only be a distribution
device designed along the same lines as the peripherals
it supports. The level of computation provided by the
central processor must be established early in the design
phase because the peripherals would need to "take up the
slack" for the computational capabilities not provided by
the central processor. For example, the averaging of the
revolutions per minute may be accomplished at the peripheral
(which is recommended) or at the central processor on the
request of the inquirer. Again, keeping this device
simple (only the necessary switching and monitoring routines)
will provide for more independence and faster information
transfer
.
50
APPENDIX A
CELESTIAL FIX PROGRAM LISTING
LO
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51
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52
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69
APPENDIX B SAMPLE PROGRAM RUN
ENTER DAY20
ENTER MONTH6
ENTER YEAR75
ENTER ALTITJDE (FT MSL)60
EMTER COURSE (D.MS)270
ENTER SPEED (KNOTS TRUE)5
ENTER ASSUMED LAT (N/S) +/-(D.MS)40
ENTER ASSUMED LONG(E/W) +/-(D.MS)15.2224
ENTER NUMBER OF BODIES THIS FIX3
ENTER STAR/B3DY NUMBER1
ENTER GMT 3 = OBS (H.MS).56
GMT (HRS)= .9444+3ENTER HS (D.MS)37.04
ENTER IC (D.MS)
HA= 36.5709GHA OF BODr= 230.043'DEC OF BODY ( D.MMSS)ZN OF BODY (D.MMSS)DISTANCE TOWARD BODY (NM)BASED ON H: (D.MMSS)
28.572883.42 3 1
8.?5D7136.4854
E^TE46
ENTE1
GMTENTE48.
ENTE
HA =
GHADECZNDISTBASE
R STAR/33DY NUMBER
R GMT DF OBS (H.MS)
(HRS)= 1
R HS (D.MS)39R IC (D.MS)
48.3209OF RODf= 19.1425OF BODY (D.MMSS)F BODY (D.MMSS)ANCE TOWARD BDDY (NM)D ON HC (D.MMSS)
12.3+36237.46 230.930349.D3D3
EMT40
ENT1 .
GMTENT42
ENT
HA =GHADECZNDISBAS
ER STAR/BODY NUMBER
ER GMT 3- OBS (H.MS)04(HRS) 1.07778
ER HS (D.MS).11ER IC (D.MS)
42.0409OF BODY= 61.123'+OF BDDY ( D.MMSS)
OF BODY ( D.MMSS )
TANCl I DWARD BODY ( MM
)
ED ON HZ ( D.MMSS)
74.1533339„ 15314. 4 + 8341.4942
70
ENTER SHOT DF DESIRED FIX TIME2
CORRECTED DISTANCE TOWARD BODY 1
7.92129BASED ON CORRECTED HO (D.MMSS)36.4834
CORRECTED DISTANCE TOWARD 30DY 2-30.9003BASED ON CORRECTED HO (D.MMSS)49.0303
CORRECTED DISTANCE TOWARD BODY 314.3302
BASED ON CORRECTED HO (D.MMSS)42.0402
FIX (LAT/LONG D.MMSS)=40.3313 15.3354
TIME OF FIX ( ,DAY) =
PROGRAM COMPLETE. 3 41 S 5 66
71
BIBLIOGRAPHY
1. Weir, Joseph, Interactive Information Systems , BellTelephone Laboratories . Hayden Book Co., Inc. , RochellePark, New Jersey, 1974.
2. Peebles, Richard W. , "Design Considerations for DistributedData Access Systems," Technical Report, University ofPennsylvania
.
3. Electronics , "C-LAD Steers Ship by Computer," April 18,1974, p. 31.
4. Electronics , "Low Cost LORAN, Transit Developed,"Sept. 11, 1972, p. 32.
5. Rudnick, Steve, "Microprocessors Unmasked," DigitalDesign, June 1974, Benwill Publishing Corp.
6. Wolf, Helmut F., "Microcomputers-Revolution or Evolution,"Digital Design , June 1974, Benwill Publishing Corp.
7. Dejka, W. J., "Navy Opportunities for Microcomputers,"Nav Sea Journal , Jan 1975, Published by Naval SeaSystems Command.
8. Nuese, Carl and Schneider, Dr. Alan, "Celestial NavigationUsing a Hand-held Programmable Calculator," NELC TechnicalNote 2873, 22 Jan 1975 (A tentative and unpublished report)
9. Fox, E. J.s"Proceedings of the Symposium on Computer
Communications Networks and Teletraf fic , " PolytechnicInstitute of Brooklyn, C. R. 1972.
10. The American Ephemeris and Nautical Almanac publishedannually in Washington by the Naval Observatory and inLondon by Her Majesty's Nautical Almanac Office under thetitle The Astronomical Ephemeris , viii, 568 pages.
11
.
Explanatory Supplement to the Astronomical Ephemerisprepared jointly by the Nautical Almanac Offices of th
e
United Kingdom and the United States of America.
12. Intel Corporation, "A Guide to PLM Programming," Rev. 1,Santa Clara, CA, 1973.
13. The Nautical Almanac published annually in Washingtonby the United States Naval Observatory and in Londonby Her Majesty's Stationery Office, xxxvi, A4 , 276 pages.
72
14. Fricke, W. , and Lederle, T., Apparent Places cfFundamental Stars 1975, Heidelberg, AstronomischesRechen- Institut , 1973, xiiv, 510 pages.
15. Digital Design , Dec 1974, Benwill Publishing Corp.,p. 8.
73
INITIAL DISTRIBUTION LIST
No. Copies
1. Defense Documentation Center 2
Cameron StationAlexandria, Virginia 22314
2. Library, Code 0212 2
Naval Postgraduate SchoolMonterey, California 93940
3. Chairman, Computer Science Group, Code 72 1
Naval Postgraduate SchoolMonterey, California 93940
4. Asst Professor V. M. Powers, Code 72 Pw 3
Computer Science GroupNaval Postgraduate SchoolMonterey, California 93940
5. Asst Professor G. A. Kildall, Code 72 Kd 1
Computer Science GroupNaval Postgraduate SchoolMonterey, California 93940
6. LTJG G. M. Raetz, Code 72 Rz 1
Computer Science GroupNaval Postgraduate SchoolMonterey, California 93940
7. LT Jon P. Moore, USN 1
771 Ladysmith DriveEl Cajon, California 92020
8. LT David R. Rainsberger, USN 1
113 Coman StreetClinton, Michigan 49236
74
1 4 FEB Tf• • • ~ ~ ~
2 FEB79
?U2522 U 9
24420
Thesis
M802c.2
/
161025
MooreThe design of a
celestial navigation
microcomputer with
thoughts on an integra-
ted information distri-
bution system.
T
H
14 FEB 77 JM, 12-78
ft
2 FEB 79
? U 2 5 2
2 4 4 2
161025ThesisM802 Moorec.2 The design of a
celestial navigationmicrocomputer withthoughts on an integra-ted information distri-
bution system.