NPS55-80-009

NAVAL POSTGRADUATE SCHOOL

Monterey, California

•

AN ALGORITHM FOR POSITION DETERMINATION

USING LORAN-C TRIPLETS WITH A

BASIC PROGRAM FOR THE

COMMODORE 2001 MICROCOMPUTER

by

R. H. Shudde

March 1980

Approved for public release; distribution unlimited

Prepared for:

Naval ResearchFEDDOCS , Virginia 22217D 208.1 4/2:NPS-55-80-009

DUOLEV KNOX UBRAM

NAVM. POSTGRADUATE SCHOOi

MOHIEREY. CA 93940

NAVAL POSTGRADUATE SCHOOL

MONTEREY, CALIFORNIA

Rear Admiral J,

SuperintendentJ. Ekelund Jack R. Borsting

Provost

The work reported herein was supported by the Office of Naval Research,

Fleet Acitivity Support Division, Code 230 and the Commander, Patrol Wings

Pacific as part of the Tactical Development and Evaluation Program.

Reproduction of all or part of this report is authorized.

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1. REPORT NUMBER

NPS55-80-0092. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER

4. TITLE (and Subtitle)

AN ALGORITHM FOR POSITION DETERMINATION USINGLORAN-C TRIPLETS WITH A BASIC PROGRAM FOR THECOMMODORE 2001 MICROMPUTER

5. TYPE OF REPORT & PERIOD COVEREDTechnical

6. PERFORMING ORG. REPORT NUMBER

7. AUTHORfs;

R. H. Shudde

8. CONTRACT OR GRANT NUMBERf*;

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Naval Postgraduate SchoolMonterey, Ca. 93940

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65155N,R0130,NR 128-217

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Naval Postgraduate SchoolMonterey, CA 93940

12. REPORT DATE

March 198013. NUMBER OF PAGES

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Unclassified

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Approved for public release; distribution unlimited.

17. DISTRIBUTION STATEMENT (of the abatract entered In Block 20, It different from Report)

18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse aide It neceaaary and Identify by block number)

Loran, Fixing, Geodetic Distances

Loran-C, Hyperbolic Fixing,

Navigation, Radio Positioning,Position determination, Geodetics,

20. ABSTRACT < Continue on reverae aide If neceaaary and Identity by block number)

An algorithm for position determination using Loran-C triplets and an imple-

mentation of the algorithm in the BASIC language of the Commodore 2001 micro-

computer are presented. Modifications of the geodesic direct solution and

reverse solution algorithms of P. D. Thomas are also presented; these modi-

fications eliminate all of the special positioning and quadrant determina-

tion requirements of the original algorithms.

DD FORM1 JAN 73 1473 EDITION OF 1 NOV 65 IS OBSOLETE

S/N 0102-014- 6601I

UNCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE (When Data Enlarad)

AN ALGORITHM FOR POSITION DETERMINATION

USING LORAN-C TRIPLETS WITH A

BASIC PROGRAM FOR THE

COMMODORE 2001 MICROCOMPUTER

by

R". H. Shudde

Naval Postgraduate SchoolMonterey, CA 93940

March 1980

Ztt,

The program in this report

is for use within the Navy

and is presented without

representation or warranty

of any kind.

CONTENTS

Pace

A

.

Introduction 1

B

.

Loran-C Fixing Algorithms 2

C. The Direct Solution Algorithm 10

D. The Reverse (Inverse) Solution Algorithm 12

E

.

Program Accuracy 14

F

.

References 17

Appendix: BASIC Program Listing 18

ABSTRACT

An algorithm for position determination using Loran-C trip-

lets and an implementation of the algorithm in the BASIC

language of the Commodore 2001 microcomputer are presented.

Modifications of the geodesic direct solution and reverse

solution algorithms of P. D. Thomas are also presented;

these modifications eliminate all of the special position-

ing and quadrant determination requirements of the original

algorithms.

A * Introduction

Loran-C position determination programs for the Hewlett-

Packard HP-67 programmable calculator for use aboard U. S.

Navy patrol aircraft (P-3) have been prepared and are reported

elsewhere [Ref. 1]. During the development and testing of

the HP-67 programs the need for a high accuracy program for

cross checking purposes arose. The program presented here was

developed as a refinement of the HP-67 algorithm.

The basic methodology of this program is contained in

the formulas of Paul D. Thomas [Ref. 2] for the direct and

reverse problems of oblate spheroidal geodesy. The direct

problem is to determine the latitude and longitude of a point

P2when the latitude and longitude of a point P, as well as

the azimuth and distance of P2

from P-. are known. The

reverse (or inverse) problem is to determine the distance,

forward azimuth, and backward azimuth between two points, P,

and P2

, when the latitude and longitude of both P, and P2

are known. In both problems P, and P2

are on the surface of

a spheroid. Unfortunately, Thomas 1 algorithms contain several

restrictions and numerous subcases that are too awkward to be

programmed on the HP-67. For this reason portions of these

algorithms were rewritten so as to eliminate all of the original

restrictions and subcases. These modified algorithms for the

direct and reverse problems are presented here with notations

about the modifications made.

B. Loran-C Fixing Algorithms

The principles of Loran lines of position (LOP's) and

fixing are adequately covered in Reference 3 and will not be

repeated here.

The basic Loran-C equation [Ref. 4] can be written as

T = [Ts

+ p(Ts)] - [TM

+p(TMH + [TB+ p(T

B )] + 6 (1)

where

T is the "indicated time difference" in microseconds,

TM is the distance, in microseconds, from the master

to the receiver,

Tg

is the distance, in microseconds, from the slave

to the receiver,

T„ is the distance, in microseconds, between the

master and the slave,

6 is the assigned coding delay, in microseconds,

and p(T) is the secondary phase correction, in micro-

seconds, for a surface water path of length T.

The quantity

At = [Tfi+p(T

B )] + 6

is a constant for each master/slave pair. The following

World Geodetic System 1972 (WGS 72) values have been adopted

for Loran-C navigation [Ref. 4] :

Vq = 299792458 meters/second is the velocity of

light in free space,

n = 1.000338 is the index of refraction of the

surface of the earth for standard atmosphere

and 100 kHz electromagnetic waves,

a = 6378135.000 meters is the equatorial radius

of the earth

and f = 1/298.26 is the flattening factor (1-b/a ,

where b is the polar radius) of the earth.

With these parameters the secondary phase correction for

an all seawater path has been taken to be of the form

p(T) = aQ/T + a

1+ a

2T (2)

where T is in microseconds and,

1. For T>537 ysec:

aQ

= 129.04398,

a±

= -0.40758,

and a2

= 0.00064576438.

2. For T<537 usee:

aQ

= 2.7412979,

a-L = -0.011402,

and a2

= 0.00032774624.

If one uses a spherical approximation to the earth's

surface (f = 0) , then a spherical hyperbola can be represented

by the equation [Ref. 3, page 175]

tan r = 2 cos 2a - cos 2c(3)

sin 2c cos co + £ sin 2a

where the origin of the coordinate system is at the prime

focus of the spherical hyperbola, 2c is the spherical arc

joining the foci, 2a is a constant for any one hyperbola,

and r and oo are the spherical coordinates of a point on the

hyperbola. If the base line of the coordinate system is the

arc joining the foci then w is the spherical polar angle from

the baseline to a point P on the spherical hyperbola and r is

spherical polar distance (or arc) from the prime focus to P.

Using the Loran system we take £ = +1 if the prime focus is

at a master station and we take C = -1 if the prime focus is

at a slave station.

If we take v = vQ/n to be the velocity of 100kHz

electromagnetic radiation at the earth's surface then, for a

spherical earth, we can relate the parameters in Equations 1

and 3 as follows:

2c = vTQ/a e ,

and 2a = v(Tg

- TM )/ae .

Using the spherical approximation for now, we see that 2c is

known for any Loran pair. The "indicated time delay" T is

measured by the receiver at point P, and to determine a hyper-

bolic line of position we must determine 2a, but Tc - TM

cannot be computed from Equations 1 and 2. If afiwere zero

in Equation 2, then it would be possible to determine T„ - T„s M

uniquely. As a first approximation we use the following

parameters in Equation 2:

aQ

= 0,

a±

= -0.321,

and a2

= 0.000635.

These values have been obtained by setting aQ

= and determining

4

a-, and a2

by linear regression of the T > 537 values over

the interval of 1000 < T < 8000. This approximation is quite

good (within 0.03 ys) for distances up to 10,000 microseconds

where small changes in the LOP's can cause large position

errors. At short distances the error increases from 0.05 ys at

1000 ys to 0.58 ys at 10 ys; although these errors are large for

small distances, the LOP's are not as sensitive to these

changes as they would be at large distances. These errors are

well within the 4 n.mi (24 ys) accuracy that was requested by

COMPATWINGSPAC. When this approximation is substituted into

Equation 1, we obtain

[Ts

+ ax

+ a2Ts

] - [TM + ax

+ a^] = T - At,

or

Ts

- TM = (T - At)/(1 + a2 ) (4)

and hence 2a = v ( Ts~ TM^ /'ae

is determined for use in tne

spherical approximation.

Consider a Loran-C triplet with the master stations colocated

Let E,^ and ? 2denote the azimuth angles of slave 1 (S-,) and

slave 2 (S2 ) , respectively, measured from North toward the East

from the master stations (M) (see Figure 1). Further, let a

and r be the azimuth and spherical polar arc (distance) of the

receiver (R) from M. For this geometry, Equation 3 can be

written in the form

B.tan r. = ^

, (5)1 C, cos (a - ?

•) + A-

N

Figure 1. Geometry of a Loran Triplet and a Receiver

where

Ai

=^i

sin 2ai'

B- = cos 2a. - cos 2c.,

and C. = sin 2c.

for the i Loran pair, i = 1,2. Since r, = r2

= r,

we can eliminate tan r between the two equations. The

resulting equation can be rewritten as

C cos a + S sin a = k, (6)

where

C = 6^2 cos C2

- B 9C icos

^i'

S = 6-^2 sin C2

- B2C-| sin ?,,

and K = B2A1

- B-^.

If we define p > and y by the equations

p cos y = C , (7)

and p sin y = S,

then

./FTP.P

and Y = qatn (S,C)

.

Here the function qatn(y,x) is the arctangent of y/x adjusted

for the proper quadrant according to the signs of x and y.

7

A compact form of this function is

-i yqatn(y,x) = tan

where t(z) = 1

and t ( z ) =

rgx + io t (x = 0?)

when z is true

when z is false.

+ 7it(x < 0?)

When convenient we will use the notation qatn(y/x) inter-

changeably with qatn(y,x). Now we can substitute Eq. (7) into

Eq. (6) and solve for

-1a = y ± cos (K/p)

to obtain the azimuth angle a of the two points of inter-

section of the spherical hyperbolic LOP's. Finally we can

obtain a value for r by substituting each a into either

Eq. (5) . We find that

B,r = qatn

Ci

cos (a-Cj) + At

for i = 1 or 2.

To obtain the first solution, r and a are entered into

the "direct" solution algorithm; latitude<J>

and longitude A

are the outputs.

The solution is improved using a two-variable Newton-

Raphson search for the zeroes of the functions

fi(<J>,A) f. = (ds

. - dM )/ae

- 2zi

for i = 1,2,

where d , d ,, and d are the distances from R to M,

S-,, and S„, respectively, and are computed using the

"inverse" solution algorithm. The flow of the improvement

algorithm follows:

8

(8)

2.

3.

4.

5.

6.

Input the latest approximation to the receiver latitude $

and longitude X.

Compute dM , dgl and d

2using the "inverse" solution

algorithm.

Compute TM = <3M/v and Tgi= d

si/v for i = 1,2.

Compute Tsi

- TM= (T-At). - P(Tg.) + P(TM ) and

2af

= v (Tgi -TM )/ae for i = 1,2.

Compute fi(<p,\) =

( d si-dM )/ae - 2a

ifor i = 1,2.

Compute

and

8f. fi

(<() + A(J),X) - f^^A)

£i f i<+' X +AA> - f

i( *' X) for i = 1,2.

3X AX

-4(AX = Ac}) = 10 radians is used in the BASIC program.)

7. Replace 4> by

* -[«. !f2 _ f-i

3X2 3X

J

and replace X by

X -3f„ 3f,

_ _ f i1

L2

3<j) 3<j)_

where

J =3f

x3f

23f 3f

2

8.

3(f) 3X 3X 30

Repeat from Step 1 until $ and x are stationary

C . The Direct Solution Algorithm

This direct solution algorithm is a modification of the

second order in flattening (f) algorithm given by Thomas

[Ref. 2, pp. 7-8]. Thomas' notation has been followed as

closely as possible for ease of comparison of the algorithms.

The qatn function is defined in the previous section. West

longitudes and South latitudes are negative. We are given the

point P-j^c^A-^) on the spheroid, where c^, \. are the geodetic

latitude and longitude (geographic coordinates) ; the forward

azimuth ct,2

and distance S to a second point P2

( cj)

2 , A2 ) ; and

from these we are to find the geographic coordinates $ 2 ,A 2and

the back azimuth ot2,. The given quantities are <t>, , A,, a-, 2

and S. No assumptions about the relative location of P, and P2

are required. The modified direct solution algorithm is:

81

= tan" [(1-f) tan <fr^] , M = cos 6, sin a-,2 ,

N = cos1

cos a12 , c1

= fM, c2

= f(l-M 2)/4,

D = (1 - c2 ) (1 - c

2- CjM) , P = c

2fl + (l/2) ClM]/D ,

a1

= qatn(N, sin 0.^, d = S/(aeD),

u = 2(a1-d) / W = 1-2P cos u, V = cos (u+d)

,

2 2X = c

2sin d cos d (2V -1) , Y = 2PVW sin d,

Aa = d + X - Y, Za = 2o1

- Aa,

cu-. = qatn [-M, - (N cos Aa - sin1

sin Ao)] ,

10

2 2 1/2K = (1-f) [M + (N cos Aa - sin 6

1sin Aa) ]

7,

cj) = tan [(sin 9, cos Aa + N sin Aa)/K] ,

An = qatn (sin A a sin a, ,cos 0. cos Aa - sin 6, sin Aacos a, ) ,

H = c-, (l-Cp)Aa - c-,c?

sin Aa cos £a,

AA = An - H, A 2= A

l+ AA

In addition to the introduction of the qatn function for

proper quadrant determination the following changes have been

made to the original algorithm:

is no longer computed from the equation M = cos

Since P, is no longer required to be westerly of P2 ,

a, 2 is no longer required to lie in the interval

[0, 180°]. Consequently M, which was originally

required to be positive, can be negative. With this

change 6Qwas no longer properly determined from

M = cos 8Q

.

With the elimination of 8 the determination of

a, from the equation cos a = cos 8 /sin 8 became

impossible. The following figure shows the spherical

triangle involving a and 8 .

90°-i

11

Using the " 4-parts formula" [Ref. 5, pg . 12] we can

determine a, directly from the equation

o, = qatn(cos 0, cos a,,' s ^ n t)

3. The original equation for 4>

2 ,

tan <f>

2= -(sin 6

;Lcos Aa + n sin Aa) sin a

21/(l-f)M

becomes indeterminate when a_2

= 0° or 180° since

both M and sin ct become zero simultaneously.

From the equation for a*

21 one can determine that

sin a21

= -M/[M 2 + (N cos Aa - sin 6 sin Aa) 2]

1/2#

Using this equation to eliminate sin ot in the equation

for tan 4>

2allows the M in the numerator and denominator

to cancel thus eliminating the indeterminancy in the

equation for <1>

2.

With these changes the restrictions that P, be West of P2 ,

and that if p, and P2

both have negative latitude the symmetric

positive latitude problem be solved, have been eliminated.

Also eliminated are rules for the determination of the quadrants

of a2

, and An.

D. The Reverse (Inverse) Solution Algorithm

This reverse solution algorithm is a modification of the

second order in flattening (f) algorithm given by Thomas [Ref. 2,

pp. 8-10]. Thomas 1 notation has been followed as closely as

possible for ease of comparison of the algorithms. The qatn

function is defined in Section B. West longitudes (A) and

12

South latitudes ( cj>) are negative. We are given the points

P]( 4>-w A, ) , P^^r^) on fc^e sPner °icl and are to find the

distance S between the points and the forward and back azimuths,

a._ and a2 i» Given quantities are cf>, , A-,,

<t> 2and A

2- No

assumptions about the relative location of P, and P2

are

required. The modified reverse solution algorithm is:

ei

= tan_1

[(l-f) tan 4k], i = 1,2,

6m

=(ei+

e2)/2, A0

m = (92-e

i )/2, AA = X2

- A-^

2 2 2 2AA = AA/2, H = cos A6 -sin = cos 6 - sin A6 = cos 6, cos 6~m mm m m 12L = sin

2A6m + H sin 2

AAm= sin 2 (d/2),

1-L = cos 2 (d/2), d = cos_1

(l-2L),

U = 2 sin 6m cos 2Ae

m/(1-L), V = 2 sin 2A9 m cos 2

B m/L,

X=U+V, Y=U-V, T = d/sin d, D = 4T2

,

E = 2 cos d, A = DE, B = 2D, C = T - (A-E)/2

n±

= X(A+CX), n2

= Y(B+EY) , n3

= DXY

,

Sjd = f(TX-Y)/4, 62d = f

2(n

1-n

2+n

3)/64,

S = ae(T-6

1d+6

2d) sin d, F = 2Y - E(4-x)

M = 32T - (20T-A)X - (B+4)Y,

G = fT/2 + f2M/64, Q= - (FG tan AA)/4,

13

AV =( AA + Q) / 2 '

t, = qatn(-sinA8 cos AA', cos fi sin AA_')r

t2

= qatn(cos A6 cos AA • , sin B sin AA '),

°12 = fcl

+ fc 2'a21 = fc

l " fc2

The only changes made to the original algorithm are the

computation of t, and t2

and the determination of cl and ou

as the sum and difference of t-, and t2

. Minor though these

changes may seem, they have eliminated the requirement that

P, is West of P2

and they have eliminated four cases for the

quadrant determination of ol and a21 . Quadrant determination

is still required, but it is implemented with the qatn

function; the qatn function is available on the better handheld

calculators in the form of the rectangular-to-polar function.

E. Program Accuracy

Several programs were written for the Commodore 2001

computer. One program implemented only the direct and reverse

solution algorithms presented in the previous two sections.

Initially these algorithms were validated against the long

line computations with the Clarke 1866 spheroid model presented

in Reference 2. Later the reverse solution algorithm was

compared with the WGS 72 data for 40 Loran-C pairs contained in

Reference 4 (data for the 9930 stations were not included)

.

In these comparisons the algorithm error for the baseline

distances was 0.16 meters high for the 7980W pair and 0.15

meters low for the 7980Y pair. For the remaining stations

all of the baseline errors were high, but the largest error

14

was only 0.08 meters. It should be mentioned that the Micro-

soft BASIC for the Commodore 2001 carries 10 digits of floating

point internally, but will display only a maximum of nine

digits; the baselines reported in Reference 4 are printed to

the nearest 0.0001 meters. The computed one way baseline time

plus secondary phase correction was also computed and compared

to the 40 Loran-C pairs data. In three cases the algorithm

was high by 0.01 ys, in three cases the algorithm was low by

0.01 us, and there was no error in the remaining cases.

Another program was used to generate the indicated time

delay between Loran-C pairs and test positions for a receiver.

Combining the time delay for Loran-C pairs into allowable

triplets enabled the position fixing program in the Appendix

to be evaluated. Typical results are presented in Table I.

In all cases the Commodore 2001, running at BASIC interpreter

speed required 8 seconds from entry of the time delay input to

the display of the first pair of solutions. The improvement

algorithm will improve only one user selected solution. Each

iteration requires 14.4 seconds, and each improvement is dis-

played so that the user can monitor the improvement process.

Usually the solution has stabilized after two iterations, but

occasionally a third iteration is generated. In Table I the worst

fix took six iterations for the triplet comprised of pairs 9930W

and 9930X where the radial position error is 0.91 n.mi. In fair-

ness to the algorithm it should be noted that the three stations

are 776 n.mi, 2130 n.mi, and 2514 n.mi from the receiver and

are all within 6 of azimuth as viewed from the receiver.

15

Table I

Receiver Location: 52°N, 35°W

StationPair

ComputedDelay

StationPair

ComputedDelay

7970W 32845.12 7930W 16673.77

7970X 18889.03 7930X 30899.81

9930W 16067.09 7930Z 49369.30

9930X 28012.61

TriadFirstSolution

ImprovedSolution

No.Iter

7970W/7970X

9930W/9930X

7930W/7930X

7930W/7930Z

7930X/7930Z

7930X/7970W

7930Z/9930X

52°0034°59

51°5635°21

52°0035°00

52°0035°00

52°0035 00

52°0034°59

51°5934 59

14"N,34"W

13"N,23"W

01"N,01"W

01"N,01"W

01"N,01"W

04"N,57"W

52"N,26"W

52°0034°59

51°5935°01

51°593 5°0

52°0035°00

52°0034°59

52°0034°59

51°5934°59

00".14N,59" .66W

45".25N,25" .37W

59".69N,00" .02W

00".03N,00".07W

00".00N,59".96W

00" .01N,59".96W

59" .60N58".27W

16

F. References

1. R. H. Shudde, "Position Determination with LORAN-CTriplets and the Hewlett-Packard HP-67/97 ProgrammableCalculators", Technical Report NPS-55-80-010, March1980, Naval Postgraduate School, Monterey, CA 93940.

2. Paul D. Thomas, "Spheroidal Geodesies, ReferenceSystems, and Local Geometry", SP-138, U.S. Naval Oceano-graphic Of f ice, Washington, D.C., January 1970.

3. J. A. Pierce, A. A. McKenzie, and R. H. Woodward,editors, LOBAN , M.I.T. Radiation Laboratory Series,McGraw-Hill Book Company, inc., 1948.

4. LOBAN HYPEBBOLIC LOP FOBMULAS and GENEBAL SPECIFICATIONS FOBTHE LOBAN-C (20 June 1977) were obtained from G. R.Deyoung , Acting Chief, Navigation Department, DefenseMapping Agency, Hydrographic/Topographic Center,Washington, D. C. by private communication, 5 March1980.

5. W. M. Smart, Spherical Astronomy , Fifth Edition,Cambridge University Press, 196b.

17

18

APPENDIX. BASIC Program Listing

This appendix contains the listing of the BASIC position

fixing program for the Commodore 2001. A number of the

cursor control and formatting symbols on the listing require

explanation. These symbols are given below by line number at

first occurrence.

130 Reverse field 'heart' means 'clear the screen'

130 Reverse field 'Q' means 'move cursor down*

250 Reverse field 'R' means 'turn on field reverse'

250 Reverse field '_' means 'turn off field reverse'

250 Use of the field reverse symbols highlights the 'Y' in

'YES' and the 'N' in 'NO' to prompt the user to type a

'Y' or 'N' on the keyboard. Similar highlighting is

used on lines 390, 790, 800 and 810

740 CHR$(34) generates the double quote symbol to designate

'seconds of arc'

740 The symbol between the double quotes which are between

N$(l) and N$(2) is used to designate '°', the 'degrees

of arc' symbol

910 The first symbol following the double quote means 'move

cursor up', and the next symbols each mean 'move cursor

right'

The DATA statements on lines 50001 through 50044 contain

the pertinent parameters for each Loran-C pair. The fields

contain:

18

1. The Loran-C station pair designator.

2. At, the sum of the coding delay plus one way base-

line time, including the secondary phase correction

for an all seawater path, in microseconds.

3. The master station latitude.

4. The master station longitude.

5. The slave station latitude.

6. The slave station longitude.

Negative longitudes are West longitudes. The latitudes and

longitudes appear to be in decimal form, but the actual format

is DDD.MMSSFF where

DDD designates degrees,

MM designates minutes,

SS designates seconds,

and FF designates hundredths of seconds.

19

50001 DATA 4998X .15972.23. 16.444395. -169.383128. 28. 144916. -155.53097850002 DATA 4998V 34253.18. 16.444395. -169.383128. 28.234177, -178. 17382850003 DATA 5930X 13131.38. 46.482728 -867.553771. 41.151133, -869. 58338950004 DATA 5930V. 28755.82. 46.432720. -867.553771. 46.463218. -853. 18281650005 DATA 5998X

.

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Coverage of Loran-C Systems

Station

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5930

5990

7930

7960

7970

7980

7990

8970

9930

9940

9960

9970

9990

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East Coast, Canada

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Norwegian Sea

Southeast U.S.A.

Mediterranean Sea

Great Lakes

East Coast, U.S.A.

West Coast, U.S.A.

Northeast U.S.A.

Northwest Pacific

North Pacific

26

INITIAL DISTRIBUTION LIST

NO. OF COPIES

Defense Technical Information Center 2Cameron StationAlexandria, VA 22 314

Library, Code 0212 2

Naval Postgraduate SchoolMonterey, CA 9 39 40

Library, Code 55 2

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Naval Postgraduate SchoolMonterey, CA 93940

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27

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Submarine Development Group TwoGroton, CT 06340

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Bethesda, MD 20034

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San Diego, CA 92132

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Code SA3 3

New London, CT 06 320

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Hyattsville, MD 20782

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Panama City, FL 32401

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Code 370Washington, D.C. 20361

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Naval Underwater Systems Center 1

Newport, Rhode Island 02 840

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Naval Surface Weapons Center 1Dahlgren, VA 224 4 8

Anti-Submarine Warfare Systems Project Office 1Code ASW-137Department of the NavyWashington, D.C. 20360

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Naval Amphibious BaseLittle Creek, VA 23511Attn: Code N32 and C. Cartledge

COMNAVSURFLANT 1

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VP-24 1

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29

NO. OF COPIES

Assistent Wing TAC D&E Officer 1

ASW Operations DepartmentNASCecil Field, FL 32215Attn: Code VS-24

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PROCAL-Code 18 1

Fleet Readiness OfficeNOSCSan Diego, CA 92152Attn: Jim Grant

Chief of Naval Materiel 1

MAT 8D1Department of the NavyWashington, D.C. 20360Attn: CDR Philip Harvey

LT Jan Smith 1COMCRUDESGRU TWOFPO New York, NY 09501

Dr. Thomas Burnett 1Dept. of Management ScienceOR Study GroupU.S. Naval AcademyAnnapolis, MD 21401

U. S. Naval Oceanographic Office 1

Washington, D.C. 20309Attn: Paul D. Thomas

Navigation Department 1Defense Mapping AgencyHydrographic/Topographic CenterWashington, D.C. 20315Attn: G. R. Deyoung

30

NO. OF COPIES

LT Michael D. Redshaw 1Helicopter Antisubmarine Squadron 7

FPO New York 09501

Mr. Raymond F. Fish 1

Naval Underwater Systems CenterNewport, RI 2840

LCDR R. R. Hillyer 1

Code N311Commander, Carrier Group FourFPO New York 09501

LT L. R. Erazo 1

ASWOC SIGNOELLAFPO New York 09523

LT Richard 0. White, J. 1

USS Dwight D. Eisenhower (CVN-69)FPO New York 09501

LT David E. Hebdon 1

USS John F. Kennedy (CU-6 7)

FPO New York 09501

LT M. D. Clary 1

USS PAIUTE (ATF-159)FPO New York 09501

LCDR Robert M. Hanson 1

Helasron FourNAS North IslandSan Diego, CA 92135

LT Michael D. Thomas 1

2476 Ridgecrest Ave.Orange Park, FL 32073

LT Carl E. Garrett, Jr. 1

Class 65, Dept. Head CourseSurface Warfare School, Naval BaseNewport, RI 28 40

Naval Postgraduate SchoolMonterey, CA 93940Attn: Prof. R. N. Forrest, Code 55Fo 1

Prof. R. H. Shudde, Code 55Su 200

R. J. Stampfel, Code 55

31

I 18732T2 7?96VK

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position determinationusing loran-C tripletswith a Basic programfor the Commodore 2001microcomputer.

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MINIM

3 2768 000 42899 9DUDLEY KNOX LIBRARY