kAD-A079 916 BAlTELLERCOLUMBUS LASS OH FIG 17/1IA SOFTWARE PA C'.AGE FOR ESTIMATING TIME DIFFERENC ES F OR ARTILLER--ETClU)INOV 79 L C LUDE MAN DAAG29-7 6_0_010

S

UNCLASSIFIED ERAOCOM/ASL-CB-79-S1Si NL

ASL-CR-79-0100-6 Reports Control SymbolOSD 1366

DA07991 6

A SOFTWARE PACKAGE FOR ESTIMATINGTIME DIFFERENCES FOR

ARTILLERY SOUND RANGING APPLICATIONS

NOVEMBER 1979

Prepared by

LONNIE C. LUDEMANElectrical and Computer Engineering Department

New Mexico State UniversityLas Cruces, New Mexico 88003 D D C

181 JAN 291980Under Contract DAAG29-76-D-0100 LT'1

----- Battelle Columbus Laboratories

CON ACT MONITOR: BERNARD ENGEBOS A

COD Approved for public release; distribution unlimited

US Army Electronics Research and Development Command

ATMOSPHERIC SCIENCES LABORATORYWhite Sands Missile Range, NM 88002

80 1 20 6

NOT ICES

'The findings in th is report are not to he construed as an of'-flejal Department of the A rim position. uinless so designatedhx other authoriied d0cu~ments.

The citation of' t rado niames anld nme11s of' man i fact Lirers inlthis report is not to ne construed as official (io\ eri nient inl-dorsenlent or approval of' comm iercial produIcts or sers icesreferenced herein.

Dis position

IDestorN this report Mi en it is no Iontver needed. Do rnotreturn it to the originator.

I -o

. ., o

fI

SECURIT C SIFICATION OF THIS PAGE (When Data Fntered)

READ INSTRUCTEONSBEFORE COMPLETING FORM

1. REPSL2. T GOVT ACCESSION No. 3. RECIPIENT'S CATALOG NUMBER

5. TYP OF RPORT a PERIOD COVERED

A ,OFT WA RE -PA C KAG E FO R4 ST IM AT ING T IM E "IFFERENC E S , T ech n ical e w t'FOR ARTILLERY SOUND RAgING APPLICITIONS. n.-RFORIG ORG. .

REOR NOBR

7. AUTHOR(&) 8. CONTRACT OR GRANT NUMBER(e)

Lnnie C. Ludman DAAG29-76-Dp!iO J

9. PERFORMING ORGANIZATION NAME AND ADDRESS / 10. PRO -RAM ELEMENT. PROJECT, TASKElectrical and Computer Engineering Department - UNI NNew Mexico State UniversityLas Cruces, New Mexico 88003 _

I1. CONTROLLING OFFICE NAME AND ADDRESSUS Army Electronics Research NovImmW79

and Development Command 2 UMBE-- AGESAdelphi, MD 20783 4314. MONITORING AGENCY NAME & ADDRESS(If different from Controlling Office) 15. SECURITY CLASS. (of thie report)

Atmospheric Sciences Laboratory UNCLASSIFIEDWhite Sands Missile Range , NM 8800 . lr ia. DECLASSI FICATION/DOWNGRADING

SCHEDULE

16. DISTRIBUTION STATEMENT (of thie Report)

Approved f'-r public release;, distribution unlimited jp' L..I17. DISTRIBUTION STATEMENT (of the ebstract entered In Block 20, If different from Report)

18. SUPEENARY NOTES / r

Contract Monitor: Bernard Engebos

19. KEY WORDS (Continue on reverse side If necessary and identify by bl ock mnuber)

Sound rangingTarget acquisitionSignal processingMath model

A0 AsS-R ACTr(Conttsue am rverse slob If nac..eacy =d identify, by block number)

The Fortran program entitled "Time Differences Estimator PrograV' is presentedand documented. The program will accept a given number of microphone signalseach containing a specified number of data points from a fixed data format anddetermine the time differences between signal bursts that appear within therecord length. It also gives a measure of reliability to associate with thetime differences and provides, through a least square error procedure, a con-sistent set of relative times that can be used as input data to a position -,'

D IJA731473 EDIION OF INOV 61 IS OBSOLETE i--jSECURITY CLASSIFICATION Oft THIS PAGE (IWPn Date Entered)

SECURITY CLASSIFICATION OF THIS PAGE(fte1 Da Bnterod)I20. ABSTRACT (cont)

'estimator. Results from using the program on a numbi-r of recorded signals fromC4 explosions approximately 12 km away are presented showing target locationerrors of approximately 200 meters.

SECURITY CLASSIFICATION OF THIS PAGE(UWien Data Entered)

ACKNOWLEDGEMENT

I would like to thank Bernard Engebos and Walter Miller of the U. S. Army

Atmospheric Sciences Lab for their excellent assistance during the tenure of

the contract. The work was supported through the Scientific Services Program,

Battelle Columbus Laboratories under Contract DAAG29-76-D-OlO0, Delivery Order

No. 1205.

"do

I - .' "

"i "r,

_ de

iiieia

TABLE OF CONTENTS

Page

ACKNOWLEDGEMENT .............. ................................. 1

I. INTRODUCTION .............. ................................

ii. GENERAL DESCRIPTiON TIME DIFFERENCES ESTIMATOR PRIOGRAN. ..... .......... 2

A. Initialization and Acceptance of Data ................ .2

1. Initializing2. Data File Format

3. Bringing in Data from Master File

B. Determination of Time Windows and Energies ...... ..............

1. Computation of Rough Arrival Times2. Computation of Fourier Window Starting Points

3. (UOmpujtation of Signal Energy within Fourier Window

C. Prefiltering Operation ......... ........................ 8

1. Determination of Starting Point for Noise Window2. Determination of Estimate of Noise Spectrum

3. Determination of Estimate of Signal Plus Noise Spectrum

4. Computation of Prefilter Values5. Application of Prefilter6. Application of Comb Filter for 60 HZ and Harmonics

D. Pair by Pair Correlation ........ ....................... 12

1. Positioning of Signals for Determining the Cross Correlation2. Finding the Raw Time Differences between Windowed Si.,nals

3. Determination of the Normalized Correlation Coefficient

4. Determination of the Rough Time Differences between Signals I and L

E. Determination of Least Square Time Fit .... ............... 14

I. Establishment of Weights for Least Square Time Fit2. Determination of Least Square time Fit with MIC 1 as a Reference

3. Adjustment of Time Differences4. Selection of MIC to be used as Reference5. Determination of Relative Times for the Position Estimator

F. Printing the Output .................................. 18

1. Shot Information2. Window Information3. Time Differences Information4. Met and Timing for Position Estimator

V

III. USING THE PROGRAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

IV. RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

V. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

Appendix A Time Difference Estimator Program Listing ... .......... . 31

Appendix B Subroutine RDATA Program Listing ..... ............... ... 38

Appendix C An Estimate of the Noise Power Spectral Density for a PASS Run 39

Appendix D Derivation of Weighted Least Square Solution .. ......... ... 40

Glossary of Program Variables ......... ...................... . 42

References ............ ................................ 44

vi

LIST OF FIGURES

Figure Page

1. Processing Structure of the Time Differences Estimator Program 3

2. Illustration of the Data File Format ....... ............... 5

3. Example of the Program Output Format ..... ............... ... 19

4. Results from PASS Shot Sl-D341-MB-] ...... ................ .21

5. Results from PASS Shot Sl-D341-MB-2 ...... ................ ... 22

6. Results from PASS Shot S2-D341-MB-I ...... ................ .23

7. Results from PASS Shot S2-D341-MB-2 ...... ................ ... 24

8. Results from PASS Shot S2-D341-MB-4 ...... ................ ... 25

9. Results from PASS Shot S3-D341-MB-2 ...... ................ ... 26

10. Results from PASS Shot S7-D341-MB-2 ...... ................ ... 27

LIST OF TABLES

Table Page

1. Comb Filter Frequency Bands ....... ................... . 12

2. PASS Data Shots Used in Program Testing ..... ............ .. 20

3. Miss Distances for PASS Data Examples .... ............. .. 28

vii

1. INTRODUCTION

The main problem of sound ranging is to determine the location of a tran-

sient sound source by examining tile signals received at an array of microphones.

Tile problem can be logically broken down into two main parts. First the deter-

mination of the relative arrival times of the sound at the microphones and

second, the use of this information to estimate the position. In this paper

we concentrate on the determination of relative arrival times.

In the past, the arrival times at each microphone were determined by visu-

ally selecting a point of charge, the so-called "break point", from strip chart

recorded signals [1]. Some methods used to determine these break points have

been: first inflection, first maximum after inflection and first cross over

after inflection. A comparative study of these methods is given in Dean [2].

In contrast to the break point methods, the author [3] proposed a procedure

to obtain more accurate timing information from the received microphone sig-

nals by using the correlation between signals. The method when implemented

on a digital computer would not only speed up the determination of the rela-

tive arrival times but provide more accurate results with less chance for read-

ing errors than the visual techniques.

The purpose of this paper is to document a Fortran realization of the cor-

relation technique described in [3] and present results from using field data

from the PASS [4] experiment as input. These limited results indicate that,

under a controlled experimental environment, the overall method provides reason-

ably good time differences estimates which, when used with the proper meteoro-

logical data, give good position estimates.

2

I. GENERAL DESCRIPTION OF TIME DIFFERENCES ESTIMATOR PROGRAM

The overall structure of the computer program for determining the rela-

tive time differences consists of the following basic sections: (A) Initiali-

zation and acceptance of input data, (B) a determination of the time windows

that would enclose the signal received from the source and a calculation of

the energies within the windows, (C) a prefiltering operation that would over-

come wind and extraneous noise, (D) a pair by pair correlation to determine a

rough time difference and a measure of correlation, (E) the determination of

an overall least square time fit, and (F) an outputting of re 'ts. A general

flow chart indicating processing structure is given in Figure 1, the program

listing is given in Appendix A, and each main block is described in detail in

the following sections. Each of the subheadings under the main blocks are set

apart by comment cards in the program for ease in presentation.

A. Initialization and Acceptance of Data

1. Initializing. In the initialization portion of the program there are

a number of parameters that must be specified and dimensioned. The main param-

eters are:

NMIC = Number of microphones

NL = Number of data points for each microphone

NSW = Number of points in the sliding window

NPFW = number of points in the Fourier window

The number of points in the sliding window is chosen to be approximately

the number of points in the expected signal. By examining the C4 data from

the PASS experiment, an example of which appears in Appendix C, it was seen

that signals were in the 300-375 msec length and at a sample rate of I K

samples/second this means approximately 350 samples. The number of points in

the Fourier window was selected to be 1.5 times the number in the sliding

hi

3!

,ICROPttONF SIGNALS

INITILAL.I ZV ION AND

A(:(IACCPTANCE O F lmA

SHOT INFORMATION 'N

DETERMIINAT ION

PREFILTERINGOF TIME WINDOWS

AND ENERGIES OPERATION

WINDOW INFORMATION

PAIR BY PAIR

CORRELATION

CORRELATION ROUGH TIME

COEFFICIENTS DIFFERENCESDETERMINATION

OF LEAST SQUARE

TIME FIT

METEOROLOGICAL POSITION ESTIMATOR

INFORIATION TIMESCORRECTED TIME

DIFFERENCES

Figure 1. Processing structure of the Time Differences Estimator Program

4

window to make sure that most of the signal was within the window. For the

C4 this meant approximately 500, and since the Fourier transform can be ob-

tained faster for powers of 2 by the FFT, NPFW was selected to be 512 and

NWS = 342. The data files provided by personnel from the Physical Sciences

Laboratory (PSL), Las Cruces, New Mexico, were constructed to be 1920 samples

per signal in length; therefore, NL is set equal to 1920. The following

dimension and complex cards would then be required:

DIMENSION IDAY(NMIC), IHOUR(NMIC), IMIN(NMIC), SEC(NMIC), MIC(NMIC), TIME(NMIC)

DIMENSION TAU(NMIC,NMIC), IT(NMIC), NR(NMIC), E(NMIC), RTAU(NMIC,NMIC),

CTAU(NMIC,NMIC), CAM(NMIC,NMIC)

DIMENSION SMIC(NMIC,NL,LRST(NMIC, G(NMIC,NMIC), AT(NMIC), A(NMIC,NMIC),

JC(NMIC-l), V(2)

DIMENSION CMEAS(NMIC), MCOM(ll).

CMPLEX X(2.NPW), Y(2.NPFW), WORK(2-NPFW), XX(2-NPFW), YY(2-NPFW), ZZ(2"NPFW)

2. Data file Format. The input to the program was data taken from the

PASS Experiment that had been transferred to files in the UNIVAC 1108 system by PSL

personnel. The format modified slightly to include MET data and file identi-

fication for these data files is illustrated in Figure 2. Each data file is

728 lines in length with the first eight lines containing timing and shot in-

formation while the remaining lines contain the data for each microphone. To

be more specific in the format we have the following line by line structure.

12 12 13 12 12 F6.3 r4.l 14 12

Line 1: 6 1 341 12 36 2.024 06.7 6380 09

a b c d e f g h i

a = Number of microphones

b = PASS source number

c = Day of Pass shot

d = Hour of Pass shot

e = Min of Pass shot

i5

6 17341 12 36 2.24 6.76330-

6 SOLUCI.i MII\L )kk<y P F1LE(S1-[j41-Ms--1.)1 192_0 120 2 ' 341 12 3 r, l i t6E1DE

2 1920 120 28 341 12' 36 .'07 HEADER3 1920 120 29 341 12 a .37.42

1 a210 1-10 750 341 1 :2 , 39.4 i ,1

1920 120 31 341 12 3,6 41.49 -6 1920 120 32 341 12 3,S 43.803

14 15 14 11 10 11 I 9 8 9 12 12 12 13 15

15 16 17 .14 13 11 10 11 1) 10 10 11 1. I15 15 161

14 15 16 16 14 13 12 10 9 8 10 10 12 14 13 141

MIC(27)

8 10 9 7 6 6 7 5 5 2 2 3 6 4 4 6

6 7 9 8 6 6 7 7 6 3 1 1 3 3 26 7 8 9 8 8 10 11 8 6 5 5 6 6 7 81

-

9 10 9 12 13 12 10 11 10 9 10 8 7 8 7 61

6 9 12 14 13 13 11 12 13 13 i 10 7 6 6 7MIc(28)

0 0 1 2 3 2 1 3 2 2 2 4 4 3 1 -l1-2 -1 -2 -1 0 3 2 3 3 4 4 4 4 2 1 0-1 0 0 -1 0 2 3 4 6 7 4 3 5 5 4 31

3 3 3 4 3 4 6 6 7 8 8 8 8 9 85 3 3 4 4 5 6 8 10 10 9 8 9 8 7 7

)MTIC(29)

4 3 3 0 1 0 1 -1 -1 2 3 2 2 2 4 41

3 1 0 0 -1 0 -1 -1 0 2 3 2 2 3 4 414 4 3 1 2 2 2 1 1 1 4 5 6 8 8 7

8 10 9 5 3 3 5 6 4 3 5 7 8 9 10 11110 9 7 8 10 10 8 7 7 6 7 8 11 11 13 141

* 0 :1 MIC(30)

6 t5 5 6 6 7 4 3 2 2 3 5 3 3 4

4 6 7 7 6 7 6 6 4 0 2 1 2 4 6 67 9 10 11 10 10 11 10 8 5 3 4 6 6 5 618 9 12 13 13 13 14 14 13 11 11 9 10 9 9 101

12 12 12 15 16 17 18 17 17 15 14 13 14 15 14 141 -MIC(31).I

-11 -15 -17 -18 -20 -22 -24 -27 -28 -28 -28 -32 -33 -39 -38 -37

-37 -35 -35 -32 --28 -26 -23 -20 -18 -15 -12 -9 -7 -4 -1 217 10 13 18 22 24 27 30 32 35 35 36 35 36 36 351

34 31 29 29 31 31 29 27 24 20 18 16 17 13 7 211 -1 -1 -4 -5 -5 -7 -6 -3 -2 -4 -5 -5 -3 -4 -4

* .• MIC(32).i

7 4 3 4 3 3 1 2 6 4 4 5 4 5 7 711

L 7 4 2- 2 -3 _3 1 _4 4 5 5 7 8_ 8 8 j_

Figure 2. Illustration of Data File Format

6

f = Second of Pass shot

g = Effective temperature in Deg C. for shot

h = Wind direction in MILS

i = Wind speed in KNOTS

12

Line 2: 6 SOURCE I MIKE ARRAY B FILE (SI-D341-MB-l.)a b

a = Number of microphones

b = Indication of source position, microphone array and file identi-

fication

12 14 13 12 13 12 12 F6.3

Lines 3-8: 1 1920 120 27 341 12 36 35.611

a b c d e f g h

a = Microphone index J

b = Number of values per microphone in record

c = Number of lines of data for each microphone

d = PASS microphone number: MIC(J)

e = Starting day of microphone record

f = Starting hour of microphone record

g = Starting min of microphone record

h = Starting second of microphone record

F5.0 F5.0 F5.0

Line 9: 12 14 15

a1 ai a16

ai = value of microphone 1 at time i = 1,..., 16

Line 10: ai = value of microphone 1 at time i = 17,..., 32

Line 128: ai = value of microphone 1 at time i = 1905,..., 1920

7

In a similar fashion

Lines 129-248: values of microphone 2 at times i = 1, 2,..., 1920

249-368: values of microphone 3 at times i = 1, 2,..., 1920

369-488: values of microphone 4 at times i = 1, 2,..., 1920

489-608: values of microphone 5 at times i = 1, 2,..., 1920

609-728: values of microphone 6 at times i = 1, 2,..., 1920

3. Bringing in Data from Master File. In the original version of the

program a subroutine was provided by PSL to read the data files and transfer

this information to the SMIC(J,I) indexed array. In the present version the

new subroutine RDATA(SMIC,MIC,IDAY,IHOUR,IMIN,SEC,TEMP,MILS,KNOTS) was written

to obtain a desired output format and include meteorological and other cata-

loging information. A Fortran listing of the subroutine appears in Appendix B.

To bring in the data to the program arrays simply requires the Fortran state-

ment:

CALL RDATA(SMIC,MIC,IDAY,IHOUR,IMIN,SEC,TEMP,MILS,KOTS)

The indexed arrays: SMIC, MIC, IDAY, IHOUR, IMIN, SEC are described in

the previous section and represent the values and starting time information

for each microphone signal, while the TEMP, MILS, and KNOTS are defined below.

TEMP = Effective temperature at the time of the shot in degrees Centigrade

MILS = The angle of wind in mils at the time of the shot

KNOTS = The speed of the wind at the time of the shot

B. Determination of Time Windows and Energies

In many cases the time intervals of the received signals are much larger

than the transient signal searched for and if the correlation procedure is used

on the entire length of each signal an exorbitant amount of time would be con-

sumed. Therefore, windows are established around the location of the signal

bursts. This part of the procedure consists of computing rough arrival times,

starting points for windows and the energies within the windows.

8

1. Computation of Rough Arrival Times. The rough arrival times are deter-

mined by the use of an energy detector for each signal. That is the energy

within a sliding time window (I, I+NSW) is calculated for all values of time I

equal 1 to NL-NSW. The point in time IMAX for the Jth microphone signal where

the energy is maximum is called the rough starting time LRST(J). If X(J,I)

I = 1,2,...,NL is the input to the energy detector for the Jth signal, the

running value of the energy within the Jth sliding window becomes

I+NSWE(J,I) = X SMIC 2 (J,k) I = 1,2,... ,NL-NSW

k=I

LRST(J) = value of I such that E(J,I) is maximized.

2. Computation of Fourier Window Starting Points. The starting point

NR(J) for the Jth signal Fourier window is selected by bracketing the rough

starting time on both sides by NSW/4. Care must be taken to make sure that

the beginning and ending points of the window remain within 1 and NL. This

is done by making the following assignment for NR(J).

1 if LRST(J) - NSW/4 1

NR(J) = LRST(J) - NSW/4 if I < (LRST(J)-NSW/4) NL - 3NSW/2

NL-3"NSW/2 if (LRST(J)-NSW/4) > NL - 3NSW/2

3. Computation of Signal Energy within the Fourier Window. Once NR(J)

has been determined the energy within each Fourier window can be calculated as

follows:

NR(J)+3NSW/2

E(J) = SMIC 2 (J,k)k=NR(J)

The starting point of the Fourier window and signal energy are then printed

out for each microphone.

C. Prefiltering Operation

In many cases there is noise present on the lines during the duration of

the signals. The noise could come from a wide variety of sources including

9

wind noise, sixty cycle interference, and machine related noise. To charac-

terize all these noises analytically becomes almost impossible. The program

was designed, however, to try to minimize the effects these noises would have

by prefiltering the data. This was done by using estimates of the spectrum

of the noise, and the spectrum of the signal plus noise.

1. Determination of Starting Point for Noise Window. The noise window

for each signal, selected to be before the Fourier window which contains the

signal plus noise, consists of 512 points consistent with the Fourier window

in size. By keeping the windows the same size the determination of the pre-

filter and application of the prefilter is simplified. The starting point for

the noise window for each signal was determined by

Start Point (J) = NR(J) - 512

If this was less than zero for some J then the starting point for the Jth noise

window was set equal to the first data point of that signal record. Since most

of the data records had over 500 samples, i.e. 500 msec worth of noise preced-

ing the signal, few cases of signal and noise window overlaps were reported.

2. Determination of Estimate of Noise Spectrum. For each pair of sig-

nals SMIC(I,L) and SMIC(J,L), and respective noise window starting points KXX

and KYY, a rough estimate of the noise spectrum is desired. The estimation

procedure used was that of obtaining the spectrum for each signal and simply

averaging the results. To provide a spectrum compatible in samples the FOURG

SUBROUTINE was used on each of the following signal vectors.

512 samples 512 samples

XX = [SMIC(I,KXX), SMIC(I,KXX+l),..., SMIC(I,KXX+511), 0, 0,..., 0]

YY = (SMIC(J,KYY), SMIC(J,KYY+I),..., SMIC(J,KYY+511), 0, 0,..., 0]

The addition of zeros will not alter the spectrum determined and provide the

proper frequency indices. The spectrum was then estimated by

10

Spectrum for noise = FOURG(XX) • FOURG*(XX) + FOURG(YY) FOURC*(YY)2

The noise spectrum was stored back in the real part of the complex array

YY(L), L = 1,2,..., 1024.

3. Determination of Estimate of Signal Plus Noise Spectrum. For each

pair of signals SMIC(I,L) and SMIC(J,L) and respective Fourier window starting

points NR(1) and NR(J) the following signal vectors were defined.

512 samples 512 samples

XX = [SMIC(I,NR(I)), SMIC(I,NR(I)+I),..., SMIC(I,NR(I)+511), 0, 0,..., 01

ZZ = [SMIC(J,NR(J)), SMIC(J,NR(J)+I),..... SMIC(J,NR(J)+511), 0, 0'..... 01

The signal plus noise spectrum was stored back in the real part of complex

array XX(L), L = 1,2,..., 1024.

4. Computation of Prefilter Values. The prefilter that is to be applied

to each pair of signals was selected to be of the form

H(L) = ¢s(L)/( ss(L) + n(L)) L = 1,2,..., 1024

where ss(L) and nn(L) represent the value of the energy spectrum density of

signal and noise respectively at index L. Since the ss(L) was not known the

prefilter frequency response was written in the following equivalent form

H(L) = 1 - nn(L)/( ss(L) + nn(L))

Since only the estimates of nn(L) and 4s (L) + (nn(L) are available, care

must be taken to insure that H(L) does not go negative. The program uses

Real (XX(L)) and Real (YY(L)) to represent ss(L) + nn(L) and n (L) re-

spectively and defines PRC and PRD as

PRC = REAL(YY(L))/REAL(XX(L))

PRD = REAL(XX(L))

The prefilter value ZZ(L) at frequency index L is described as follows for

L = 1,2,..., 1024.

ii

(0,0) If PRC > I

ZZ(L) = (i,1) If PRD < .001

CMPLX(H(L),H(L)) otherwise

5. Application of Prefilter. Once the prefilter values have been deter-

mined and the product of the DFT of each positioned signal is eventually put

in Y(L) L = 1,2,...,1024 tile prefiltering operation is done simply by multi-

plying each frequency component by ZZ(L) that is

ZZ(L) = CMPLX (PREF,PREF)

Y(L) = Y(L)*ZZ(L)

6. Application of Comb Filter for 60 HZ and Harmonics

The power spectral density was obtained for microphone noise signals

from the PASS experiment showing dc power, power in 60 HZ and harmonics, some

low frequency wind noise, and some unidentified interference of approximately

7.8 HZ and higher harmonics. An example appears in Appendix C. To minimize

the effects of these interferences a comb filter including a low pass filter

was applied in the frequency domain. For the 1024 point Fourier transform the

frequency indexes and corresponding analog and digital frequencies are given

by:

index digital frequency corresponding analog frequency

k (k-l).27/1024 radians (k-l).27/1024T radian/sec

Since the time T between samples is 1 msec for the PASS data the corresponding

analog frequencies are spaced 27/1.024rad/sec or .97656 HZ apart. The D.C.

component index is one. Since 60 HZ and harmonics do not fall exactly on in-

dex numbers this causes a leakage to a band of frequencies that must be con-

sidered. The apparent index given in Table 1 is determined by:

Apparent index = freq.(l.024) + 1.

The unper index band required because of symmetry of the DFT is determined by

ku = 2*NPFW + 2 - k = 1026 - k

12

TABLE 1 Comb Filter Frequency Bands

Frequency Apparent Lower Index Upper IndexIdentification Band Index Band k Band k

u

a D.C. 1 1 1

b 0+-7.8 HZ 1-8.9 2-10 1016-1024

c 60 HZ 62.44 60-65 961-966

d 120 HZ 123.88 121-126 900-905

e 180 HZ 185.32 183-188 838-843

f 140 HZ 246.76 244-249 777-782

The index information for the comb filter was given in the following data card

DATA MCOMB/I, 2, 10, 60, 65, 122, 126, 183, 188, 244, 249/

a b c d e f

The comb filter was applied by setting the values corresponding to the index

bands equal to zero in the frequency domain output of the pair by pair corre-

lation.

D. Pair by Pair Correlation

The pair by pair cross correlation R xy(L) of the windowed signals is

accomplished in the frequency domain by use of the FFT algorithm. That is

R (L) = IDFT[DFT(X(L))-DFT*(Y(L))]

xy

Since the above operation performs circular correlation it is necessary to

position the data signals X(L) and Y(L) such that the circular and linear

correlation are the same. The * means complex conjugate and is needed to

provide correlation rather than convolution.

1. Positioning of Signals for Determining the Cross Correlation. To

obtain linear convolution resulting in proper correlation, the signals SMIC(I,L)

13

and SMIC(J,L) L = 1,2,...,512 are positioned as follows

11 1 .. 2 ... 512 513 514 ... 1024

Real X(L) SMIC(I,l),SMIC(I,2),...,SMIC(I,512), 0 0 ... 0

Imag X(L) 0 0 ... 0 0 0 0

Real Y(L) 0 0 ... 0 SMIC(J,I),SMIC(J,2),...,SMIC(J,512)

Imag Y(L) 0 0 ... 0 0 0 ... 0

2. Finding the Raw Time Differences between Windowed Signals. Once the

DFr(X(L))'DFT*(Y(L)) is prefiltered and comb filtered the cross correlation

R XY(L) is obtained back in the real part of array Y(L) L=1,2,...,1024 by taking

the Inverse Fourier Transform. The Fortran statement uses a +1 to indicate in-

verse as follows.

CALL FOURG(Y,1024,+l, WORK)

A search is then performed on IReal(Y(L))I, L=1,2,...,1024 to obtain the maximum

value CMAX of the cross correlation and the time TMAX of the maximum value. Be-

cause of the positioning of the signals the raw time difference is then given by

TAU(I,J) = TMAX - NPFW - 1

3. Determination of the Normalized Correlation Coefficient. The normalized

correlation coefficient GAM(I,J) is obtained by dividing the maximum value by the

square root of the product of the energies and is given by

GAM(I,J) = CMAX/((E(J)*E(I)) **0.5)

If the signals [SMIC(I,L)] and [SMIC(J,L)] are identical in shape but of dif-

ferent amplitudes the GAM(I,J) will be equal to 1. If there shapes are signi-

ficantly different the value of GAM(I,J) will be approximately zero. In this

way the normalized correlation coefficient provides a measure of similarity of

the two signals tested.

4. Determination of the Rough Time Differences between Signals I and L.

The raw time difference represents the time difference between the signals in

the windows. To obtain the rough time differences between microphone signals

14

the raw t imc di frence TAU(I ,L) must be adjusted by the starting times of the

windows as It lows

KTAU( I ,L) = FLOAT[ IT(f)-IT(L) I + TAU(I ,L)

These r,,ugh t ilc difitv rnces TA(I,I,) I=1,2, . . .,NMIC, and L=1,I+ ,..., NMIC

are part o the intut to the least square adjustment section.

E. D)etyrminat ion of Least Square 'rime Fit

The rough time difference RTAU(I,J) and normalized correlation coefficient

GAM(t,.) 1=1,2,...,NMNI . J=l,2,...,NMIC are now used to obtain a consistent set

of time differences by using a weighted least squares procedure. Each step in

the procedure is described in the following paragraphs.

1. Establishment of Weights for Least Square Time Fit. A weight is at-

tached to each one of the rough time differences indicating a measure of relia-

bility of those estimates. The measure or weight G(l,J) assigned to RTAU(I,J)

is defined to be a function of the normalized correlation coefficient GAM(I,J).

Different functional relationships have been played with, but at present no way

of favoring one over the others has been established. The program in the present

form uses the f -lowing weighting.

G(I,J) = (GAN(I,j)) 2 if GAM(I,J) < 0.5

= (GAM(I,J))11 2 if GAM(I,J) > 0.5

This attaches slightly more influence to time difference values that have a

normalized correlation coefficient greater than 0.5 over those that have cor-

relations less than 0.5.

2. Determination of Least Square Time Fit with MIC I as a Reference.

The weights G(l,J) described above are used to define a measure of performance

e given by

NMIC NMICe = Y G(I,J) (RTAU(I,J) - (TIME(l) - TIME(J)))

2

1>J J=1

IL

15

The objective is to find the times TIME(I) 1=1,2,.. NMIC such that e is mini-

mized. A solution of this problem for G(I,J)=l is given by the Author [3] and

requires solving for n microphone signals a set of simultaneous linear equations

in n-I unknowns when a given microphone has been selected as a reference. In

Appendix C a solution for arbitrary G(I,J) with MICI as a reference is presented

resulting in the following set of simultaneous equations in t i where t. is the

relative time of arrival of the ith signal.

atl G(1,1) G(2,3) G(2,4) G(2,5) G(2,6) tI

OL G(2,3) G(2,2) G(3,4) G(3,5) G(3,6) t

_X G(2,4) G(3,4) G(3,3) G(4,5) G(4,6) t3

G(2,5) C(3,5) G(4,5) G(4,4) G(5,6) t4

6 G(2,6) G(3,6) G(4,6) G(5,6) G(6,6) t.

where

G(l,i)=-(G(l,2)+C(2,3)+G(2,4)+G(2,5)+G(2,6))

G(2,2)=-(G(I,3)+G(2,3)+G(3,4)+G(3,5)+G(3,6))

G(3,3)=-(G (i,4)+G(2,4)+G(3,4)+G(4,5)+G(4,6))

G(4,4)=-(G(1,5)+G(2,5)+G(3,5)+G(4,5)+G(5,6))

G(5,5)=-(G(1,6)+G(2,6)+G(3,6)+G(4,6)+G(5,6))

and

a 2 = - G(I,2)R(l,2)+G(2,3)R(2,3)+G(2,4)R(2,4)+G(2,5)R(2,5)+G(2,6)R(2,6)

a 3 = - G(I,3)R(I,3)-G(2,3)R(2,3)+G(3,4)R(3,4)+G(3,5)R(3,5)+G(3,6)R(3,6)

= - G(I,4)R(l,4)-G(2,4)R(2,4)-G(3,4)R(3,4)+G(4,5)R(4,5)+0(4,6)R(4,6)

a5 = - G(l,5)R(l,5)-G(2,5)R(2,5)-G(3,5)R(3,5)-G(4,5)R(4,5)+G(5,6)R(5,6)

a6 = - G(I,6)R(I,6)-G(2,6)R(2,6)-G(3,6)R(3,6)-G(4,6)R(4,6)-G(5,6)R(5,6)

with

R(I,J) = RTAU(I,J)

'1i

16

This set of equations was solved by using the (JR subroutine package from the

1108 Large Scale Systems Math Pack which is fully described in 15]. The sub-

routine is accessed with the following call

CALL CJR(A,6,5,5,6,$400,JC,V)

abcde f g h

where

' = augmented coefficient matrix

b = maximum number of columns in A

c = maximum number of rows in A

d = the number of rows in A

e = the number of columns in A

f = statement number control is returned if an overflow is detected

g = control array

h = on input V(l) is the option indicator,which to solve equations is 4,

on output V(2) contains the value of the natural log of the absolute

value of the determinant and V(l) contains the sign of the determi-

nant

On output the last column of A is the solution vector [t2,t3. . .t6] and is

called AT(2),AT(3),...,A(6). Since microphone I was defined to be the reference,

AT(l) is set equal to zero. The AT[I] represents the starting time for the

signal in the Ith window relative to the signal in window 1.

3. Adjustment of Time Differences. Using the AT vector,a raw corrected

time difference can be found by the difference of the components

TAU(I,J) = AT(I) - AT(J) 1=1,2,..., 6 I<iJ6

The least square corrected time difference in milliseconds can then be formed by

CTAU(I,J) = TAU(I,J) + FLOAT[IT(I)-IT(J)J

4. Selection of MIC to be used as reference. To select a microphone as

a reference for determining the relative times for the position estimator requires

17

a specification of a performance criterion. We would like to select the !iC

as reference that gives the best possible relative times for the position esti-

mator. Upon examining data, it was found that position estimates were sensi-

tive to the selection of a MIC reference even though a least squares precedure

had been performed on the time differences. No direct relationship was es-

tablished however and the following procedure represents a reasonable way to

select the reference with no sense of optimality implied. As the normalized

correlation coefficient is a measure of reliability of the time differences

determined, the sum of the correlation coefficients for all time differences

associated with a particular microphone represents a measure of reliability

of the time differences for that microphone. This measure was called CMEAS(l)

1=1,2,...,6 and given by

6

CMEAS(l) G C(IJ)J=lJ#I

The value K for which CMEAS(K) K=1,2,... ,6 is a maximum is called KMAX and

represents the number of the microphone to be used as a reference. In the out-

put of the times for the position estimator the reference microphone is identi-

fied by having the time 0.000.

5. Determination of Relative Times for the Position Estimator. The

position estimator USRANI[]] requires six relative arrival times and the

proper meteorological data as input to determine the position of the source.

The number (KMAX) of the microphone signal that was selected as a reference

was determined previously. To find the times relative to this microphone

could be easily accomplished by filling out the lower triangular part of the

CTAU(I,L) array with the negative of upper triangular part. In this way the

time differences with respect to each microphone appear on the rows of CTAU(I,L)

and the selection of the KMAX microphone corresponds to selecting a row.

4 ... .... ...

18

F. Printing the Output

An example of the overall program output format is given in Figure 3 and

consists of the four basic parts described below.

1. Shot Information. The header information is in reference to the data

files from the PASS experiment and gives the day, time, and position of the

shot as well as the position number, starting times and lengths (MSEC) of the

data record for the microphones recording.

2. Window Information. The window starting time in MSEC determined by

the program relative to the starting times for each microphone record are

given along with the signal energy within the window. The microphones numbered

I through 6 correspond to the normal ordering of the PASS microphone numbers.

The window signal energy and starting time could be used in an interactive

mode (not programmed at this time) to allow the operator to check if a signal

appears in the window or not.

3. Time Differences Information. The normalized correlation coefficient,

time differences in MSEC, and corrected time differences in seconds are given

for each pair of microphone signals. These results may be used to infer the

overall reliability provided by the normalized correlation coefficient and a

measure of consistency by examining the changes made in the rough time dif-

ferences RTAU(I,J) to get the corrected time differences.

4. Met and Timing for Position Estimator. The times in seconds and the

Met information that could be used as input to a position estimator are pro-

vided for interfacing purposes. The timing information appears in an array

TIMF(J) J=1,2,...,6 while the temperature, wind direction and wind speed are

labeled TEMP, MILS, and KNOTS respectively.

III. USING THE PROGRAM

The procedure given in this section will apply to the use of the program

on the WSMR UNIVAC 1108 system. Presently the program is stored under file

19

It,' I HI i ItI Y U T I 0E 1 .1 11, y~ 1 . I I1

M1111 * 1 3: 10 HI'. 1. I 'L A C IC , 30 :2 :10 Ill 3'.379 31 Lmint 2 '''' lltWS ZK'j7j 311 MI(Ws P3s :15 HNG 37.6n9? ALC

:3 I", HINS 33,483 SECI p1132): A:t 11k = 31.41L SFC

THE) WINUL''IW KrkrI(NG~C 331)PLLrl~ TO) AOO

nICL p11k 2 MIC 3 M11: 4 MIC '3 MV 6

IME I MW 2 " p1C 3 MIC 43 Mtn I L

1-5 13:) 241%6. 132227?. 21112us3. 3511O" 3W903,9.

.:11:! -r roo- Fl~ u[ 1-1L 1,1 1 OW Mp1C' (Wrf L I CIK'iIME rfilI k5U1NCCs ____1

GAMMt, 1 ') . 71 h'iill I, '7 CT,1ll(I , 2) - .014GA *n I - 5) ./0 N~ fIi 1,F 3 -122. C (AU~i 5 - -.436

h,~t7 ?''l' I I111 41 121 CTAU II, -1 -1.340R r.tiM) Il j ) 5 .0 c r) i. 0 .-1 . 1,4 :

GAMMA, i *w ./As I,,)W 4329.0 CTAUIJ±) 411 3 19GAMitMW'',! S .674 I'TAII(2,3) -455.0 Cr401 ,3: -.45,1

GAOM 1-) 703 561 INaS4) 3'tY~ CTC*I("'.4 -- 1.34'iAr'4r'4,11 .<F 7130 Rl'Tl*'2,-26-, C CfAIJn ',5i 656

FAM0-) .' 3 Rfflun-2 133.0 CTFU(2,6)--4.333Gi'sA' .- .774 R,tI ..'-,", .1) : -9 0'! 0 CTAIJ(3 4) 903GAjiA13-1 .,7W RIAUk3 ""'-201 0 CTAII' 3,5) .206ii, rTI-61 .2 RI'i'U1 6)--3377 0 CTAIII3.' 3 3 82OGiMni100 .9 1116154.5)--L298,0 £14014..)--1.30306656" +53) W5fR0m1 4.6 ) '-9 74 .0 CTfLI (4 6 )z2 9 79I,6CMMAiF .70 ISA('5,6' i16Th,0 CTAUI 0 .,6)= 1.676

T1I 11- lit,1 IN H , C Eri [F Iii FORk IP ULT TO A I 13 1110H- ELI' MATUf

rIiui) -4.319 SEIC

riMEC+4)" -2.979 SEC3

F111116)1 .000 SE1C

TI' mF r' roj t N I d It' '1 A 'l TO P0 ' Il T [ON1 IST 55 p4(0

TELMP- 3.4 trCll' C.

W II Nc 'r Il i. . r ilON 61130 MJILL'.1 r1 'i-EED 9 5140(3

Figure 3. Example of the program output format

20

name and element LCLPF.SOUNDR in both a symbolic and absolute form. The

following control statements will execute the program;

@ASG, AZ S3-D341-MB-I. Assign data file to run

@USE 12., S3-D341-MB-I Use file S3-D341-MB-l as logical unit 12

@XQT LCLPF.SOUNDR Execute program.

If the program is to be executed on another computer a duplicate of the

symbolic form of SOUNDR must be obtained and if a different data structure is

to be usea the subroutine RDATA must be rewritten. The main program and sub-

routine can then be compiled on the computer to be used.

IV. RESULTS

The program LCLPF.SOUNDR was run using various signals from the PASS ex-

periment as input. The results for the test shots given in Table 2 are shown

in Figures 4 throughl0. The times and Met data indicated in Figures 4 through

10were used in a position estimator program resulting in the Miss distances given

in Table 3.

TABLE 2. PASS Data Shots Used in Program Testing

UNIVAC 1108 IdentificationFile No. Source Day MIC Array Number

SI-D341-MB-I. 1 341 B I

SI-D341-MB-2. 1 341 B 2

S2-D341-MB-1. 2 341 B I

S2-D341-MB-2. 2 341 B 2

S2-D341-MB-4. 2 341 B 4

S3-D341-MB-2. 3 341 B 2

S7-D341-MB-2. 7 341 B 2

21

DAY> 341 i: S 1-10 T Tn 1: 1-. 56 i-los :' * o 4 SEC.thIRIL MIL AKE o rc091

MltSl 27,23,29,30.3n '32: 120 VA! IWl2/IC

I i [111 N' I HIT S I 101' zOO I MHAIl>(iJN S 10802JA

M1) >7:): 5:36, 131c 3>.AIL VC 310(M S222 :&, HkS< 39. 4C,1 301811>28): 5:36 HNSi 36.50Z SIC M I Q C 1 5:136 0822 43.49Y &I FM (0(29): 5:36 I-RS 37.78/ UCO MIU 32): 5S6 MOO 43.* 03 300

[lHE WINDO1W 3 Tm 18 [8. (Millst 2 cELO [1 TO AWWI:

310 1 MIC 2 810 3 (11ll 4 MG I 11 OI6.

303) 603 6"-10 /16 701 747

THE SIGNAL Lt"rkS, Y WI THIN EACH WINDOW

810 :1 MIh 2 810 3 Mit 4 Mt S MICt 6

3622710. 207322. 9752S13. 26270144. 11629675. i3905'643.

TE COOkoLATION, 11ME P5001 <1 HCESK(SEC 2' AND ( 008250 lt TIME D'IRIT 01MCI SECIBET[WEEN EOCM I-OlE Or MICROPHONEJ0 SIGNALS

GAM8(l,2)- .2323 =TU(i.2> -(4.0 Cl'>1)-.34OAMMA(1,3)- ~. 5 I AU (1,3, '21llL" l(>11,GAMM3(f0j4), .4/1 RTAU'A ,4)- m60.() C TA2 1,4)-3.86IGAIMA( j,E): .42 H 5:1I12.5 mp 'S 0 CISLII 00-5).>0531>1M8A(1,6)= .534 NrAL'(1.6 2>'')''0 C fliI(J,6) 3., 16GAMM(2,3I- .391 P U(2, 3) 4 ( 2'' A (121 , '3) -1 .- ;(2OMMi'iO2,4) .412 kTAtJ(.4) ">1''' 0 CIAU(2,4) -. 9n7GAMMA(2.S).= .36 R38) AT Q I. 4'Y3 >.0 C1 ' I O(25)-4. "98IIAMIA(2,6)> 41 IAU12 6)- 734.0 CiOU( 26-.31GAleM(3,4O- .4 1 FTfl(ll ).4-- '.0 01002 3.41 I '79L>OMM(3.>l- .370 kOiTAk"- -2369".0 CTAU1( 3.' 70GAMMA(3,6) .457 EIOIB 3,6)- 603' 2 CI1i(3,6)-,.34GAMM(4,5)= .42 CT)(4~ I2 AU (> 0 4,5 ) - . 022OOMMA01.60- .43'9 R108(4,6)-43' 6.0 CTAIJI4 * 9' 4.3 55GAMM015,6)= .376 R-TOU(',,' ) ''10 u 01h51,61 ,33'

IME TIMES IN SEC TO 10 U301' F Oh INFIT To A TOO] TEON ESTIMTOR

TIMI i), .000 SECIE( 2) .84 SECTim) (3)= 2.182 SEC[[MI (4)= 3.861 SECTIM) (51 5.833 SECTlML(6)= 8.2.16 SEC

THE M0T To A sE UJSED' w-, IMFUT TO [OSITIOM ESTIMAT OR

TEMP= 6.7 PEOGS C.WIND t'(I'.I lION: 6380 M1EfS

WIN' SI III 9Y KNOTS

Figure 4. Results from PASS shot Si-D341-.ME-l.

22

1AY 341: :H1')T 131 1 : , tl.::i 1 .640 srC':ef C - I M11,17 AH:. ," [:

2'': 13: I IKQ Ildt81312: 2,'.2II,0,3~l ,32 1 i.')611.1C3'l MIC

I Hi- s rA.: r I i IIMU , I rl: ,I -'0 ll I1 . 'IIIUNl- 1.1 '336

rI C( :c5', 141<S Z5,.- 22 ) i" MIL( 30 : ' H[ 3 .5 7 CM13: 25)): V:-' HR' 3 1:23 :3(" MIL '111): , 5, I3IP,'S 41. [t. "',iCMIl .1Y : [: '" lllk 3;.40t " C Mlt:(3''): 1-1.j, I5 Z 41Y'A *.{C

Till: WIN4DUW 'SAFRTIN) Tie ,' C ,*E o-LA IVU TO AbHVC

lIC I Mit 2 MC I ul 4 Cc m 8c 6

3'3 / 797 360 372 894 USA,

1W'' ILNAL LNI-:I:GY WITIl N EACH W. INDO3

MiW I HIC 2 11fc 3 M]C 4 8I3 3 MI.

203 E2q3. 49',21. 10737'72. 15422260 30297281. 1 5',b 63.

TIl I- 5115 , I 113 F1)13 flIr r IR K'MCF'; '8SCC), AND CUI ECTI-[r TIM- rIFF[MENESS1(31C)E i LIA 1 4I- 11 F'A.nI OF ,Tr'jI-'CINI:. SIGNALS

)H-2:iM,', 1 '.) ) I091,ll 1,') k' W.9.0 11601 1, -21,7

G 11.-( 1 4 ) , [ '"31 1, 1 •4 3. 0 V" TAl 1,4 3 -. 30SrrIA( , IMR AI I I -.Y)) ' 42 . L , TAII J,5) -- j .1U6,

H MMA (1 '6 - .197 U ( 1 ' /9c-0.0 CT AU1,6) 8. 14 GrpniA ( ,3) * 160 R [Tlf23) U 1308.0 CIAU(23)- . ; 16

iAfM8)F (2 , / 07 R TAU (24) -3034.0 I'12,4P -3.03368i (2 1 .306 ) i A , U ( -42 .0 (10)U2.5 -. ) 40. (2 , ..1; 2 71.1U (2,6) ')3.0 E AI (2,6 .27

'368iM ( :3?4) .4,j RIAU ( 3,4 -1733.0 C'IAU(13,4 '- 1. 11606 11,86(3 .. .496 RI AU (3, )-3740. 0 CTA(.3)-: 3.7236,"8MM (3,6) .30 I3 TAU (3-6) 6003.0 CIAU(3,6)l 6.011u .i'i.% 4, '5 '8 XS RTI AU ( 4, '5 -2007.0 C I AU (4,) -'. 007Gib&'h( 4,6) 7 7 1 F16A1 (4,6) -4302.0 C AU (4 ,5) -4. 294GAMfMA 5,6):: .O I. 1TU', 6 ":295,0 CTAUI('5.6 -2.287

11-1F ITMES IN SI-C ro 0l31 UsEtI I -Cli INFU TO A POSITION ESTIMATOR

TIrrIt ) 1 ..... W. 860 SECriI83(2) = .040 SECT IM (3) ). ' 3 SECTIME ( 4 . 007 SE:CFMl () .000 SEC

TIME (S)- 2,287 SEC

II-1 cUFT TO A BF 1111 A3 INPUT ro POSITION ESTIMATOR

TFEMF'= 5.6 DEGS C.

WIND 1IRECTION' 6380 MILSWIND SFEUI3[ 8 KNOTS

Figure 5. Results from PASS shot SI-D341-MB-2.

23

D'-. i41 : i'd F FM! 12:14 llle 7 6tt SEC

0)12 I I N 1111 .'I1 )Y It

it.: /L'.' 3.,3 [32 [20 YLUUIS/MIC

I U t11, I [C4I-, I 10 E 'S I ii I o A1 I I.-tItf lrfl

1-7 1 :1': oi;S 33,C I-v (lEC It:1 3o) I21 IR 3'./ SEE,riILIJZI : [2:12I I liztO 35.1J]9 Si; I -C r W318 12:1: Ilr s 31.4.1W SELC111 L (2) Ii 14 (1.4 H :, 4.33 1 SEE M IFc( 32) : 1u j:. -I'S 3z'9 SEC

fl-IL IJ [NOW I. A1 T ING 1IH I HO (M Er TEE 1"L I1I411 TI) ABOVE14

rIlE .1 6H1C 2 I11C 3 11IC 4 MJC 15 HIC 6

6 23 713J 73Z0 /46 779 701

111 1 kl-CIM~) WI THIH EACH WIN['OW1

rlITC I M IFCE? Ill1S 3 FilE 4 HIC :5 IL e

35537 3194, 377331. 540671. 330044. 362Y04.

Fillt, l~-L~f18 FAME .iE1< CLLlI : ANID COIIkkEC TED 1 IMF DIl LEF CLL' . EE1-fl rwil I - .51- [I'A 111 f 01 [CR01-ION. ' SIS O 511 ;(

1 1ii: 1,Q MAI j 1 ') L4 0 C1I150U ' ' .014'' I5 k' rA' IT-IJ- I ,EF- ?; AU ( 1, 3

I 1' 3 1A(I.1 ALF(I 1.4' 1399 0 Cl',(1([4)- 3',".IufI'i .k TAL -4flI . 082.0 TAU~Ijj, 1 '0,

uriNV L 16'- 71 In t1 UI -,6 4 '110 0 U: 2AIJ(1 .6' 4 . 411;L,,,Cni4 ('0 I-- .441 i;FII2 'U :?- 4t4 0 ClI th 2'3 ) -. 4'1

1 2il.',T 1/* IT.M'W .4 1 '4 '3011 -TA 1- .39',)'IHM(' k I TLl' ..- c92.0 C41 'TAU'9

',iu1.3,) 4 '1 P 1 6 6- 4-101 -1 1'1 1 T , r' -4 4(OI !" (5113 * I '8 IT114 , i -10 ?Q ) I C AU 3 - 4 0' 1

-11.1( ) . 'xt,, I. fI01') 72 20 ., ITAL) I , '.1).lA,' "Is I Si i.n ; -.6 392..O0 51514 3,, 5. -('

112185V1 s 1iT. It J)44i 130 8.0 C 'T A(.1I4 !~ . il'S)1.I1A 46- l FI 1d 4 61-5 013.0 C FA.

1( 4 g ;j 1'1?

I 'IMMA 6 I tF AUl e'. I)- . 10.4'TA (451 6 1 1 1

111 II M '., TO II TO BEL l14)1. FO LI N[ 1 IT ill i 0 Fo0 l TISM 518 CS IA LI

TFi 1.) -1i.3 , SEC1182).. - I *3134.,- SEE

1 I-lI' .000 S"E C

rim/ 3.019 512 r

0~lM,10. IlI'')HI) FlPOSIT I IN EQ ,imnA oR

TI~M)- 7.9 ['fillS c.141 HI WkI EEC IFIN' 60 M Ill-.

WI FF41',;, -111 83 KNOTS

Figure 6. Results from PASS shot S2-D341--MB-l.

24

1S 3 1t : 1it l I r6! : 1, I-WS< 1 89 1 6 LEC:0i11-A 1, Mii rE AI<NR C Ii

Mh"; 2;, 2oY1v1,: 1920 VALU- '1MI

317(I) 581, FIN5 - .':z rq57 (1((30): H:11', HIRS 3t'.371, 618:[ll"/' I NS 34.Y1.Z 5 MI~c It: ', HI'S 3.5 6' ? " I S

2 311, Hk<5 V-5. 4 13 SEC C [1.751 3- :1: li . ,5 S

111H. 141 MIUW ST FIUING lll 1 0 (f315- ITES I IVU TO AU

'11( I M I 2 M IS 3 MIS 4 M11 I C j rIE 6

t742 726 677 666 6836 6

MIC ICt MIC 3 MicS 4 M IS M IAI

4 331 6Y. ''64966. 0322272. 2 11 -2426 Z. 3'5-4 1 3 84 7. 3 4, 9 3 879.

C: R FI I N iFA1, '.I- I' 10N, II. 1111 1 1l HON SJ N I (KMC EC)- AN S'E T-1T M D F-SE C

(-)fI6(I V ~1"A1~ '1 , j .Q C.1 (.11 (1 2~ .014'.'lIMA)I I I, r iS( .i 2 0C(I1'. 1 ; .36

.''N~ir-l. (.4 61 Ig.flIJ I 1 24.0 C' 150( 1 41 1 . 340Wir -(fl M.' L 61; 5JR iI -2/'' .20 1 0 .4

t 4 *IA94/- I,'T.lIC 1 1". 0 CIAII1 pI' /1 '3]

i,'l'li( -1.^ 14 /13 kl I t AL * 4 -A3'01.0t .4 L1 3S

Mn HA C , P) I 6U (21 26' .. "56A

1--:i,.,l 175 Al1 3 9 ''1<(t4.''

Il-u I IIE' IN 5(2 11 itT 551 I CT 3! O IC '. I i Cl '1/ U IMN 101

(,AM .V3-- ) '2 FTALFI 3 - 6 ( 1 l / t.QC ~10 MA4 j YIM! 1IJ 4 L 'ELt 0

INIM6TMS( p' SEE. l,

I h. I Tf. F- I N S (- iC 1 't< I~I I- iiiDFO I C T 10(1 'ill,1 1 0'l ; IM^,0

II Ml- 4 3 3' ;LC~S

r.11 I , iM 1- 4u 610 "?i S -C

fill, ~ ~ ~ ~ ulu MSil4 db 10 11 O ','1TLN b I l t'l

Figure 7. Results from PASS shot S2-D341-MB-2.

25

',I Ii IT I i i: W , 1./6 : .1 U.

'II I( ' J I , 2Y ' I Y I I I Ii C

Ilt rT ^. i IN I I1d [1: 1 1 A1, 1 jil iii 11100. 710855OI~t : [, d I V 1('i F I ill; 1A F .3l<tl'llfl SI-1,01 01NAL, 3 1 '

tilt ) C- .it v [ I1 34.c;43 SIC M I.,Ct 1 : '7:1 1-11 b .3 7 , 1 1-_CIl . Y o t-"; i.3'u, '.lC InlaI 2 1: 9: i fS 3 9 . E C L.

III: L I L8001W S IAl I 1 V F Ii 1 5 ( M -1 : 7I ) RI I A lIE 4F Af:AVE

MIC, I lil 2 I1(; 3 M.1lC 4 MIt 5 1,1C 6

Z; /,4 762 95) 804 71 /

TIl. SIN L ENrl<iGY I.1 li I EACH w9 NltOW

IC 1I MIC 2 1It) 3 MIC 4 MIC 5 MIC 6

.'4947/0 31I 31 405041 61962710, 2551576 S t3 t 78.

TIE I siili [ON , i]Mi IfIFI 1I N1 I II 1)1 AND CORRNItTlItI fIMF EII-FI- t)E (SfCl'. 1197.i, I 1i1i I-ilk'i OF 1 1Ci 1-1P0IONI '16113 . ,-

1.i iil .i144 1I:1ALI 1 ) 4.0 TAC U(1.2AU -, . 020

iG llii' J. i ,C3) 10 Rrrti I A 4 i 1 ,3) - . 6Gtl ,i M 1 ) .4.1.0 01 1 r4(I i t4 0, .. C0 C lU I,4 -- 1 . 34YU

j[ ~ivfl' "' . 3IJ 9 _',:- I:,' F, U( < I h -. 2 2 .0 C, C TAM 1,'5) .2. 67"'1

1tii llt( [ 6 .3215 R I Al( UI,. 43,/1.0 CLAU(l 3 - . A(2i3. 1 [0 RTIlU(2,3) -41 B.0 C flAJ(2 , 3 .- ." 6

U, , IIilh, V .2 1 ... 160 I',)II 2 , 4) 1 4'YO . 0 I, I l( 2. - -1 .4/"1

G"Mtiiint2,'5 .106 RInliU(2,,) ''Il 0 C IAIJ (2, - .L II u'I' ' IT 1 " , o) lI I I V Li 2 6 4331 .0 C l(0(2,6 . .3~Li"~ M ' 3 , )

"' ;2 _ I. I AU J ,3,1 -4 1 1 0 .0 C IAoU 5, - I S 37.

3it ., .1; 2 'tIA"i(:3,4) 100 20S . 0 C TAI.5 I . 21I)'1e1ih 3-6 252 FR .r LJ( 3,6T3) - tz' .0 C ILI ,) - o.7.3

iAMMA 4,5) 37,2 RiIJl i , 114. 0 C TIAU( ,51--1 , 132t-ilMMA i4,6 .444 I (U 4, 6 -. 1414.0 CTAULI 4,6 =-2. U54

(iMi1iA (5,6i .,54 k T AU, - 1702. 0 C IAU(5.6>-1. 722

f II) I ilrIL, IN SEC. TO I.-l USI1' IOR iN'UT TO A FPOSITION ESTIMAI OR

7 1Ml ( 1) . i.'36 1 Si CT I 111 .2 . 611 SEC

IiF (31 -2.215 SECTI1i (41 1.132 SECI I I t.; .000 SECT tMtCi6i 1.722 S7C

Tlll M T 110 A DE USED AS INf'UlT 10 F'WOl ON ESTIMATOI

TtL) MlP: 0.6 DEGS C.W IN 11 I lt l' I IN 638i0 ti1_.5-

WIND' SFEErl I \NOT'S

Figure 8. Results from PASS shot S2-D341-MB-4.

26

',-LJ l.l I In I Id r I:

7 Fil I l No T 1fi 1! 1 W!R L:)CH I CkilO 'IN 1100 ]1 (00_

7TC, ''): ,M' ,:0 11k,. U6l ':, I .C i I C.(3 , 3 HP!, ,144 1 ,I-L"i1( , 0k 3" .3,51, ",. A IC MIC(3 ): 3 II'S A, mcMnIF(2 " 11 ,

, 4. 84,3 A C M1c(32); t2 3 1IS 36I2A1 SEC

TH 1 W10D.W 5TA1iN(K I I 1-:( MSLC) 1 , 1, 0 1LV1: To AItiVI.

,IC J. IlC riiC :3 M IC 4 HICS M]C 6

799 747 S824 713 709 529

ri4': I INAL lN[ GY UITH N If 1J1W WINDOW

MIC I 11IC 2 M1C 3 M.tIL 4 MIC 51 MIC 6

5,33733. 300650. 4;48.166'. .Y98839Y6. 3/22458. 259196/S.

TI1F CO I-LSO IUN. 1.[1]- FEIIIEE(NFE AND tE, FL TEIr lIMP 1')FEIIPENLL5 ;I.EP.. IW I- N 1l l I[ -HI i' 1C I 'KINE SIGN..d-S

G.) il. (1, ' 1 ) '34 kfAUli.( I ,2'- 90b.0 CTAEU( , 2 902(;^1MM .1.3) .c0D RI U(1,3) 1400.0 CA (S I ,3)- 1 401GA MMiA 1- )- . 30 R EI A1. 1,) [1423.0 CIAU(I,4)- 1 .429AM MA(I ,, ") ( . R1AIJ I ,5) 1031.0 C TAU( ,!) 1 .033

Li,01f'1M) I 16 e/ 00 ",6 ITAU(1 6 1- i1Y. 0 CTAU(1,6) . 115L IM' . o3 .526 F, IAU (2,3 . 49 .0 CIAU( 23) -199GU M A , I R ftL', 4 )- '48. 0 CfAU (2,4 ; ,26-. "1 ." ,6 ,9 , 1 AU (2,.5) 23. 0 CTU J(2, 5)

- L31

,,)I'M CSk ; ..430 RIAUt(2,6) -78o.0 CTALI (1,6 1IA)rl (3,1 1 1 RTAU(3-4* 2 2 0 CTAU(3.4) .027bA 1 .'. * D i I U(3,5) .-.. 0 Cr TAU(3, 5 366L,,Mf n 3.)3 .'32 R7A L(3,) 128 0 CTALt 3,6) ',6;AMMI(4, , . 40 RTAU(4,5) .- 39'.0 C'T0AU 4, -.39,GAMMA1( 4,6 .,36 kTAUJ(4,6>- 1302. 0 CTAL (4 ,6) 1. 313GAMMA(5,-6) .6,4 RTU(5,l N -936.0 C1AU(1,6) -. 918

THE fTIMI.S I.N SEC ff DI: USL- FOR INF'UT TO A POSITION ESrIMATOR

TIMEI(l)= 1.033 SECT I MIE (2)= .131 SEE:

TIME(3). .368 SECrt Ml (4) z .. 395 SE:

T[MI (6) .000 SECF It Mi.- ( 6 1 918 SEI_"C

THE- mi TO A PL USED AS INF'Uf TO E[sUfTION ESTIMATOR

fEH-lMP 5 .4 DE0S C.WIND [IIRFECTIUN 6180 MIL.K.;

WINI' SrEEt' 9 KNOTS

Figure 9. Results from PASS shot S3-D341-MB-2.

27

DiY 341: !I iT II MrL 6:2" lot I 1 "1- IC

o',; IIIC[ 7 MlIk: AriIA,"Y [BMl1C1: 27, B,29,30,31 , 3 19'.0 V.w11 I /JIS/MI:

iM '; IAR TI] T]NTI M1,', ON Ilfll M]I (<1101-1301: ,! NAI

110(-U( 7) : 6 2' 11R0 '4. 683 H,I-C MIi k 101 J .' Hl ,; / 0

UIC ,2'EI) 6 25 1[1i , ? 1,i21 , CC M CM I S i 6 2' 11k3, 49.0', SIECI C ( ,9 6:2'.5 HO11' I . 212 SO C 1LC3 ): 62:., HtS 41.411 0IL

IHI 1,OjU r lo NOi r t'Cil. I ik LA! V0 1 V [ u 0V[_

MIt I M ' 1 ,1 (UX C I MIC 5 MIC e

(1 .1 L 14 3/0 70, 731 2 B

fillS Ii .N L I IiSOGY WlII I iACH WINDOW

110 I MI [i MIC 3 M.[C 4 Ml I C MT C 6

]3 ( 6

61, 1 64 0 0 429, 180 1 1'53. 1266'2,; . 12637Y1U.

Tl TIMEII n l1ON 111 iii 1 05IEN E W,(M%1 C;, AND TO MI1:I'T TIM! R lk i L -I(-1C)DO SOON IACH I OF' 'Ii- I IL li-I. INON 01 ,rA

Gf~lh 11 ( . ' . :7 I:1 U([ '- xt 0 C ITAIJ( L I.? J • /4OH!! A ( , k I!AU! 1 3) '- 3'l3 0 0 c IAiJ i y ) 14.,:,Ar111,. ( I *5) .1 ' 1 1 AU (I ,3 - 41) , 0 C"F0111(1 ,1) 1.462

Githlr.i 1,41 4 1 r,511 1 ,4 4/4/.0 CTALI 1,4) ',.7;3',

1,040, ) 7 I/ At I( I f-3'.-0 0c r ( L ,, - 2. 0 3A i,5) .4,4 i lfoJ( 1'- 6 4/ 0 LI,^ (1,9 ) 6. (,yP

G (, l ,",, A 6 1(! iT iU(:1,4 '.V. 0 (TALi.,3 ) - !i1

, , 6 .i'A4' ',' 41 I A U 46 1 Y00.0 U IAl .. : .',1LTMN, iS4, , 0 ) .' 11,- I 1 0 . 0 F lu! '.. I . ',i

Vl')( ,.6 .p1 I AL 3, 6 3 599.0 I fAU 3,6)

f1.11 11ME, IH SECo TO BE Itoh Fo i INPUT11 I L A I:Wt" (IT! N I011 11 uL0

Tli !: I )- 4 7W3, ! 51C

t !MI 1 ) . Y II SECi"[MI: (3) 1 . 3.1, i SE ,C

T I M

4 .000 I,-I-]I MI , ) 1 .)'1 SI :T.1 ML 6 ! 1 .71 SiE C

l11i 0' 1 To . 01 S141 oa o i 10I'1: . i ;OSJ. ION E(FIMATOO

IFMP- ',.4 DILGS C.41 NI DIR I I 1 -ON , ;0 II]IS

W I NI l Il - 9 KNOTS

Figure 10. Results from PASS shot S7-D341-MB-2.

28

Table 3. Miss Distances for PASS Data Examples

Distance to Ratio of Miss

Fig. Miss Distance Center of Array Distance toFile No. No. (Meters) (Meters) Total Distance

SI-D341-MB-l. 4 430.0 12,678.5 .034

SI-D341-MB-2. 5 195.5 12,678.5 .015

S2-D341-MB-1. 6 176.4 11,784.8 .015

S2-D341-MB-2 7 192.8 11,784.8 .016

S2-D341-MB-4 8 1015.2 11,784.8 .086

S3-D341-MB-2. 9 395.54 11,471.9 .034

S7-D341-MB-2. 10 291.8 16,900.7 .017

29

V. CONCLUS I ONS

The present edition of the "Time Difference Estimator Program" has been

presented in the first three sections of this report and the results from its

application1 to a number of arbitrarily selected signals from the PASS experi-

ment was given in the fourth section. The results show good time duration esti-

mates, based on the concept of miss distance; however, one should realize that

with only seven samples not much can be said of the programs statistical per-

formance other than it is looking very promising.

From Table 2 and Figures 4-10 it is seen that the program satisfactorily

determined relative times such that target position could be estimated with

miss distances around two hundred meters for targets of about twelve kilometers

in range. It appears that as one would intuitively expect, correlation coef-

ficients much lower than 0.5 for the time differences, Figure 4 and Figure 8,

result in the considerable sized miss distances given in Table 2.

The application of the progxam to existing data has pointed out need for

further research into several areas in order to improve the procedure.

(1) In order to eliminate inaccurate data a threshold value for the

correlation coefficient must be determined for which the associated

time difference estimates with less than that threshold are claimed

unreliable and discarded.

(2) A procedure should be developed to assign realistic weights for use

in the least squares procedure perhaps as a function of the normalized

correlation coefficient.

(3) The overall effectiveness of the procedure should be established by

providing the variance or a bound on the variances of the time

301

di ffrenc e~tii~te. Tbis will require a theoretical development

,11ong, With an exaffination of a large amount of data for experi-

muntzil verification.

(4) Tht- program Should be altered to present a workable procedure for

handling tile mnultiple? target problem.

31

APPENDIX A

Time Differences Estimator Program Listing

L:TLI ['ii I I I:I 4'.l . I ,I [i ,(Ij, I I.l,IKIl1

* 0 Ill- ri I t Ht l ,I I 1 1111.. A I ,r4, l I I l I f"il, ]' I Il I. r I3: 24 c I- , N 1 I c r il, 1 1 1 1.,M I I (i0 t J I Ir' I I m w_ i i ,L[M I v 1t I rIrl I i ,

1 c I l .: l I* L N I l 1 1 N I i ( O N I l , I I 0 1 1 1 1 1 1 1

1 : 4F [W i I," i ) IN I I [U M A I 1 1 D I .'i, I I-. t J, , 3 W 11 1 f, 1 i T >i 0.

l I~l ,J Wt i I I I4 I 1111 I I. I W .' I II Ii i TIII

y :C

12 :c 1:1-IAM . ^Mh ) L II 11 LIII 1 PI I I5,

NIi.ir l I ll I'INlla l I]f :f'Jlil I (i l I M ;If-~in

4 ('11 ~ ~ I I Siii 1 x I Ui~ f fil I 114 IIW I VI ')I I f1

1t4iC * 1- 1 If 'Ul .[i 0ff' 41W m i ii IIC0 , L il lIY()1112,iC 1 1f 1 RNf I I II : ', ' -64e, 1 I

1 ,C

I s',C OII UF VA ,,[obL E S

21 I I 1 11: 1 LllM Il R C311 . 4I 11, 1-I 0PFI tI.-

1

2I I illI k OF I'F) 0 1 , I0 'A; Iit I MG 1 Al' 'DO

I4 :C NI.F I N 11i1,1. 1 (Fi W 1 0 1 ' ' I IN F i I l. l , uk.11-1 111A:". 3 0 J I I [L7N , ,I iiM" I 'I-IF'L 1i 1i I: L I d II C 1 J 1 I4 I II

L : C I ( ) i ^ A' I I l' 11 1L Fl O : m '' l'l' ii i A [ , J i ,: '.I L [-: 1 1 II i l l.

C I- I .J I(OlIGH [ l AI I INo I i NI I(tIF I l' I 'lk -i i' I tI TI[ I

O R: I . e I l . I 1I_. I I1 I l: I ItL L ,

-Jf 4 1 NI. 1, 1 W ITlI I I I N 1, 1I L A 11. (IN A i '1 , J f[i, 1 'IN 4611. i 1 I (l', I I I 1( I l I I-F IrI'II f:1- f . M lh ,11 ,.I D I C N 'I fJlli.II II. 'i IkI 1 [ J ) I*M(;(( I I Mi. ill] !:I 1 ,,ILf 1, 1 10 1 14 )a l 11I)N. 1£J 'lld: ; 1 "., ' .

. I , ' .IJ ) I m It, 1 li l i I I III Il li Vi T.i lii IJ I ' ,1 F01 1'H t l f'; KiI ,10]0 1 1

_I Et)l SI 0 ,14 1 1 1 4 Ii l I I (1. LI ) 1 .:t ti( 1 -1, iWL L -1. II L i I , I I ON t I. l q 11 I -I i N,,!

'I'i , I I I [l 'l Ii I tI II I ) W Ii I J L ;I l ( NON l l 1!] 1i1A; .' 11 I ) I1 l IHI: : : I_[A : I .:L 1 I.t 1 I.I L I l U l,-

r I I '41 i I I I E ,(lr'NI I II S'I ,A Ill l iT 1 iz 11 1 it,fooS i 1 I I I ^ i11 Ill I 'if ill I I I I 1 1 -'l w I...[ I I !, I 0i i

1 j" I I % 11 I 1It tll I I I 1 I -I C Ti M l I I il. i ill) il 1( I (0 ( I- l [ -, I Tli, l l 01.1; fI 1) 1 1 tU I I) l ilt I il 11 I

Y .i [0 IN I] iyi 1 ,, ,I:, IV ( 21 )l I L2 I O I I .' I U l I itU l i,

tII 1

, L I It I: M Ii A' .

I ; L I i

l 1,,'l~ 0I i'tLlk : : Cld~ -I ~ i Ii~ 'I I_ 1, - 0i. n t 1

• : :, ~ ~ ,T (IFt ( i INC,~ AN.1 D f i fil-1,10C[. FIVLIII .C ,h, Ill . I- ni', e ) I I

'U'. 1,1.1>1 III M4111' Ii(WH I l I PI I 1I4 :, ~ ~ ~~ I() J t ll',LII! I ! ll,'-! i; !N,)id_ F(J l ;'J 'lCl2 , ~ )' [01. t: Il

-1 ' f I Fi Vl I !1-l 01 1 I j.JI" ! F 1 l!<l'a /:> ,:I W UN4 00 t1'U I

-1 ','t "(I) I I W t Ui~ ll- ,I .U: ND: ',;'.N L_ F lk fClOY g ,

COW)A17 I ('I ILIj 1l,41 111

', I TH ,i A U F Jl I-:IuF L: I I JtFR T :I N{:; N I I I-1'rt+ 0 N 1311 It LTl

I.W: LJ tI , ) f I1,10 , -'I. S I L I I [1-11 D y I t! ll.,(, i; LII;(I I [N i-

X, If I( L H l VfLt Wil (11 I-,, TI m I I - 0 1- H ( I itI',i I .NtI i,{ Ik '~ : i I - i Il

YJ f( I( I I W ) LI_ l fI ; T: I li T11. III I, tlh I'4U"d NljlL:l ,; i t M UMJP

.4 : r -Z I / I~ 1.1( l 0 1 'T I{ IR' 1 01? FillH I ) 11 M IC I.1i II I I(] .)i

1'1011. 0ilY : I ifi 1 T Ill ; T. Il (! IH IA I I I I M It- I I lt O. N I <:;l 1J , )I

'.6 I I I(1 1 IN II~ l l 10 11 1 ' M I FI I F f 11 1_ I II I N O I] b; ll' l N I_ ; 11,', 1

I,.f,~ ;I ONDlN 01 itlil ~ THI "'k I 1.11 r1il I I M] !III III[ I}~~D

ri, I I;[ : jl {Ill l 6 { T l " 0 01 N1 I lj, I(' W ll f¢ q 'lhll "llI , L,

C.

SI

32

,,:L [LIII I [ L I Z tN G61 C:62" 11iLM BWIM I[DA((),ItI I,;((),JIM(6 ),SI(( e,MIC(6),1[ r1',)

6 : i4'Ist . IO , S1[ ,, ?'O) I';fr ) .t,,c,),, t(i), (.,,,,.J(- ,),YVt )

65 : [t I - Wr I ON MiCL: , ) M)iiiHt' ( t tCiFLI-C X X( lO2t 1 Y ( 24) 1 t ,tlIv I 4' , (1024 ,f Y I 1 12 . %i10 4

67: r6611. 66(,1 : L_- 122?06

' NSW -.5, U

/0: Nil W512

72 :t. blI 4INGING [N D[ (i- FIO< M MoTIR* F:l ii/3:2

7?: CAL ('I I ((SMlC ,t MLC, I1 f ,tl'IjAi Irl;N, I C : ,fFML,M _Si140P!715: t to 1 I .NMIC/6: 13FL2EL'i ) 1 100077: f () > 11 iOi,' ( I) t 000 F [M i N60*i 000+ l COI

/8: so CONTINUE7Y C30 L: COMI' U TAT ION OF I.tOUNL A I IVAL rIll'S

,13 D 10() J-i ,NM-D

'4 [MAX 0.0,I.MAX N0

6 ')0 I\ I ,

L-J r f : ( j [ ,: 1, r8'tJ. - f (~

: 90 Ft)IN f I NUtC,o I FMAX - TII-9 1 Im.,.X:;;O)

I.--NI. -NI t W

II: wi T L i? \ I NI I"

Y"'., r I-( T L. I. I IM0X,. GO To YU,,'6 F ~ MAX 11' I:97 LA MAX It

YS '/5 C 00T it E X1-1.1"_I< , r ( J. );.I LrtAX

i.00: 1o o') :ON r INiaiv

l. 01 C11,')2 C 1 0 FH'LJT t)T 10N Of W IN DO0W C- rT II N G 1-'O N T'

10 [ [NS W::= N SU/4:101 M MRS I ;: L N'ST ( L ? I[NSW,/

10 7r IF(F sT.,I o) [-w0 "ro 1I Or; N NR .1 ): ::0109: Go] ro ii0

1 L0. t0. CON! Iit tJ

I I I NI -I. --NF:' 1412: :[F(MR f. . ;l-'I I(t -(I 106

it 1 tlNCr rf tC

1 6 1 06 ( IF' !! I tO r ,

I r( I fI I Pt I15 I 'AN Tt I NIll

33

I (I III fill( U l W LlI'i4 I16 I N OG II I~ I1 rilL Ii.M 2

Wt ' IJK~ IIL I 816 Li6 816 )1

I IC'6' "

I 6)I F (A' , :"A 1) 1rji"' Lu o VoIiii r ( tXc x 10)

I '(10 C* I~~ u' I ll f I LN 0I I2 I;PIL O 161c W ril- IN F 01,IR W I N (low

13 1 *

13 1 l it, o1 J 1 I

133: iM0.0I i4: r*Al"1d' NRdO H-i

1 32: 1I" ,fur Il ) +NF*Fw

136: 11o 1 2 v Ii " u) k I-flYI\Esdro k

13 7: PI IC ,1( J, I*S M I C( j4K

138: SMon SlIM Wt

139: 1 L2 CON TIJNUC140: 1L5u 1(j) SliM

t142: C -PIN TING TIHI 5l [COAL ENit WIA HIN Il III W NDLIL

14 4: 111 WiiiE6,2007'

14:5 2007? roiLmni(/ 11 fl ; 51 Ui-'fl LI). 2 ( 14 1lit-LI N I i^C1 I WEINDOW'

1 -16 LPIt TL ( 62014 )

14 7:-o 2(11 [I oimff r (116 I NIL .2 MIl. 3 1l C

14 8 Nil . 5 fill;C 6 /

1"0' '000 FSCNMA I ( 61: 13.0)

I I

1.4. [DO 2100 1 1,IN I I I fI

ill) EAN 1 J .1 1 h 1

I II8. 110 120 L -,1.2V5j9 : AL '-M) H.L

16 0 SM =5M1 C: I , KAL

11: X L ) -Ltl FLX (SMlr.0

162: y YL ) tlt'LX (. 000

1631 120o CON rINUE-164: DO 1:30 L -- ,13, 1024

16b5 X ( L Y' CMIX ( 0, 0 . U)

166: Nlt=NP <J)16 7 KAI!'I KT4-5I2

1 691 Y (L t:-CMI'L'X(SKAI ,O0.O017o: 130 LUNTI1NUL*

I /I1: CAL I. (101i;GJ<X, 1024,- t 1406, 'N

172: CALL I (3066. Y,1024. -1 Wol"k

[ 7310C17/4 C' lIL 11168 [Nortr OF I STAT IN( I iiNT FO06 Nfl]:F WINDO11W

16: 1 IX Xm't( I t-5S

17 7: kYY=Nk(-J '113lit)11 122, L [,'jliS

1791 L 16: I'L KI.

'34

yiL I) t I? 11i 1, tt I . I dc I

1 3 M X.X 1, 1 L

114. " ~ XX )t

(, I.MLXX0

WI6 * I O1 t l Hll t -tI I- 'I i r I U I I UO 0 1 XI

1 9 'IYY 306'Jy

(Y(L L MIIX (U YY 0.0

* IIs XXII1111 (.0OQ

1GO TO1

I 1ys : C

299: CrA1 L I 011C(XX. 10.'4, 1' WO10-coo: CALL I- OlJGu( Y Y10 '4 lntORK

20: o tt 35 ',Z(L)-LCeJG'XX'l )

27(: K(t--(L ) ll 2 2(L)2Q4: //' 0- CJNJG (YYl Q.

205 (I- f Yr L. ) *Z' (L.

22. CI tkill I rlt4AIM t (A- ES C IrAM 1 1 l(iN~r.. I-L W", N I(3SE 31 C [1034

101 zitS ) y(L.

212 ((1 (( 2(L. ) L213: 1' (I rrrJG X 1-

214 ~ l G (

.x1 1XL+iIL El .

2 19 Il, 1,EA k1 tXX (L)0 I -r "Lrl In Y(L.)

22 1 hRItV=.

76 CONT rql

227' 1 F (7 PRC.Fr. J GO 11(1[ 71 Y22 81. I-hI) -1 .0--i

230:9 71 CIzT ,.U

231: 721 COiNT INUI

232: 2 ? Zi L ) 'CMPILX I -'ClIC, I,-lIC

2,4 YL-zY (Ll '1,02'4.

2 3/I C21 C. ((Clti M14YOf'I*ZZII 11.12397

35

2 O C 0PI If~ I Ht 1'1" R- ~ F I( Fl FOR 60 (:Y(i. I AND' IlAlMIN [C;241 : C24-2: 131, CLP fI F 041112 4.3 l,)IA hC MC Op! t; 0 I0, 6 ' 1'271,126 13 1 l,124 4.2y

N44 Xl MtOMi (I1245: 1I (NX.l1 . 0) GO Fo 131

46: Y ( I )M CLX (0. 0 . 0214?: 13_1 D'Ol1 133 N;2,10 ,22 43: NX MIOM (N )2 49 T1I (NX . LU .a0: GO TO 1 38

0o NY -MLOMI. (0 f1)21-1 DO 132 1-1 tlI,JY

3: MX 'iPI112 L.'14 YQMXI rf,II_.X(0,0.0)

2 5u.132 COINT (I U-.. ,6. 133 COINTI(NUE

2',7 138 ()NFTI NUIL

29 C IFINDI NO il FRI AW FIC 0 1FITE.ILFNCLS 1I TIIECN THlE WINOE P01'21 INLS260:*C

261: CALL FOIJIr(Yi024,f+1.W~kK)262: CMAX-0,263: FMAX ()26 4: Wi It0 I 11.024

2-66: CA :At11-..( Y(I

2 67: 11 (CP,.fl I CMAX) GO TO 140

26,1: C MAX- xI

270: 140 CINFTI NUI2_,,1: ( )IMAX Ml:FW-12712:C2 73 : C roll Ti- iP r NA FE tiN olr TOI NOPMAI 71'o COR-RE 1 AT I ON ClJILF I C II _N I27i4:C7

2/: 13 (1,J) lMIJ1AX/ (E..IJ)I-II)*O

2/6: UA j CIJN=Ff1N Ii J

2/7& 200 LLINTINUr

2 8 0 ' C, F DIE fEMINA'TI UN OF' k*UGl-I F EMIL 1i II'FERINLES i' I-L'JNV 17 IUNALL I iNt 1_

,8: WITE(l 6,2016)283: WRITL(6,2017)

2814: 203. / I 11MI BE OTWEEN EACtI FAIR OF MlIIKOI'I IONL I SIGNALS '/28: DO 250 1-:1.,

286: l-KX;- I -f12037: DO 240 L'l(XNMIC208: 1(1t.FtO (I l -()1-TtlIt)269: 20 16 FORMAT (/ THEN CORI . LAT rON, T FIME L I F1 EIENCI; (NOEC I ANT' COILECTCtI290: T IMIE t Ill FI.IC 0NECS 1--cC291: 240 CON T INUCl292" 2:,0 CONFTI NUT

29 4: 1 PSIlLiIFION OF NI C TI) It( 1)3110 AS RIEFEL:tNCIT'2951 C296: Cr11S nb 1) 01 I I 1-1, 3 f0U I i4'+1-1.0 fO iG

297 ( il AS, G (f.21,(', 3)f (2, 41lI-C2, l0+i42/C

2980 tilA A'(31 G(Itl1fG12, 3)1 G(3 ,4 41(;(3 . ) fI 3.

279: Ltd-A' 14) G1,4)1(2, 4) IG(3-4ft3(45((4 .6)

36

r, i)l A (', h .I5 )' s I, ',?),5(.i'; )fI,(4 ',1I 6 )(''1: I11 tI_()l t1(,I1. )ItisV'v6)*j S.(6i5-5it{(4,61)|I.(U..66

60.' IL ' . )e, f ."1' 1 G 16

.A-)4 1I i111il As ? .I .r. l 13(A 10 2 "1(It ; l. 1.4116, (5[)SI', I

,0j -3 5 ' 1f L. ON I UE

I I'

1 IfC IsO 27, 1 L1,531 \U If I

.6 1 1 D 0' '-10 .1 -1,[J,6I5' iF( i1,,I)LI,0..) G 011 2.66

316 26t, G ( 1,,) J 3Gll ,J) *t0..

1117: GO To 2703181 266 G ( I , j - GA ( I ,J 14,l I I ,J)

319 270 CON I0NUE.3 71 LINI114JL

-' L L:c I-rI-k r ,r oN o1- 1 F 5 I M " I'5ELJAIL TIME 1 I I i- MI:I C . S Ik F-FI.-RIE.NCE

324 DO 290 [ .,4j,2 ,,1 KX.::I fl

326 : DO 200 , J Ikx,32 , 0(6 1

7J) - G(I f 1 -4 )

3 2 3 A(J, I = ,Ji'9' 2,0 CONTlIsL)[

339. 290 CONr tINUE3 31: o(II ):::G( 2 ) 1 G (2,-3) f ( .G 2 2 4 f - G 62 &

332 A2',' I=0I, ) H3 2 3).1,3,4 1-1 (, ft-, 6)333 A(3,3) G(1,4) .0(2,4) oG (3,4,t .41 )46'334 A(4,4) ::=(GI5) (+6 , 5) fG( , ft.;-(4,'.)-o (,,6)335 A(55,5) 6(1 ,6) fG 6)5-G 3,6) fG 4,6).*, 4 6'.336 A( 1-Gi.)*J, u(1,2)'fG(,3*)'TI(2,3).f02,4*2 TU1(,37' A ( 1.6) AA fG(2,5l*( TAJ(2-5. ) f3 2(2,6)TAU( 2,6)'3.3 [.F-6 (,3 ) 1IAL(1, G( 2,3)*TAI2 -3)fG(3, .)*1AL)U(3.5)339 A (2 ,6 f6(3,4): rALJ (3,4) +G(3,6'- 1 AU (3,6)340. CC:-G( J ,4)TAU( 4 )- G (2)IA,4*( 2 424) -- G(3 ,4) IAU(3,4)341: A(3,6) CC5G(4,5)*TAUJ(4,5)-i(4,6),*1 I U(4,6)342: DD: -G ( 1,5)*'IU -:1. ,5)"-O (2P5 I*TA1( ,, ) -G1 (6, * IL II,, 5)!43: A(4,6) -i -G,(4 ,5) ITU(4,;),H3(!26)*TO5 ,,6344 EI--:=-G (L,6)rAU( iS) '-13(2v6)Tr(-i( )6) -G (3,614TU(3,6)-'4'5: A ( .6)) : - (4 * TALI (4,6)-OG (5, 6 AU)*1L(,6)346: V( 1 ):=4347-: CAL.L GRA6556,$0,,V

343 (1(1)=O.

349. 010 295 1:2,6";0' AT(1)=A(K-- 1,6)3'1: "91 CONTINUE

353:C- ArJLJTMVNT OF TIME Ti[Fl IT 4fI-NC,3 54:C3'155 DO 310 1:.- 1

5'7 110] 300 J: 1~,,3581 T A ( I I, )J):AT 'I)- I (J)3.9 C f 3l( 1 -,J I AU I J) H:1., 0, T I I I FT J

S . .. ... . .. . ... . .. . . . ... . 3 ._ . .. ,1 < [ . . . . . . . .. .. . . .

37

3o0: C I (,Li I ,J -C I (1 rI J / 1000.361 :C3 6 ' : C I I N I lth L, ICI IA [ON CU}l TN) r1 oui (ri , 1C: CE : l Li 1 IrL [ [-i il:L0 n1

36 3: C

3,64: k F 1 1M-( 6x ,0 L)IA ( l,'M .' ') ('I6.3,, X, '(yI T CT I 'L ,', I .) i ,I

,i,'6 . X, "'CT,^U ( "[ ,','[. :" 6

36/: 300 ON I 1114U

568) 3j0 CONTINUI369: C3 /0 C ['F II' INA [[ N. L L F : LAT(lE TINES FON 1111 I'OSIT 1ON L T) [M TOR

3 7 1 C

3/2: iO 620 -l,'I3/3: ,X-I f1i3/4 DOI 610 I_-hX NI'rilC

3/5: LTAU(L F) -CIAU(TI)376: 6LO CONTINUI377: 620 CON FINUE378: 10 640 I IrA379 II-(J.NL.I\lAX)CO TO 630

3i10: TME>J)'0.00381: G0 TO 640382; 630 CUN F LNUL303: frl (J) c> I';AU(.JkMAX)

384: 640 CONTIIIUL335: C326: C 1I$:TNIT INC TH CCL O[IVI. TIMES FOR L'OSTTION 0-S11MO FOR

380 : WR T IF (6 200':)389: 2005 FORMAT(//' THE TIMES IN SE.C TO BF USED FOR INI'UT TO A LOSI 1 100 I-T390: .IMAOi '/)391: D'0 503 1::1,NMIC392: WRITE (6,2003)I ,TIMiE( I)393: 2003 FORMAT(3OX,'TIIE( 'Il'):='I 7.3,' SEC')39: 503 CONTINUE395: WR I T6-.r,2025)396: 2025 1LORMAI('3'?7 :C398: " OUTFIF ING THE NOT INFO-RMATION

39? : C400: WRITE(6,2021)

401: 2021 FORMA Ti ' Tii mT TO A B4E USED AS .NF'UFT I0 FOSI II(IN ESTIMA O' !

402: WRITE(6,2022)TEMP403: 2022 FORMAT ( 32X, ' TEMP= 'F4 . . ,' DIGS C.'

404: WRIT- (6,2023 I.ILS405: 202 FORMAT(22X, b iNE DIRECT ION= '14,' MILS')

406: WRITE(6,2024)INOTS407: 2024 FORMAT (26X, ' WIND SPEED= ' 14, ' KNOTS'

408: GO TO 401409: 400 WRITE(,r201.5)410: 2015 FORMAT(3011 AN UVERFLOW I-HOS BEEN DETFECTEDa411: 401 CONTINUE412: STOP413: END

38

APPENDIX B

Subroutine RDATA Program Listing

2:11: SIB :Lt 511 NE Srt

3:C2

6: inIN-61,till b( 2 lll / Ml ~ S*I :MltlIIi4 ''3 C l

10: usItri(6t,5ii : Is J'. IJMoTI'112: wfiriF( 6, 11 ') MD'MH.,MMIj,4SSl7(13: 1.12 fOSMA1(4XY' DAY '1h3,' SHOT0 TIME '12,':'12,' IS'S F: 6.3.' SEC')14: REI 12~i,221i5S: 221. I BRxtAlI X,16: 14N11 T(6,2"1)17. ' rio 11 j ,MIKToT

19: iI)U(RRI)flllIOUlRl)--720: 333iUIrAi(X16,X,1.41.3.?*32 -1: 11 LIOJ IINUL

23' 2"5 IliliMA*T(4X,' MUCS?'2' 1..'2' 'l I!' I..6 VAL-UES-4. /M't(C

'16' 22" ' *I INA'TI /' TlI 1 STARTING TIMES :Ol. LACH MLCRcIPlONE SIGNAL..' /)27 DO 25 1- 1,3.i. Wl*"IITE'(6. "'9)riIE(I1) I HOUR (I ) -IMNN(I) SEC (I. IC(,J)'J .HOUIR(J)

30.: IM IN (J) .SECJ)31 229 FORSMAFT(4X, ' MII.1,' 12: ,'MS 'FP6.3.' SEC'5X.'MC'£

32: .- ' ) '12,' '£2.' FIRS 'F6.3,' f1:*E'33: 2,, CONTINUE34: 110 22 J:= J - M I1K r0135: VALs VAL.UES (I)>36: REAU(i2,444) Si(.JJiVL37: 22 CONTINUE38:. 444 'ORMAF I iAS.0)39: RE-TURN40: END

39

APPENDIX C

An Estimate of the Noise Power Spectral Density for a PASS Run

N

NCWc.~.E-1 N

En z

0 -

V-6 4

N

_- 0

00 -0

-:T

0 0 *

40

APPENDIX D

Derivation of Weighted Least Square Solution

The performance index to he minimized is given by

N Ne = Y i[ " .- (t.-t ) ] 2

i~j j=1 1] i j

In this expression T.. represents the estimate of the rough time difference1j

between signals from microphone i and j, yi. is the weight associated with

that estimate, and t. is the time of arrival of the signal at microphone i.1

If we select ti = 0 as a reference and use six microphones, e can be written

as follows.

e = y12(T 1 2 -(-t 2 ))2

+ y 1 3 (t 13-(-t3 ))2 + "'-+ -" 16(T16-(-t))2

6 6+ X X Yi.[Tij-(ti-t.)]2

i>j j=2 1. I- ' J

A necessary, in this case sufficient because of convexity, condition for e

to be minimized is that

@ti

Taking the partial derivitives of e we have the following set of simultaneous

linear equations in t2 , t3,...,t 6 that can be easily solved.

C2 -'22 Y23 2. 1 25 Y26 t2

(t3 -23 Y33 Y34 Y35 Y36 t3aI

4. y 24 134 Y4 4 Y 46 t

355 Y25 Y35 Y456 Y5 Y5 ts

6 Y26 'Y36 Y46 Y 56 Y66 6

where

41

+, +I3 + '>' Y I 4 5 + y. :I

+ [ + + YI13 2323 34 34 35 3 36 36

't • , . 31 4 3 5 ' 46 + 46

5 15'15 - IY5 2 -- 13 -- +- [l 'f 5

=51 -1. S -- 56

162b - 36 36 4 C F,

and

Y 12 + 2 + Y2 4 + Y' +

Y2

=-' _ y +y + +y33 1' 3

4 2' 31. '.5 3 6

Y = (y + + +y4 +y

Y15 25 +

35 '.5 56

y = _ (v + y + -y +-y +-y )Y6 16 26 36 + 46 56

In the present edition of the program this set of equations was solved by

using a canned subroutine. If computer storage becomes a problem the solution

vector can be obtained by using a form of the steepest descent algorithm.

42

GLOSSARY OF PROGRAM VARIABLES

NMIC = Number of Microphones

NL Number of data points for each microphone

NSW Number of points in the sliding window

NPFW Number of points in the Fourier window

SMIC(J,I) = Signal amplitude for MIC J at time I relative to IT(J)

IT(l) = Starting time for microphone I in MSEC relative to blast

LRST(l) = Rough starting point for microphone I relative to IT(I)

NR(I) = Starting time (MSEC) for Fourier window for microphone signal I rela-

tive to IT(I)

E(I) = Energy within correlation window for signal I

TAU(J,I) = Raw time difference between windowed signals J and I

RTAU(J,I) = Rough time difference between signal from microphones J and I

determined by correlation

CTAU(J,I) = Corrected time difference between microphone J and I by least

squared error fit

GAM(J,I) = Normalized correlation coef between signals from microphones J and I

G(J,I) = Reliability weight assigned to RTAU(J,I) for the least square procedure

AT(l) = Time difference shift of signal I relative to MIC 1 signal

TIME(I) = Relative time of the Ith signal for position estimator

A(J,I) = Augmented coefficient matrix for least square fit

JC(I) = Control variable for Subroutine GJR

V(I) = Variables V(1) and V(2) for input to linear equation solution subroutine GJR

CMEAS(I) = Overall measure of correlation for microphone I

43

X(1) = Ith value of first signal for cross correlation on input

Ith value of Fourier transfer on output

Y(1) = Ith value of second signal for cross correlation on input

Ith value of Fourier tranform on output

WORK(l) = Work space specified by FOURC subroutine

XX(l) = Ith value of estimate of noise spectrum

YY(l) = Ith value of estimate of signal plus noise spectrum

ZZ(I) = Value at Ith freq for prefilter

IDAY(1) = Day of the start of the Ith microphone signal

IHOUR(l) = Hour of the start of the Ith microphone signal

IMIN(l) = Min of the start of the Ith microphone signal

SEC(I) = Sec of the start of the Ith microphone signal

MIC(I) = PASS microphone number associated with mic I

KMAX = Microphone number selected for reference

TEMP = Effective temperature at time of shot in Deg. C.

MILS = The effective wind direction at time of shot in mils

KNOTS = The effective wind speed at time of shot in knots

KXX = Noise window starting point for SMIC(I,L)

KYY = Noise window starting point for SMIC(J,L)

PREF = Real and imaginary value of prefilter

44

REFERENCES

[1] Artillery Sound Ranging and Flash Ranging FM6-122, Department of the

Army, Washington, D.C., 1964.

[2] Dean, E. A., "On the Determination of Arrival Times for Sound Ranging I;

Effects of Finite Amplitude Propagation, Vertical Meteorological Gradi-

ents and System Transient Response, "Atmospheric Sciences Laboratory

Report No. ASL-CR-79-OI00-2, WSM'R, N.M., May 1979.

[3] Ludeman, L. C., "A Procedure for obtaining More Accurate Timing Informa-

tion for the Sound Ranging Problem," Atmospheric Sciences Laboratory

Report No. ASL-CR-79-100-2, WSMR, N.M., February 1979.

[4] Barnett, K. M., "A Description of the Artillery Meteorological Compari-

son at WSMR, October 1974-December 1974 ("PASS"--Prototvpe Artillery

[MeteoroLogical] Subsystem), U. S. Army Electronics Command Report

ECOM-5589, April 1976.

[5] Univac 1108 Multi-Processor System Math-Pack programmers reference UP-7542.

Univac Division of Sperry Rand Corporation by Advanced Computer Techniques

Corporation of New York City.

e, U S GOVERNMENT PRINTING OFFICE: 1979 - 617-119/47