LOCATION OF UNDERWATER OR SURFACE SOUND SOURCES BY 
MEANS OF COMPUTER-LINKED CABLED-HYDROPHONE FIELDS 
by JAMES H. MORRISSEY, Engineering Specialist 
Philco Corporation 
Philadelphia, Pennsylvania 
ABSTRACT 
A method is described whereby 
the position (xyz) of a sound source 
already detected by multi-atatic 
sonar field of hydrophones may be 
determined, from observed time delays, 
by means of a data processing algo- 
rithm involving pre-esolution of two 
redundant systems of linear simulta- 
neous equations. Geometrically this 
algorithm, now designated MULCAP 
(MU1ti-station Linear CArtesian Po- 
sitioning)+, may be interpreted as 
sound-eource location by means of 
intersecting planes. The direction 
cosines of these planes are deter- 
mined only by the hydrophone-field 
configuration; they are independent 
of the position of the sound source 
and of its velocity. 
INTRODUCTION 
During pre-proposal effort on 
undersea surveillance systems, there 
was developed, early in 1960 by the 
Advanced Systems Group of the Commu- 
nications and Weapon Systems Division 
of Philco Corporation, the new geom- 
etry-oriented data-processing technique 
since designated MULCAP. Although 
this new data-processing technique is 
believed to have potential applica- 
bility to many systems, radar and 
sonar, existing or proposed, involving 
acquisition or tracking of trans- 
mitting or reflecting vehicles, its 
first implementation with realistic 
input data has occurred in connection 
with a proposed precision underwater 
tracking system. An error analysis 
of MULCAP, with particular emphasis 
on errors attributable to refraction 
effects peculiar to the ocean mediun, 
is now being carried out by Philco 
Corporation under contract with the 
Naval Underwater Ordnance Station, 
at Newport, Rhode Island. 
The vehicle located by MULCAP 
methodology is assumed to be a source 
of sound in either of two senses: 
(1) 4t may carry a transmitter, by 
design or by necessity; (2) it may 
reflect a transmitted signal. In the 
former case the inputs are the differ- 
ences in arrival time among the n 
fixed receiving stations(hydrophones). 
In the latter case, where the n 
stations are assumed to consist of p 
transmitters and q receivers, the 
inputs are the pq possible transmitter— 
to-vehicle-to-receiver propagation 
intervals. The first case is desig- 
nated the "passive" mode; the second 
case, the "active" mode. 
Before the advent of MULCAP, 
systems appropriate to its passive 
mode were known as "hyperbolic systems" 
because the mathematical routine 
whereby the transmitter was located 
involved the simultaneous solution of 
quadratic equations representing hyper-— 
bolas or hyperboloids, respectively, 
for plane or space applications. 
Systems appropriate to its active mode 
("pinging", for example) were known, 
before its advent, as “elliptic 
systems" because the mathematical 
routine for determining position 
coordinates of the reflecting vehicle 
consisted of the simultaneous solution 
of quadratic equations representing 
ellipses or ellipsoids, respectively, 
for plane or space applications. 
MULCAP makes it possible to 
eliminate completely from the multi- 
station vehicle-location routine the 
simultaneous solution of quadratic 
equations. In situations where the 
hydrophone configuration effectively 
spans the surveillance space, MULCAP 
locates the vehicle by a completely 
linear process, i.e.,by a series of 
matrix—-by-vector multiplications. On 
the other hand, in those situations 
where physical or economic factors 
prevent effective spanning of the 
surveillance space, MULCAP's linear 
Superior numbers refer to similarly numbered references at the end of this paper. 
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