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Conventional target motion analysis (TMA) relies for the most part on regressive techniques (modified by Kalman filtering) tor contact solution. While generally robust, even low levels of data contamination will frequently result in significant error, and even solution divergence. This article outlines a revolutionary target motion analysis technique. The synthetic solver (SYNSOLVE) presented here is intended to provide rapid (two leg), accurate solutions to primary and secondary contacts when more conventional solvers are either not available or fail due to mathematical difficulties. Developed during a recent deployment on USS LA JOLLA (SSN 701) when fire control system problems threatened the ships mission, SYNSOLVE was found to be both user friendly and capable of providing reasonable solutions to most non-maneuvering targets.

Fundamentally, the solver relies upon the generation of synthetic bearings arrived at by bearing rate extrapolation. Muoh like the Spiess, modified Spiess, or Darby ranging, the solver develops target ranges based on fictitious bearings. Unlike the methods mentioned above, however, the solver provides course and speed estimates by regressing on a number of ranges developed over time.

Consider the following example. Own ship is on course 045, speed 10 knots. A contact is gained bearing 000. Over the course of three minutes, the target’s bearing rate is estimated to be left one degree per minute. At the three minute mark (target now bears 357) own ship turns (instantaneously, for simplicity) to new course 315, speed 10. Three minutes later, at time six, target bearing rate on own ship’s new course is estimated to be zero (target bearing 357). If own ship had remained on it’s initial course of 045, target bearing at the six minute mark would have been 354 (this assumes linearity in bearing rate, an assumption to be discussed at a later time). In other words, two lines of bearing are now available at time six. They are the one actually measured (357), and a synthetic bearing (354) generated by a bearing rate extrapolation. By solving for their intercept point we arrive at a target range at time six. This is in essence the mechanics of synthetic ranging.

It should be obvious that similar ranges are available for time seven, eight, and so on. If the linear bearing rate assumption were valid, then simply regressing on these range/time pairs would result in contact solution. What may not be quite so obvious is that synthetic ranges exist for times prior to the first own ship maneuver. Using the example described above, these synthetic ranges are developed as follows. At time one, the measured target bearing (359) is available. A second bearing can be generated by extrapolating the second leg backwards in time to estimate the synthetic bearing at time one. In the example outlined above, this would be 357 (zero bearing rate with a measured bearing of 357). Thus at time one (and all times prior to target maneuver) synthetic ranges are available. By regressing on all of the triples data (range/bearing/time) a synthetic solution is developed. If appropriate corrections are made for nonlinearity effects in bearing-rate estimates, this estimated solution should rapidly converge to actual target solution.

Weighting Scheme

Considering the realities, it seems reasonable to develop some sort of scheme which recognizes the various problems and is able to estimate intelligently the value or weight each data triple should have in the regression.

Our ability to model this accurately is highly dependent upon the level of noise present in the measured bearings. Unless this noise level is extremely low, or the time over which bearings are measured during a single time motion analysis leg is extremely long, any attempt to determine the appropriate coefficients would be fruitless. Since present sensors are incapable of providing the requisite level of bearin~ fidelity (in all but the best of acoustic conditions) we must explore alternative solutions to the non-linearity issue.

One option would be to collect data only over those periods where the linear approximation is relatively accurate. This presupposes that the observer is cognizant of the engagement geometry and is thus capable of determining when nonlinearity effects might be minimized. Another option would be to extend the synthetic own-ships track out a very short period of time, thus obviating the need to perform non-linearity corrections. In this case, the short baseline formed by the extension will itself yield inaccuracies due to algebraic intercept considerations. Again, if the observer knew of the engagement geometry, he could intelligently estimate when non-linearity effects become an overriding concern.

It appears that any reasonable method of performing non-linearity corrections will rely on some sort of precognitive knowledge on the part of the observer. It is here that the synthetic solver provides strengths not available through more conventional methods. Since the solver will not begin to produce solutions until after the second TMA leg is commenced, we have available a variety of range estimates (Ecklund, cross bearings, etc.) with which to filter the synthetic ranges intelligently. With a variety of statistical data bases indicating that target speed can be reasonably pre-supposed by a point estimate, we are left simply with choosing that target course which results in a worse case error equation and adjusting our weighting scheme accordingly.

Included intercept angle:

As the included intercept angle decreases, the sensitivity to either real or fictitious bearing error estimated synthetic intercept synthetic baseline heavily. that used rates.

increases. Errors in either real or bearings lead to large errors in ranges. Since, in general, a small angle may be directly related to a short baseline, it would appear that longer extensions should be weighted more This line of reasoning is counter to in our discussion of non-linear bearing

Artificial Intelligence Module

It is apparent that instead of the lack of information generally associated with conventional TMA methods, SYNSOLVE suffers from an abundance of target triples (along with ancillary data). The integration of data necessary to produce a most likely target solution indicates the need for an adaptive statistical data base, one capable of recognizing the many idiosyncrasies of the various data points and, accounting for the vagaries of the particular fire control party, producing the requisite target solution. Generally referred to as A~tificial Intelligence, this module would consist of a comprehensive data base and associated weighting scheme, making it capable of objective evaluations of proposed solutions. In addition, 1~ would recognize the expert rules applied by the ships commanding officer and thus provide real-time subjective evaluation and modification of target solutions.


The methodology discussed provides a revolutionary method of estimating target solution in the presence of noise corrupted bearing information. By providing continual ranging data through the use of synthetic bearings, target solutions are continuously updated and refined. The solver is sensitive to a range of measurement and geometry specifics and relies heavily upon a weighting scheme to provide for a robust regression. In addition, the cognitive analysis of the data triples will probably require the utilization of an AI module to aid in both objective and subjective evaluation. Implementation on the ยท stand alone HP-9020 computer would provide a first cut evaluation for this solver and is recommended for an Automatic Data Entry configured submarine.

LCDR P. Kevin Peppe, USN

Naval Submarine League

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