Target Motion Analysis (TMA)
 

I decided to write a computer program simulation of TMA (Target Motion Analysis), to see if how well collecting info from passive sonar works in determining a targets range/heading/speed.

The idea is to take at least four bearings, and then use this information to determine target info. The computation is a simple brute force approach which simply iterates through the possibilities given a range of reasonable constraints and finds the one which minimizes the error. So its not using "real" methods. Needless to say, the program takes a couple of seconds to find the best match :-)

The first thing I noticed is how important being a moving observer is, at least after the third bearing.

Another observation is how bearing accuracy is really important, particularly when the range gets to be big (> 15 km).

This probably means that a hydrophone-only attack in games like SH3 would be really hard unless at short range (< 5 km), as the bearings you get are only accurate to a single degree.

I am not finding that making many measurements makes up for the loss in bearing accuracy, at least for a small number (like, increasing from 4 to 8)

Here is a screenshot of some results. Real target heading is 135 degrees travelling at 7.8 knots and initial range of 15 km. Bearing accuracy of 0.25 degrees. In black is the true course and purple is the predicted course

https://i.ibb.co/BzNzsmk/tma1.png