Multiple Ping Sonar Detection.

In the design of multiple ping sonar there is an additional complication which is not present in the analogous radar problem studied by Marcum. In the radar case all of the targets characteristics are assumed to remain stationary for the duration of the pulse train. This is a reasonable assumption since the entire pulse train may last only microseconds. But in the 20 to 30 seconds between sonar pings the target location and other characteristics can change markedly. The problem, then, is to detect the presence and estimate the location of a target whose path of motion is subject to certain constraints but otherwise unknown to the observer. In this report a formulation of the optimum multiple ping detector is presented which takes into account the stationarity differences between the sonar problem and the ideal radar formulation by Marcum.