A Bayesian Method for Localization by Multistatic Active Sonar

The question of localizing a target with multistatic active sonar is reexamined from the perspective of finding a peak in a probability distribution function. The probability distribution function is constructed using straightforward Bayesian principles. Both a position estimate and a covariance matrix can be found, provided that an implementation of a numerical algorithm for finding a local maximum is available. The localization method developed herein can account for transmitter and receiver location errors, sound-speed errors, time errors, and bearing errors. A Monte Carlo test is conducted to compare the accuracy of the proposed method to that of a more conventional method used as a baseline. In each iteration, a transmitter, several receivers, and a target are positioned randomly within a square region, and the target is localized by both methods. The proposed method is generally more accurate than the baseline method, within the range of parameters considered here. The degree of improvement over the baseline is greater with a larger region area, with a larger bearing measurement error, and with a smaller time-of-arrival measurement error, and slightly greater with a larger number of receivers.