A Statistically Motivated Likelihood for Track-Before-Detect

A theoretically sound likelihood function for passive sonar surveillance using a hydrophone array is presented. The likelihood is derived from first order principles along with the assumption that the source signal can be approximated as white Gaussian noise within the considered frequency band. The resulting likelihood is a nonlinear function of the delay-and-sum beamformer response and signal-to-noise ratio (SNR).Evaluation of the proposed likelihood function is done by using it in a Bernoulli filter based track-before-detect (TkBD) framework. As a reference, the same TkBD framework, but with another beamforming response based likelihood, is used. Results from Monte-Carlo simulations of two bearings-only tracking scenarios are presented. The results show that the TkBD framework with the proposed likelihood yields an approx. 10 seconds faster target detection for a target at an SNR of -27 dB, and a lower bearing tracking error. Compared to a classical detect-and-track target tracker, the TkBD framework with the proposed likelihood yields 4 dB to 5 dB detection gain.