Exploiting amplitude spatial coherence for multi-target particle filter in Track-Before-Detect

In this paper, we address the problem of tracking one or several targets in a Track-Before-Detect (TBD) context using particle filters. These filters require the computation of the likelihood of the complex measurement given the target states. This likelihood depends on the complex amplitudes of the targets. When the complex amplitude fluctuates over time, time coherence of the target cannot be taken into account. However, for the single target case, spatial coherence of this amplitude can be taken into account to improve the filter performance, by marginalizing the likelihood of the complex measurement over the amplitude parameter. The marginalization depends on the fluctuation law considered. We consider in this article Swerling 0 and Swerling 1 fluctuation models. We show that for the Swerling 1 model the likelihood of the complex measurement can be obtained analytically in the multi-target case. For the Swerling 0 model no closed form can be obtained in the general multi-target setting. Therefore we resort to some approximations to solve the problem. Finally, we demonstrate with Monte-Carlo simulations the gain of this method both in detection and in estimation compared to the classic method that works with the square modulus of the complex signal.