Section: New Results
Participants : François Le Gland, Alexandre Lepoutre.
This is a collaboration with Olivier Rabaste (ONERA, Palaiseau).
The problem considered in  is 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 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.
The problem considered in  is detecting and tracking a single radar target with amplitude fluctuation Swerling 1 and 3 in a track–before–detect context with particle filter. Those fluctuations are difficult to take into account as they are uncoherent from measurement to measurement. Thus, conventionnal filters work on square modulus of the complexe signal to remove the unknown phase of complex amplitude and the marginalized over the law of the modulus but they lose the spatial coherence of the amplitude in the measurement. We show in this paper that complex measurements can be marginalized directly while taking into account the spatial coherence of the complex amplitude. Finally, we show the benefit of this method both in detection and in estimation via Monte Carlo simulations.