Multitarget likelihood computation for track-before-detect applications with amplitude fluctuations of type swerling 0, 1, and 3

Track-before-detect methods jointly detect and track one or several targets from raw sensor measurements. They often require the computation of the measurement likelihood conditional on the hidden state, which depends on the complex amplitudes of the targets. Since these amplitudes are unknown and fluctuate over time, this likelihood must be marginalized over the complex amplitude (i.e., phase and modulus). It has been demonstrated that this marginalization can be done analytically over the phase in the monotarget case. In this article, we first propose to extend the marginalization to the modulus in a monotarget setting, and we show that closed forms can be obtained for fluctuations of type Swerling 1 and 3. Second, we demonstrate that, in a multitarget setting, a closed form can be obtained for the Swerling 1 case. For Swerling 0 and 3 models, we propose some approximation to alleviate the computation. Since many articles consider the case of squared modulus measurements, we also consider this specific case in monoand multitarget settings with Swerling 0, 1, and 3 fluctuations. Finally, we compare the performance in estimation and detection for the different cases studied, and we show the gain, both in detection and estimation, of the complex measurement method over the squared modulus method, for any fluctuation model.