The Modified Riccati Equation for Amplitude-Aided Target Tracking in Heavy-Tailed Clutter

The performance of tracking methods can most often only be assessed by means of Monte-Carlo simulations. An exception to this rule is the popular probabilistic data association filter (PDAF), whose root mean square error (RMSE) can be predicted by means of the modified Riccati equation (MRE). To the best of our knowledge, the first treatment along these lines for the PDAF with amplitude information (PDAFAI) is presented here. We evaluate the MRE with amplitude information (AI) for the case of a Swerling I target in heavy-tailed, or more precisely K-distributed, background noise. The MRE can be used to determine an optimal nominal false alarm rate. To the best of our knowledge, the first systematic approach to the determination of false alarm rates in heavy-tailed clutter is presented here. In particular, it is indicated that the PDAFAI can safely operate in the presence of very abundant clutter, while the PDAF only can cope with limited amounts of clutter.