Single Target Tracking With Unknown Detection Status: Filter Design and Stability Analysis

For single target tracking (STT), when the target detection status is unknown, meaning the system lacks direct knowledge of whether or not the target has been detected, the system state follows a Gaussian mixture distribution. The number of Gaussians grows exponentially over time, making it challenging to theoretically determine the stability of STT. The main contribution of this article is that we address the problem of theoretically determining the stability of STT. Specifically, we first design an improved generalized pseudo-Bayesian (IGPB) filter by introducing a novel
$\epsilon$
-similarity-based pruning mechanism to manage the exponentially growing data association hypotheses. Unlike other STT filters, whose stability is theoretically difficult to determine, the stability of the IGPB filter is rigorously proven, and sufficient conditions for the filter's stability are established: 1) for a
stable
system, the IGPB filter remains stable irrespective of the detection rate; 2) for an
unstable
system, the filter is stable when the detection rate exceeds a threshold value. Numerical and experimental results are presented to validate the efficacy and application potential of the IGPB filter in tracking unmanned aerial vehicles.