Posterior Cramér-Rao Bounds for Tracking Intermittently Visible Targets in Clutter

In this paper, the posterior Cramér-Rao bound (PCRB) is determined for a scenario in which a single target is only intermittently visible to a multi-sensor system, with visibility governed by a discrete time Markovian switching system. The scenario also allows for missed detections and false alarms. Two PCRB methodologies are developed. The first approach adjusts the probability of detection to account for the a-priori probability that a target is visible, resulting in a time-dependent "information reduction factor" that degrades the measurement contribution accordingly. The second approach determines a conditional PCRB by sampling potential visibility/non-visibility sequences, and then calculates an unconditional bound as a weighted average. The resulting PCRBs are compared to the performance of an integrated expected likelihood particle filter (IELPF) and an integrated probabilistic data association filter (IPDAF),for scenarios with one or two sensors, and a range of clutter densities. It is shown that there is good agreement between the best performing filter and the PCRBs in the one sensor scenarios. However, when a second high-rate sensor is added to the system, the filter performance is similar to the bound only when the clutter density is low, with the PCRBs shown to be optimistic when the clutter density is high.