Posterior Cramer–Rao lower bounds for complicated multi-target tracking with labeled FISST based filters

• Multi-target PCRLB and its iterative calculation expression are derived.
• Association relation between multi-target tracks and measurement set is got.
• Detailed expression of MT-PCRLB for radar target tracking problem is obtained.
• An indicator is extracted from MT-PCRLB for performance evaluation.

As science develops, multi-target tracking technique advances towards dealing with complicated scenes, in which target number is time-varying and unknown, detection, measurement source and data association are uncertain. Among the new tracking methods, Mahler׳s Finite Set Statistics (FISST) based multi-target tracking technology naturally suits such complicated scenes. A performance metric with rigid theoretical explanation and clear physical connotation is the cornerstone for further improving multi-target tracking methods on precision and stability. The Posterior Cramer–Rao lower bounds (PCRLB) is widely used for assessing tracking performance. While, for the complicated multi-target tracking mentioned above, existing PCRLBs do not work well. Therefore, we derived multi-target PCRLB (MT-PCRLB) under random finite set frame as well as its iterative expression through analyzing lower bound of the FISST based filters’ performance in complicated multi-target tracking. The derived lower bound is compatible with current labeled FISST based filters. Based on multi-target tracks obtained by labeled FISST based filters and association relations between tracks and measurement set, recursive calculation of MT-PCRLB is realized. Simulation results demonstrate that the proposed methods behave in a manner consistent with our expectations.