Error bound for joint detection and estimation of multiple targets with random finite set state and observation

• A JDE error bound is proposed for multiple targets within RFS framework.
• The bound is obtained based on OSPA distance rather than Euclidean distance.
• The bound is compared with the multi-target error bound of [15].
• Rigorous mathematical proof of the bound is presented in Appendix
• Simulation results show that the proposed bound can provide an important indication of the performance limitations for existing multi-target JDE approaches.

By the use of the random finite set (RFS) and information inequality, this paper studies the error bound for joint detection and estimation (JDE) of multiple targets in the presence of clutters and missed detections. The JDE here refers to determining the number of the targets and estimating the states of the existing targets. The proposed bound is obtained based on the optimal sub-pattern assignment (OSPA) distance rather than the usual Euclidean distance. Maximum a posterior (MAP) detection criteria and unbiased estimation criteria are used in deriving the bound. Then, the special case of the bound is discussed when neither clutters nor missed detections exist. Example 1 shows the variation of the bound with the probability of detection and clutter density. Example 2 verifies the effectiveness of the bound by indicating the performance limitations of three classical multi-target JDE algorithms, which are multiple hypothesis tracking (MHT) filter, probability hypothesis density (PHD) filter, and cardinalized PHD filter.