Multi-Target Bayes Filtering Based On Random Finite Sets

Multi-target tracking is a challenging problem in the complex environment, which is affected by clutter, missed detection, targets’ appearance and disappearance, etc. Sponsored by the Na-tional Natural Science Foundation of China and Aeronautical Science Foundation of China, this dissertation focuses on estimation of multi-target and multiple extended targets in the complex environment based on the multi-target Bayes filtering theory in random finite sets. The main con-tributions of this dissertation are as follows:(1) A multiple-model (MM) Bernoulli filter is presented for joint maneuvering target detection and tracking in the complex environment. A Gaussian mixture (GM) MM Bernoulli filter for linear Gaussian models and a sequential Monte Carlo (SMC) MM Bernoulli filter for nonlinear models are presented.(2) The fast implementation of the multi-Bernoulli (MB) filter is studied. Firstly, a GM-MB filter with gating is presented. Then the gating based on the Monte Carlo (MC) approximation is adopted for the SMC-MB filter. The proposed approaches improve the real-time performance of MB filters without the degradation in estimation accuracy.(3) Several MB filters for nonlinear models are studied. By incorporating the square-root cubature Kalman (SCK) filter into the GM-MB filter, an SCK-GM-MB filter is presented for non-linear models. Several MM-MB filters for nonlinear models are studied. An SCK-GM-MM-MB filter is presented for nonlinear models. The proposed approaches improve the numerical stability of multi-target estimation algorithms for nonlinear models.(4) An SMC implementation of the ET-MB filter is presented to estimate multiple extended targets for nonlinear models in the complex environment. For estimation of multiple maneuver-ing extended targets in the complex environment, an MM-ET-MB filter is presented. Then the GM-MM-ET-MB filter for linear Gaussian models and the SMC-MM-ET-MB filter for nonlinear models are derived.(5) A Gaussian inverse Wishart (GIW) ET-MB filter is proposed to jointly estimate the num- ber, states, and extensions of multiple extended targets in the complex environment. By incorpo-rating the random matrix approach into the ET-MB filter, the prediction and update of the GIW-ET-MB filter are derived with necessary assumptions and approximations.