Joint Particle Filtering of Multiple Maneuvering Targets From Unassociated Measurements

In the literature approximate Bayesian approaches towards maintaining tracks of multiple maneuvering targets from unassociated measurements have focussed on the development of combinations of Interacting Multiple Model (IMM) and Joint Probabilistic Data Association (JPDA) approaches. Initially, combinations of IMM and JPDA have been developed along two heuristic directions. Bar-Shalom et al. [4] heuristically developed an IMMJPDA-Coupled filter for situations where the measurements of two targets are unresolved during periods of close encounter. The filters of the individual targets are coupled through cross-target-covariance terms. The filtering results obtained have not been very encouraging to continue this heuristic approach. De Feo et al. [20] combined JPDA and a rather crude approximation of IMM, under the name IMMJPDA. The first proper combination of IMM and JPDA was developed by Chen and Tugnait [18]. Focus of this development was on showing that fixed-lag IMMJPDA smoothing performed far better than IMMJPDA filtering at the cost of 3 scans delay. In [9], [10] we used the descriptor system approach [8] to develop a track-coalescence-avoiding version of IMMJPDA (for short IMMJPDA¤). Moreover, we showed that both IMMJPDA and IMMJPDA¤ perform much better than just applying IMMPDA filtering per maintained track. In spite of these developments it remains unclear how IMMJPDA and IMMJPDA¤ filtering performs in comparison with the exact Bayesian filter. This motivates us to study the Sampling Importance Resampling (SIR) based Particle Filter (PF) paradigm [21, 28, 43] for maintaining tracks of multiple maneuvering targets from unassociated measurements. During the last decade this paradigm has been recognized as a practical means for approximating an exact Bayesian filter arbitrarily well. This has stimulated the development of a large variety of particle filters (e.g. [1, 22, 38, 42]) that typically outperform established approximate non-linear filtering and target track maintenance approaches such as Extended Kalman Filtering, Probabilistic Data Association (PDA), the Interacting Multiple Model (IMM) algorithm, and their combinations. The extension of these results to multiple target tracking situations has also received significant attention. Early on it was recognized that the JPDA formalism provided a logical starting point for this development. Gordon [26] developed a SIR-PF version by replacing JPDA’s Gaussian density by a density the evolution of which is approximated with help of a SIR particle filter. Avitzour [2] developed a more advanced SIR particle filter by using joint-target particles; we refer to this as SIR joint PF. Karlsson and Gustafsson [30] compared the RMS position errors of a SIR joint PF with those of a JPDA filter for maintaining tracks in an example of two perpendicular crossing targets. For this “easy” example the difference in performance