Joint IMMPDA Particle filter Preprint Proceedings 6th Int. Conf on Information Fusion, 8-11 July 2003, Cairns, Queensland, Australia Henk A.P. Blom and Edwin A. Bloem National Aerospace Laboratory NLR Amsterdam, The Netherlands e-mail: blom@nlr.nl, bloem@nlr.nl Abstract – For the problem of tracking multiple manoeu- vering targets in clutter and missing measurements the pa- per develops a Joint IMMPDA type of particle filter and compares this with other IMMJPDA based filters through Monte Carlo simulation for a simple example. Keywords: Bayesian estimation, Multitarget tracking, Sudden maneuvers, Clutter, Missed detections, Hidden Markov model, Descriptor system, Particle filtering. 1 Introduction McGinnity & Irwin (2000, 2001), Doucet et al. (2001) and Musso et al. (2001) showed that estimation of jump linear systems with particle filter approaches has certain performance advantages over the Interacting Multiple Model algorithm (Blom, 1984; Blom & Bar-Shalom, 1988). Similarly, for the problem of tracking multiple targets in clutter and missed detections, Avitzour (1995) and Gordon (1997) have reported that particle filters outperform Gaussian density approximations of Bayesian filters using the bootstrap approach of Gordon et al. (1993). The aim of this paper is to extend the bootstrap particle filtering approach of McGinnity & Irwin (2000) to situations of possibly false and missing observations of multiple maneuvering targets. Following Blom & Bloem (2002a, 2002b) this multitarget tracking problem is first presented as one of filtering for a descriptor system with both i.i.d. and Markovian coefficients. For this descriptor system we develop a characterization of the evolution of the exact conditional density function. The specialty of this exact equation is that both the IMM step and the PDA step are performed jointly for all targets. In contrast with this the IMMJPDA of Chen & Tugnait (2001) jointly performs the PDA step only. Following the exact equations, we develop a Joint 0 This research has been performed with support of the European Com- mission through the HYBRIDGE project. IMMPDA Particle (JIMMPDAP) which evaluates the exact equations through the particle filtering approach of McGinnity & Irwin (2000). Through Monte Carlo simulations for a simple example this novel algorithm is compared with the IMMJPDA of Chen & Tugnait (2001) and the track coalescence avoiding IMMJPDA* of Blom & Bloem (2002a,b). The paper is organized as follows. Section 2 formu- lates the problem considered. In this way it is ensured that there is no unambiguity which mathematical model is addressed. Section 3 develops an exact Bayesian characterization of the evolution of the conditional density for the state of the multiple targets. Section 4 develops the JIMMPDA Particle filter. Section 5 shows the effectiveness of this filter through Monte Carlo simulation results. Finally, Section 6 draws conclusions. 2 Problem formulation Following Blom & Bloem (2002a,b) the problem is for- mulated in terms of filtering for a jump linear descriptor system with both Markovian switching and i.i.d. coeffi- cients: x t+1 = A(θ t+1 )x t + B(θ t+1 )w t (1) Φ (ψ ∗ t )y t = v ∗ t if L t >D t , (2) Φ (ψ t )y t = χ t Φ (φ t )[H(θ t )x t + G(θ t )v t ] if D t > 0 (3) Target evolution eq. (1) The underlying model components are follows: x t △ = Col{x 1 t ,...,x M t }, θ t △ = Col{θ 1 t ,...,θ M t }, A(θ) △ = Diag{a 1 (θ 1 ),...,a M (θ M )}, B(θ) △ = Diag{b 1 (θ 1 ),...,b M (θ M )}, w t △ = Col{w 1 t ,...,w M t }, where x i t is the n-vectorial state of the i-th target at