A robust particle filter for state estimation -- with convergence results, Report no. LiTH-ISY-R-2822

Particle lters are becoming increasingly important and useful for state estimation in nonlinear systems. Many lter versions have been suggested, and several results on convergence of lter properties have been reported. However, apparently a result on the convergence of the state estimate itself has been lacking. This contribution describes a general framework for particle lters for state estimation, as well as a robusti ed lter version. For this version a quite general convergence result is established. In particular, it is proved that the particle lter estimate convergences w.p.1 to the optimal estimate, as the number of particles tends to in nity.