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In the paper we study interacting particle approximations of discrete time and measure-valued dynamical systems. These systems have arisen in such diverse scientic disciplines as physics and signal processing. We give conditions for the so-called particle density proles to converge to the desired distribution when the number of particles is growing. The strength of our approach is that is applicable to a large class of measure-valued dynamical systems arising in engineering and particularly in nonlinear ltering problems. Our second objective is to use these results to solve numerically the nonlinear ltering equation. Examples arising in uid mechanics are also given.

Measure-valued processes and interacting particle systems. Application to nonlinear filtering problems