Analysis of a sequential Monte Carlo optimization methodology

We investigate a family of stochastic exploration methods that has been recently proposed to carry out estimation and prediction in discrete-time random dynamical systems. The key of the novel approach is to identify a cost function whose minima provide valid estimates of the system state at successive time instants. This function is recursively optimized using a sequential Monte Carlo minimization (SMCM) procedure which is similar to standard particle filtering algorithms but does not require a explicit probabilistic model to be imposed on the system. In this paper, we analyze the asymptotic convergence of SMCM methods and show that a properly designed algorithm produces a sequence of system-state estimates with individually minimal contributions to the cost function. We apply the SMCM method to a target tracking problem in order to illustrate how convergence is achieved in the way predicted by the theory.