Iterated Gain-based Stochastic Filters for Dynamic System Identification: Annealing-type Iterations and the Filter Bank

Abstract: A novel form of nonlinear stochastic filtering employing an annealing-type iterative update scheme, aided by the introduction of an artificial diffusion parameter and based on the Gaussian sum approximations of the prior and posterior densities, is presented. The proposed Monte Carlo filter bank conforms in structure to the parent nonlinear filtering (Kushner-Stratonovich) equation, as reflected in the additive gain-based updates, and possesses excellent mixing properties enabling better explorations of the phase space of the state vector. The performance of the filter bank, presently assessed against a few carefully chosen numerical examples, provide ample evidence of its substantively improved performance in terms of filter convergence and estimation accuracy vis-`a-vis a few other competing filters especially in higher dimensional dynamic system identification problems including cases that may demand estimating relatively minor variations in the parameter values from their reference states.