Approximate Conditional Mean Particle Filtering for Linear/Nonlinear Dynamic State Space Models

We consider linear systems whose state parameters are separable into linear and nonlinear sets, and evolve according to some known transition distribution, and whose measurement noise is distributed according to a mixture of Gaussians. In doing so, we propose a novel particle filter that addresses the optimal state estimation problem for the aforementioned class of systems. The proposed filter, referred to as the approximate conditional mean particle filter (ACM-PF), is a combination of the approximate conditional mean filter and the sequential importance sampling particle filter. The algorithm development depends on approximating a mixture of Gaussians distribution with a moment-matched Gaussian in the weight update recursion. A condition indicating when this approximation is valid is given. In order to evaluate the performance of the proposed algorithm, we address the blind signal detection problem for an impulsive flat fading channel and the tracking of a maneuvering target in the presence of glint noise. Extensive computer simulations were carried out. For computationally intensive implementations (large number of particles), the proposed algorithm offers performance that is comparable to other state-of-the-art particle filtering algorithms. In the scenario where computational horsepower is heavily constrained, it is shown that the proposed algorithm offers the best performance amongst the considered algorithms for these specific examples.