Generalised particle filters with Gaussian mixtures

D. Crisan and K. Li

Stochastic Processes and their Applications, 2015, vol. 125, issue 7, 2643-2673

Abstract: Stochastic filtering is defined as the estimation of a partially observed dynamical system. Approximating the solution of the filtering problem with Gaussian mixtures has been a very popular method since the 1970s. Despite nearly fifty years of development, the existing work is based on the success of the numerical implementation and is not theoretically justified. This paper fills this gap and contains a rigorous analysis of a new Gaussian mixture approximation to the solution of the filtering problem. We deduce the L2-convergence rate for the approximating system and show some numerical examples to test the new algorithm.

Keywords: Stochastic partial differential equation; Nonlinear filtering; Zakai equation; Particle filters; Gaussian mixtures; L2-convergence (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2015.01.008

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