Generalised particle filters with Gaussian mixtures
2015 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 125, no 7, 2643-2673 p.Article in journal (Refereed) Published
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 L-2-convergence rate for the approximating system and show some numerical examples to test the new algorithm.
Place, publisher, year, edition, pages
2015. Vol. 125, no 7, 2643-2673 p.
Stochastic partial differential equation, Nonlinear filtering, Zakai equation, Particle filters, Gaussian mixtures, L-2-convergence
IdentifiersURN: urn:nbn:se:uu:diva-253224DOI: 10.1016/j.spa.2015.01.008ISI: 000353602000005OAI: oai:DiVA.org:uu-253224DiVA: diva2:824623