Application of particle filter algorithms for solving nonlinear filtering problems

Аuthors

Volkov V. A.^*, Kudryavtseva I. A.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: vlad_ell@inbox.ru
**e-mail: irina.home.mail@mail.ru

Abstract

The idea of particle filters dates back to the fifties. However, rediscovering particle filters occurred in 1990-s with the paper by Rosenbluth M. N., Rosenbuth A.W. «Monte Carlo calculation of the average extension of molecular chains». An important resampling technics was discovered. The progress in research became visible in 2000-s due to the growth of computational powers. Particle filter technique is becoming involved in many spheres of science: stochastic control theory, signal and image processing, satellite-based navigation system.

Particle filters became the very popular method for solving filtering problems in non-linear and non-Gaussian cases. The algorithms combine Bayesian approach with Monte-Carlo technique. Moreover, particle filters don’t involve local linearization or another functional approximation.

The solutions of stochastic discrete filtering problem by using Bootstrap Particle Filter with Residual Resampling, Bootstrap Particle Filter with Roulette wheel Resampling, Monte-Carlo Particle filter, Unscented Particle Filter are presented. Described task is solved by developed Software solution, based on MATLAB and Microsoft Visual Studio C# 2010 platforms. The results are compared to the results obtained earlier by other authors.

Keywords:

nonlinear filtering problems, particle filters, bootstrap particle filter with Residual Resampling, Bootstrap Particle Filter with Roulette wheel Resampling, Monte-Carlo Particle filter, Unscented Particle Filter

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