Probability density evolution filter

TL;DR

This paper introduces the probability density evolution filter (PDEF), a new Bayesian filtering approach that predicts and updates system state probabilities using density evolution equations and Chebyshev polynomial collocation, achieving high accuracy without resampling.

Contribution

The paper proposes the PDEF, combining density evolution and Chebyshev methods, providing a resampling-free alternative to particle filters with comparable accuracy.

Findings

PDEF achieves accuracy close to particle filter.

PDEF does not require resampling.

PDEF outperforms UKF in the example.

Abstract

Based on probability density evolution method (PDEM) and Bayes law, a new filter strategy is proposed, in which the prior probability of system state of interest is predicted by solving the general density evolution equation (GDEE), the posterior probability of system state is then updated in terms of Bayes formula. Furthermore, a Chebyshev polynomial-based collocation method is employed to obtain numerical solutions of the prior probability. An illustrative example is finally presented to validate the probability density evolution filter (PDEF) in comparison to particle filter (PF) and UKF. Overall, PDEF exhibits accuracy close to PF without any resampling algorithm.