Particle filtering in the Dempster--Shafer theory

• Authors: Thomas Reineking
• Venue: International Journal of Approximate Reasoning
• Year: 2011

This paper derives a particle filter algorithm within the Dempster-Shafer framework. Particle filtering is a well-established Bayesian Monte Carlo technique for estimating the current state of a hidden Markov process using a fixed number of samples. When dealing with incomplete information or qualitative assessments of uncertainty, however, Dempster-Shafer models with their explicit representation of ignorance often turn out to be more appropriate than Bayesian models. The contribution of this paper is twofold. First, the Dempster-Shafer formalism is applied to the problem of maintaining a belief distribution over the state space of a hidden Markov process by deriving the corresponding recursive update equations, which turn out to be a strict generalization of Bayesian filtering. Second, it is shown how the solution of these equations can be efficiently approximated via particle filtering based on importance sampling, which makes the Dempster-Shafer approach tractable even for large state spaces. The performance of the resulting algorithm is compared to exact evidential as well as Bayesian inference.