Particle filtering in the Dempster–Shafer theory

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.

► A particle filter algorithm is presented within the Dempster–Shafer framework.
► Ignorance can be modeled with respect to an underlying hidden Markov process.
► Recursive filtering equations are derived for belief functions.
► Importance sampling is used to efficiently incorporate new observations.
► The resulting algorithm forms a strict generalization of Bayesian filtering.