Particle filtering with analytically guided sampling

Particle filtering (PF) is a popular nonlinear estimation technique and has been widely used in a variety of applications such as target tracking. Within the PF framework, one critical design choice is the selection of the proposal distribution from which particles are drawn. In this paper, we advocate using as proposal distribution a Gaussian-mixture-based approximation of the posterior probability density function (pdf) after taking into account the most recent measurement. The novelty of our approach is that the parameters of each Gaussian used in the mixture are determined analytically to match the modes of the underlying unknown posterior pdf. As a result, particles are sampled along the most probable regions of the state space, hence reducing the probability of particle depletion. Based on the analytically determined proposal distribution, we introduce a novel PF, termed analytically guided sampling-based PF, which is validated in range-only and bearing-only target tracking.