A particle filter based on a constrained sampling method for state estimation

Increasingly in practical applications, nonlinearity, non-Gaussianity, and constraint are considered when dealing with state estimation problems. This paper proposes a novel constrained particle filter (PF) approach for state estimation, where three constraint strategies are implemented: First, to ensure the validity of prior, prior particles are restrictedly sampled in the constraint region by a constrained inverse transform sampling method. Second, if constraints are imposed on the posterior, a constrained re-sampling method, similar to the existing acceptance/rejection constrained PF method, is proposed to restrict the posterior particles to be generated from the valid prior particles. Third, the validity of state estimation is ensured through adjustment of part of posterior particles according to the posterior density function of states, which is accomplished by deleting uniformly selected violated posterior particle and uniformly selected valid posterior particle for reproduction. Compared with the existing methods, the proposed method implements constraints with better physical interpretation, and involves no numerical optimization procedure and no restrictive assumptions about the distributions. Simulation results demonstrate its effectiveness.