An Efficient Constrained Gaussian Particle Filter

The paper deals with a state estimation of nonlinear stochastic dynamic systems subject to a nonlinear inequality constraint. A special focus is paid to particle filters, which provide an estimate of the whole probability density as opposed to the local filters, such as the extended Kalman filter or the unscented Kalman filter, which provide a point estimate only. Within the particle filtering framework, there are several approaches to the constrained state estimation, mostly based on discarding samples violating the constraint with a possible increase of their number to improve the estimate quality. The paper aims at proposing a modification to an importance function of the particle filter in order to increase efficiency of sampling while keeping the computational complexity low. The proposed modification is utilized within the Gaussian particle filter which is advantageous for its low computational complexity. Complexity and estimation quality of the proposed constrained Gaussian particle filter is compared to other constrained particle filters in a numerical example.