A direct sampling particle filter from approximate conditional density function supported on constrained state space

Constraints on the state vector must be taken into account in the state estimation problem. Recently, acceptance/rejection and projection methods are proposed in the particle filter framework for constraining the particles. A weighted least squares formulation is used for constraining samples in unscented and ensemble Kalman filters. In this paper, direct sampling from an approximate conditional probability density function (pdf) is proposed. It is obtained by approximating the a priori pdf as a Gaussian. The support of the conditional density is a subset of the intersection of two supports, the 3-sigma bounds of the priori Gaussian and the constrained state space. A direct sampling algorithm is proposed for handling linear and nonlinear equality and inequality constraints. The algorithm uses the constrained mode for nonlinear constraints.