Design of Rao–Blackwellized Point-Mass Smoother for Conditionally Linear and Gaussian Models

This paper deals with the state estimation of nonlinear stochastic dynamic systems. Stress is laid on the numerical solution to the functional recursive relations providing conditional probability density functions of the state. In particular, a novel Rao-Blackwellized point-mass smoother with two implementations is proposed for conditionally linear and Gaussian state-space models, where part of the state vector is estimated by a computationally expensive point-mass smoother, whereas the remaining part of the state vector by a set of computationally efficient linear smoothers. Such decomposition results in a computationally less demanding smoother than the standard point-mass smoother for the considered models. The properties of the proposed smoother are discussed and its performance is numerically illustrated.