Rao-blackwellized out-of-sequence processing for mixed linear/nonlinear state-space models

We investigate the out-of-sequence measurements particle filtering problem for a set of conditionally linear Gaussian state-space models, known as mixed linear/nonlinear state-space models. Two different algorithms are proposed, which both exploit the conditionally linear substructure. The first approach is based on storing only a subset of the particles and their weights, which implies low memory and computational requirements. The second approach is based on a Rao-Blackwellized forward filter/backward simulator, adapted to the out-of-sequence filtering task with computational considerations for enabling online implementations. Simulation studies on two examples show that both approaches outperform recently reported particle filters, with the second approach being superior in terms of tracking performance.