In this paper, the marginal Rao-Blackwellized particle filter (MRBPF), which fuses the Rao-Blackwellized particle filter (RBPF) algorithm and the marginal particle filter (MPF) algorithm, is presented. The state space is divided into linear and non-linear parts, which can be estimated separately by the MPF and the optional Kalman filter. Through simulation in the terrain aided navigation (TAN) domain, it is demonstrated that, compared with the RBPF, the root mean square errors (RMSE) and the error variance of the nonlinear state estimations by the proposed MRBPF are respectively reduced by 29% and 96%, while the unique particle count is increased by 80%. It is also found that the MRBPF has better convergence properties, and analysis has shown that the existing RBPF is nothing more than a special case of the MRBPF.
Yin, J., Zhang, J., & Klaas, M. (2007). The marginal Rao-Blackwellized particle filter for mixed linear/nonlinear state space models. Chinese Journal of Aeronautics, 20(4), 346–352. https://doi.org/10.1016/S1000-9361(07)60054-5