Abstract <p>The paper considers the extended Rao−Blackwellization method (ERB) and the ERB-based suboptimal algorithm designed to solve the problem of estimating a time-varying state vector described by a linear time-invariant equation using nonlinear measurements within the Bayesian approach. The ERB features and the main stages of designing the proposed algorithm are explained by the example of solving a problem of estimating a Markov process frequently used in processing of navigation information, generated by multiple integration of an input signal in the form of white noise. The efficiency and advantages of the proposed algorithm in comparison with the conventional sequential Monte Carlo-based algorithm are illustrated by solving the map-aided navigation problem in its simplest formulation. Prospects for further studies, in particular, using ERB in solving applied problems of navigation and trajectory information processing are discussed.</p>