A method to solve the recursive Bayesian estimation problem by making use of orthogonal series expansions of the involved probability density functions is presented. The coefficients of the expansion for the posterior density are then calculated recursively via prediction and update equations. The method has two main benefits: it provides high estimation accuracy at a relatively low computational cost and it is highly amenable to parallel implementation. An application to a bearings-only tracking problem shows that the proposed method performs with the same accuracy as the particle filter but at a 24 times lower computational cost. A parallel implementation on a shared-memory multicore machine demonstrates that linear speedup in the number of cores is achievable.
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