Summary
Another special case where the forward and backward recursions developed in Chap. 5 may be implemented exactly is when the considered state-space model is linear and Gaussian. The corresponding algorithms are commonly known as the Kalman filter and the Kalman smoother. The recursions follow immediately from the generic formulae of Chap. 5, but in this setting they become linear algebra calculations. Various alternative, mathematically equivalently but computationally different, recursions can be obtained. This chapter provides insights into these possibilities and touches upon the practical implementation of such recursions.
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Chopin, N., Papaspiliopoulos, O. (2020). Linear-Gaussian State-Space Models. In: An Introduction to Sequential Monte Carlo. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-47845-2_7
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DOI: https://doi.org/10.1007/978-3-030-47845-2_7
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