Abstract
This paper is a tutorial survey which focuses on some developments in statistical filtering achieved since the introduction of Wiener and Kalman filters for linear gaussian problems. Kalman filters (including smoothers and predictors) are reviewed with reference to their interesting properties and also their fundamental limitations in nonlinear or unknown environments. For nonlinear filtering problems, the relevance of the near optimal extended Kalman filters, gaussian sum filters, and bound optimal filters are discussed. For adaptive linear filtering and prediction, connections of the linear gaussian theory with recursive least squares parameter estimation theory are seen to yield adaptive filtering algorithms which are asymptotically optimum, and connections with recursive a posteriori probability updating algorithms are seen to yield optimal solutions to model approximation, fault detection, and adaptive filtering problems.
Work supported by the Australian Research Grants Committee.
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Moore, J.B. (1978). Statistical filtering. In: Coppel, W.A. (eds) Mathematical Control Theory. Lecture Notes in Mathematics, vol 680. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065316
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DOI: https://doi.org/10.1007/BFb0065316
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