This chapter provides the general formulation of the optimal Bayesian filtering. Regarding the chosen criterion for optimality, different estimators are obtained including minimum mean‐square error estimator, risk‐sensitive estimator, maximum a posteriori estimator, minimax estimator, the most probable estimator, and maximum likelihood estimator. However, the Bayesian solution is a conceptual solution and must be approximated in many practical situations. Depending on the approximation method, different filtering algorithms are derived, which provide computationally tractable suboptimal Bayesian solutions. Fisher information provides a measure of the ability to estimate a quantity as well as a measure of the state of disorder in a system. In a related context, as a performance measure, the Cramér–Rao lower bound represents the lowest possible mean‐square error in the estimation. An iterative procedure is presented for online computing of the posterior Cramér–Rao lower bound for Bayesian nonlinear filters based on the corresponding state‐space models.
Bayesian Paradigm and Optimal Nonlinear Filtering
Nonlinear Filters ; 41-47
12.04.2022
7 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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