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Filtering and smoothing in an H setting. (English) Zbl 0758.93074
A fairly complete theory of filtering and smoothing with an H performance criterion is developed for a linear quadratic problem with finite or infinite horizon. Necessary and sufficient conditions for the existence of estimators achieving a prescribed performance bound are derived. For the smoothing problem a solution is presented that minimizes the performance measure. This smoother turns out to be the minimum smoother so that the optimal smoothers for the respectie H 2 - and H -problems are the same.
MSC:
93E11Filtering in stochastic control
93E14Data smoothing (stochastic systems)