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Extension of unbiased minimum-variance input and state estimation for systems with unknown inputs. (English) Zbl 1175.93213
Summary: This paper extends the existing results on joint input and state estimation to systems with arbitrary unknown inputs. The objective is to derive an optimal filter in the general case where not only unknown inputs affect both the system state and the output, but also the direct feedthrough matrix has arbitrary rank. The paper extends both the results of S. Gillijns and B. De Moor [Automatica 43, No. 5, 934–937 (2007; Zbl 1117.93366)] and M. Darouach, M. Zasadzinski and M. Boutayeb [ Automatica 39, No. 5, 867-876 (2003; Zbl 1036.93058)]. The resulting filter is an Extension of the Recursive Three-Step Filter (ERTSF) and serves as a unified solution to the addressed unknown input filtering problem. The relationship between the ERTSF and the existing literature results is also addressed.

MSC:
93E10 Estimation and detection in stochastic control theory
93C41 Control/observation systems with incomplete information
93E11 Filtering in stochastic control theory
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