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A unified filter for simultaneous input and state estimation of linear discrete-time stochastic systems. (English) Zbl 1329.93148
Summary: In this paper, we present a unified optimal and exponentially stable filter for linear discrete-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense, without making any assumptions on the direct feedthrough matrix. We also provide the connection between the stability of the estimator and a system property known as strong detectability, and discuss the global optimality of the proposed filter. Finally, an illustrative example is given to demonstrate the performance of the unified unbiased minimum-variance filter.

MSC:
 93E11 Filtering in stochastic control theory 93E10 Estimation and detection in stochastic control theory 93C05 Linear systems in control theory 93E03 Stochastic systems in control theory (general) 93C55 Discrete-time control/observation systems
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