The theory of observer-estimators for linear discrete-time systems is described. Both deterministic and stochastic cases are considered; in particular, the case that some observations are noise free while others are noisy is considered. Asymptotic properties for both time-varying and time-invariant systems are analyzed and the influence of observability and detectability assumptions is considered. The results unify approaches to deterministic and stochastic state estimation problems for linear discrete-time systems. Optimal filtering in the presence of colored noise is considered as a special case.
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Edison Tse (1973) studied this question.
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