Linear smoothing for discrete-time systems in the presence of correlated disturbances and uncertain observations

This paper considers the smoother with the least mean-squared error (LMSE) within the class of linear smoothers for discrete linear systems whose observations may contain noise alone and the probability of this occurring is known (systems with uncertain observations). Also, we assume that state and measurement noises are correlated. The present results, together with Hermoso-Linares's results on prediction and filtering, give a complete treatment of the LMSE linear estimation problem for such systems.<
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