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Abstract: The problem of state estimation for a linear system with unknown input, which affects both the system and the output, is discussed in this paper. A recursive optimal filter with global optimality in the sense of unbiased minimum variance over all linear unbiased estimators, is provided. The necessary and sufficient condition for the convergence and stability is also given, which is milder than existing approaches. [Copyright &y& Elsevier]

It is shown how the criteria of efficiency and robustness can be integrated fruitfully in a single optimality criterion within the framework of the Unified Theory (Godambe 1955). This is achieved by extending the scope of the usual model-based estimation using appropriate sampling designs. Some situations of common occurrence in survey practice are discussed with a numerical study. [ABSTRACT FROM AUTHOR]