Unbiased minimum-variance state estimation for linear systems with unknown input

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. (C) 2008 Elsevier Ltd. All rights reserved.