A framework for globally optimal state estimation for systems with unknown inputs (I): transformation approach

Abstract

In this paper, a globally optimal state estimation is addressed in light of the conventional Luenberger observer-type filter. This paper is the first part of a comprehensive extension of an original work by Hsieh, with the main aim being to develop a transformation-based filtering framework for global unbiased minimum-variance state estimation (GUMVSE) for systems with unknown inputs that affect both the system and the output. The main contributions of this paper are (i) a complete optimal solution for the GUMVSE is addressed, where both the globally optimal state filter and predictor are presented, and (ii) additional insights for implementing the globally optimal state filter are highlighted via the proposed decorrelation constraint. Compared with existing results, the proposed globally optimal filter has the most general filter form among all transformation-based globally optimal filters in the sense that it does not use any specific unknown input transformation matrix in the derivation. A simulation example is given to illustrate the usefulness of the proposed results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society