A Framework for Globally Optimal State Estimation for Systems with Unknown Inputs (II): Untrammeled Approach

Abstract

AbstractIn this paper, a globally optimal state estimation, in light of unbiased minimum‐variance filtering over all linear unbiased estimators, is addressed. This paper is the second part of a comprehensive extension of original work by Hsieh, with the main aim being to develop an untrammeled filtering framework that does not need any transformations 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 more general derivation of the globally optimal state estimator (GOSE) for the GUMVSE is presented; (ii) a more direct proof, verifying the global optimality of the GOSE by finding the global minimum of the trace of the estimation error covariance, is constructed; and (iii) an application of the proposed result to re‐derive a specific transformation‐based GOSE, i.e., the recursive optimal filter proposed by Cheng et al., is illustrated. The relationship with previously proposed results is also addressed. 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