Abstract
This paper is concerned with the Kalman filtering problem for discrete-time linear systems corrupted by finite-step autocorrelated measurement noise which is a linear function of several mutually uncorrelated random vectors. An optimal Kalman filter is presented using state augment approach. Then, by new techniques developed in this paper, the convergence conditions of the optimal Kalman filter are established by equivalently considering the convergence of the prediction state error covariance of an augmented system where, different from the existing results, the matrix difference equation of the prediction augmented-state error covariance (PASEC) has a unique structure, that is, the matrix difference equation of the PASEC does not contain the measurement noise covariance and the process noise covariance of the augmented system in the equation is not positive definite. The main novelty of this paper is the theoretical analysis of the asymptotic convergence behavior of the PASEC whose matrix difference equation has the unique structure mentioned above. An example is presented to illustrate the effectiveness and advantages of the proposed new design strategy.
Published Version
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