Adaptive State Estimation for Systems with White and Coloured Noise

Abstract

<p>The problem of adaptive state estimation which involves the identification of the Kalman gain matrix without a priori information on the noise statistics is presented. A scheme incorporating an identification algorithm and a tracking algorithm is proposed. This scheme provides a powerful approach for adaptive state estimation.</p> <p>An ARMA model for system description is derived for preliminary analysis of the noise transition matrix when the observation noise is sequentially correlated.</p> <p>The innovations process for systems with coloured observation noise is shown to be white for optimum filtering.</p> <p>Simulations are performed on an inertial navigation system for both white and coloured observation noise. Numerical results indicate the superiority of the filter with tracking over one without. Performance of the filter for coloured observation noise confirms the theoretical derivation of the ARMA model.</p>