A noise attenuation property of the Kalman filter

Abstract

A state estimation problem is considered for linear systems driven by white noise. The observation noise is assumed to be a second-order process fully unknown except for the total mean power. The Kalman-Bucy filter is adopted here as state estimator. The main result is a necessary and sufficient condition, stated in terms of the Hamiltonian matrix, for the Kalman-Bucy filter to guarantee error covariance less than that performed under the nominal condition where the observation noise is white.