An analysis of the divergence problem in the Kalman filter

The effect of modeling errors in a linear discrete stochastic system upon the Kalman filter state estimates is investigated. Errors in both plant dynamics and noise covariances are permitted. The errors are characterized in such a manner that a linear recursion relation for the actual estimation error covariances can be derived. Conditions which guarantee that the covariance matrix remains bounded are described in terms of the asymptotic stability of the homogeneous part of the covariance equation and the boundedness of the forcing terms in the inhomogeneous equation.