The Kalman filter based recursive algorithm: Windup and its avoidance

A theoretical analysis is given which shows that the covariance matrix in the Kalman filter based parameter estimator increases at least linearly when the input is not persistently exciting. This windup phenomenon which is the same as that in the exponential forgetting least squares algorithm, is undesirable and even unacceptable in some applications. To overcome it a new algorithm is proposed, in which the constant covariance matrix of the parameter variation is replaced by a time-varying sequence consisting of the regression vector.