Abstract:  In this paper we shall present a new method to analyze the convergence property of the Kalman filter based parameter estimation algorithms. This method for convergence analysis is mainly based on some matrix inequalities and is more simple than some of the existing approaches in the literature. This method can simultaneously provide both lower and upper bounds on the exponential convergence rate as the functions of  bounds of the related matrices, such as the covariance matrices. A simulation example is provided to illustrate the convergence property of the Kalman filter based algorithms.
    Key Words: Kalman filter, recursive parameter estimation, exponential convergence, convergence rate.