Asymptotic convergence properties of the extended Kalman filter using filtered state estimates

In a recent paper, Ljung has given a convergence analysis of the extended Kalman filter (EKF) as a parameter estimator for linear systems. The analysis is done for a version of the EKF using predicted values of the state vector. In this note a similar convergence analysis is done for the EKF using filtered values of the state vector. The convergence properties of the two algorithms are similar, but not identical. The recalculation of a simple example given by Ljung indicates that using the filtered estimate of the state vector gives improved convergence properties of the algorithm.