This thesis presents the derivation and implementation of a modified Extended Kalman Filter used for Joint state and parameter estimation of linear discrete-time systems operating in a, stochastic Gaussian environment. A novel derivation for the discrete-time Extended Kalman Filter is also presented. In order to eliminate the main deficiencies of the Extended Kalman Filter, which are divergence and biasedness of its estimates, the filter algorithm has been modified. The primary modifications are due to Ljung, who stated global convergence properties for the modified Extended Kalman Filter, when used as a parameter estimator for linear systems.

Implementation of this filter is further complicated by the need to initialize the parameter estimate error covariance inappropriately small, to assure filter stability. In effect, due to this inadequate initialization process the parameter estimates fail to converge. Several heuristic methods have been developed to remove the effects of the inadequate initial parameter estimate covariance matrix on the filter's convergence properties.

Performance of the improved modified Extended Kalman Filter is compared with the Recursive Extended Least Squares parameter estimation scheme.