Parameter Estimation of ARMA Process by Taking into Consideration of ∂k_x(t)/∂α^T·ε(t)

Abstract

This paper deals with the improvement of convergence rate or estimation accuracy of the estimates in ARMA parameter estimation. A recursive parameter estimator is developed by using the method of white-noise estimation for linear discrete-time systems. The main feature of the proposed method is to take into consideration of ∂k_x(t)/∂α^T·ε(t) which influences considerably to the performance of RPE (Recursive Prediction Error) or EKF (Extended Kalman Filter) estimator. It is shown that significance considering this term has the effect closing the estimation error covariances with Rao-Cramer's lower bound. Resultant algorithm proposed is constructed by linking RPE estimator with Kalman filter.
Numerical experiment indicates that the convergence rate or the estimation accuracy of parameter estimates is considerably improved compared with the standard RPE method.