Extended recursive maximum-likelihood identification algorithm

An extension of the well known recursive maximum-likelihood or extended least-squares identification algorithm to improve its rate of convergence is presented. The extension is to include explicitly in the model giving rise to the algorithm the errors in the noise-generating sequence normally ignored. The extended algorithm is related to the original, much as an extended Kalman filter is related to an ordinary Kalman filter. The paper compares the algorithm with a similar, but differently motiviated, one, recently described by Ljung. The performance of the algorithm and its optimisation are discussed with reference to computational results from Monte Carlo tests.