An improved Hessian matrix for recursive maximum likelihood ARMA estimation

Much work has been directed towards the development of recursive algorithms for estimating the parameters of a signal characterised by an autoregressive moving average signal model. Many of the techniques that have been proposed employ an approximation to the Hessian matrix of the prediction error. Often this approximation is not accurate, resulting in a degradation in the quality of the parameter estimates and an increase in the variance of these estimates. The paper presents a modified recursive maximum likelihood (MRML) algorithm that uses the true Hessian matrix. The performance of this algorithm is compared to that of other algorithms via numerical examples. A significant improvement in performance can be obtained via the proposed MRML algorithm