Data filtering based multi-innovation extended gradient method for controlled autoregressive autoregressive moving average systems using the maximum likelihood principle

This paper combines the data filtering technique with the maximum likelihood principle for parameter estimation of controlled autoregressive ARMA (autoregressive moving average) systems. We use an estimated noise transfer function to filter the input–output data and derive a filtering based maximum likelihood multi-innovation extended gradient algorithm to estimate the parameters of the systems by replacing the unmeasurable variables in the information vectors with their estimates. A maximum likelihood generalized extended gradient algorithm is given for comparison. A numerical simulation is given to support the developed methods.