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

•The filtering technique and the multi-innovation identification theory are combined.•A filtering based maximum likelihood multi-innovation gradient method is given.•The proposed algorithm can improve the parameter estimation accuracy.•The proposed method requires lower computational load because of lower dimensions.•The proposed algorithm can be extended to study problems of other systems.

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.