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. (C) 2016 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.