Filtering-Based Maximum Likelihood Gradient Iterative Estimation Algorithm for Bilinear Systems with Autoregressive Moving Average Noise

This paper combines the maximum likelihood principle with the data filtering technique for parameter estimation of bilinear systems with autoregressive moving average noise. We give the input–output representation of the bilinear systems through eliminating the state variables in the model. Based on the obtained model, we use an estimated noise transfer function to filter the input–output data and derive a filtering-based maximum likelihood gradient iterative algorithm for identifying the parameters of bilinear systems with colored noises. A gradient-based iterative algorithm is given for comparison. The simulation results indicate that the proposed algorithm is effective for identifying bilinear systems.