The filtering-based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle

For a special class of nonlinear systems (ie, bilinear systems) with autoregressive moving average noise, this paper gives the input-output representation of the bilinear systems through eliminating the state variables in the model. Based on the obtained model and the maximum likelihood principle, a filtering-based maximum likelihood hierarchical gradient iterative algorithm and a filtering-based maximum likelihood hierarchical least squares iterative algorithm are developed for identifying the parameters of bilinear systems with colored noises. The original bilinear systems are divided into three subsystems by using the data filtering technique and the hierarchical identification principle, and they are identified respectively. Compared with the gradient-based iterative algorithm and the multi-innovation stochastic gradient algorithm, the proposed algorithms have higher computational efficiency and parameter estimation accuracy. The simulation results indicate that the proposed algorithms are effective for identifying bilinear systems.