Hierarchical estimation methods based on the penalty term for controlled autoregressive systems with colored noises

This article considers the parameter estimation problems for the controlled autoregressive systems interfered by moving average noises. A recursive extended gradient algorithm with penalty term is proposed by using the penalty criterion function. By introducing three fictitious output variables, the original system can be decomposed into three subsystems based on the hierarchical principle. The hierarchical recursive extended gradient algorithm with penalty term is then proposed to achieve the parameter estimation. Finally, the experimental results demonstrate the effectiveness of the proposed algorithms.