The Gradient-Based Iterative Estimation Algorithms for Bilinear Systems with Autoregressive Noise

Abstract

This paper considers the parameter identification problem of bilinear systems, which are a special class of nonlinear systems. The basic idea is giving the input–output representation of the bilinear system through eliminating the state variables in the system. By using the hierarchical identification principle and the data filtering technique, we derive a gradient-based iterative (GI) algorithm, a hierarchical GI algorithm and a filtering-based GI algorithm for identifying the parameters of bilinear systems with colored noises. The simulation results indicate that the proposed algorithms are effective for identifying bilinear systems.