Decomposition-based multiinnovation gradient identification algorithms for a special bilinear system based on its input-output representation

This article considers the parameter estimation for a special bilinear system with colored noise. Its input-output representation is derived by eliminating the state variables in the bilinear system. Based on the input-output representation of the bilinear system, a multiinnovation generalized extended stochastic gradient (MI-GESG) algorithm is proposed by using the multiinnovation identification theory. Furthermore, a decomposition-based multiinnovation (ie, hierarchical multiinnovation) generalized extended stochastic gradient identification (H-MI-GESG) algorithm is derived to enhance the parameter estimation accuracy by using the hierarchical identification principle, and a GESG algorithm is presented for comparison. Compared with the existing identification algorithms for the bilinear system, the proposed MI-GESG and H-MI-GESG algorithms can generate more accurate parameter estimation. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.