Data filtering based multi-innovation gradient identification for bilinear systems with colored noise

System identification is the powerful tool to establish the mathematical models of practical systems. This article considers the parameter identification for bilinear systems with colored noise. First, the bilinear system is transformed into an input-output form by eliminating the state variables in the model. Then, based on the data filtering technique, the measured input-output data is filtered using an estimated noise transfer function, and a filtering based generalized extended stochastic gradient (F-GESG) algorithm is proposed to enhance the parameter estimation accuracy. Furthermore, the multi-innovation identification theory is employed to improve the convergence speed of the proposed F-GESG algorithm, and a filtering based multi-innovation generalized extended stochastic gradient (F-MI-GESG) algorithm is developed to identify the parameters of bilinear systems. The GESG algorithm is given for comparison. Finally, a numerical simulation example is provided to illustrate the effectiveness and excellent performance of the proposed algorithms.