Maximum likelihood based multi‐innovation stochastic gradient identification algorithms for bilinear stochastic systems with ARMA noise

Abstract

SummaryThis paper considers the parameter estimation problem for bilinear stochastic systems with autoregressive moving average (ARMA) noise using the stochastic gradient method. First, the identification model is derived by eliminating the state variables. Based on the obtained identification model, a multi‐innovation generalized extended stochastic gradient (MI‐GESG) algorithm is proposed using the multi‐innovation identification theory. Furthermore, to enhance the parameter estimation accuracy, a maximum likelihood based MI‐GESG (ML‐MI‐GESG) algorithm is developed by using the maximum likelihood identification principle. Finally, an illustrative simulation example is provided to testify the proposed algorithms. The simulation results show the effectiveness of the proposed algorithms for identifying bilinear systems.