The maximum likelihood least squares based iterative estimation algorithm for bilinear systems with autoregressive moving average noise

Maximum likelihood methods are significant for parameter estimation and system modeling. This paper gives the input-output representation of a bilinear system through eliminating the state variables in it, and derives a maximum likelihood least squares based iterative for identifying the parameters of bilinear systems with colored noises by using the maximum likelihood principle. A least squares based iterative (LSI) algorithm is presented for comparison. It is proved that the maximum of the likelihood function is equivalent to minimize the least squares cost function. The simulation results indicate that the proposed algorithm is effective for identifying bilinear systems and the maximum likelihood LSI algorithm is more accurate than the LSI algorithm.