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For a dual-rate sampled-data stochastic system with additive colored noise, a dual-rate identification model is obtained by using the polynomial transformation technique, which is suitable for the available dual-rate measurement data. Based on the obtained model, a maximum likelihood least squares-based iterative (ML-LSI) algorithm is presented for identifying the parameters of the dual-rate sampled-data stochastic system. In order to improve the computation efficiency of the algorithm, the identification model of a dual-rate sampled-data stochastic system is divided into two subidentification models with smaller dimensions and fewer parameters, and a maximum likelihood hierarchical least squares-based iterative (H-ML-LSI) algorithm is proposed for these subidentification models by using the hierarchical identification principle. The simulation results indicate that the proposed algorithms are effective for identifying dual-rate sampled-data stochastic systems and the H-ML-LSI algorithm has a higher computation efficiency than the ML-LSI algorithm.

For a special class of nonlinear systems (ie, bilinear systems) with autoregressive moving average noise, this paper gives the input-output representation of the bilinear systems through eliminating the state variables in the model. Based on the obtained model and the maximum likelihood principle, a filtering-based maximum likelihood hierarchical gradient iterative algorithm and a filtering-based maximum likelihood hierarchical least squares iterative algorithm are developed for identifying the parameters of bilinear systems with colored noises. The original bilinear systems are divided into three subsystems by using the data filtering technique and the hierarchical identification principle, and they are identified respectively. Compared with the gradient-based iterative algorithm and the multi-innovation stochastic gradient algorithm, the proposed algorithms have higher computational efficiency and parameter estimation accuracy. The simulation results indicate that the proposed algorithms are effective for identifying bilinear systems.

This article mainly studies the iterative parameter estimation problems of a class of nonlinear systems. Based on the auxiliary model identification idea, this article utilizes the estimated parameters to construct an auxiliary model, and uses its outputs to replace the unknown noise-free process outputs, and develops an auxiliary model least squares-based iterative (AM-LSI) identification algorithm.For further improving the parameter estimation accuracy, we use a particle filter to estimate the unknown noise-free process outputs, and derive a particle filtering least squares-based iterative (PF-LSI) identification algorithm. During each iteration, the AM-LSI and PF-LSI algorithms can make full use of the measured input-output data. The simulation results indicate that the proposed algorithms are effective for identifying the nonlinear systems, and can generate more accurate parameter estimates than the auxiliary model-based recursive least squares algorithm.