The filtering‐based maximum likelihood iterative estimation algorithms for a special class of nonlinear systems with autoregressive moving average noise using the hierarchical identification principle

Abstract

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.

Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems

“…For example, Phan et al extended the observer/Kalman filter estimation algorithm for linear systems to solve the estimation problem of bilinear systems . Li et al proposed the least squares–based iterative method for parameter estimation by eliminating the state variable in the state equation; this method can generate accurate estimates by making full use of sampled data but results in the heavy computational burden . Hizir et al studied the parameter estimation of the bilinear system excited by a linear combination of sine and cosine signals.…”

“…20 Li et al proposed the least squares-based iterative method for parameter estimation by eliminating the state variable in the state equation; this method can generate accurate estimates by making full use of sampled data but results in the heavy computational burden. [21][22][23] Hizir et al studied the Int J Robust Nonlinear Control. 2020;30:1373-1393.wileyonlinelibrary.com/journal/rnc…”

Moving data window gradient‐based iterative algorithm of combined parameter and state estimation for bilinear systems

“…When dealing with the bilinear system with colored noise, the data filtering technique can be applied to reduce the impact of the noise and improve the estimation accuracy . In Reference , a filtering‐based maximum likelihood algorithm was developed for improving the parameter estimation accuracy of bilinear systems with moving average noise. For the input nonlinear system, Ma and Ding proposed the filtering‐based multistage recursive identification algorithm by using the key term separation .…”

Recursive methods for estimating the radial basis function‐based state‐dependent autoregressive model

“…System identification is the theory and method of establishing the mathematical models of systems . Many identification methods have been developed for linear systems, bilinear systems, multivariable systems, and nonlinear systems . The methods in system identification can be applied to estimate the parameters for the RBF‐AR models.…”

“…11 Many identification methods have been developed for linear systems, bilinear systems, 12,13 multivariable systems, 14 and nonlinear systems. 15,16 The methods in system identification can be applied to estimate the parameters for the RBF-AR models. Various parameter identification tools, such as the filtering techniques, 17,18 the decomposition techniques, 19,20 and the iterative methods, 21 have been extensively applied.…”