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• The outliers in the measurements are coped with the Student's t-distribution, which assigns robustness to the algorithm according to its property of heavy-tails. • The robust identification issue is solved under recursive expectation-maximization algorithm. The online updating of the parameters are realized based on a recursive Q-function. • The degree of freedom of the Student's t-distribution is online updated with the implementation of a recursive auxiliary quantity. This paper considers the robust identification issue of linear systems represented by autoregressive exogenous models using the recursive expectation-maximization (EM) algorithm. In this paper, a recursive Q-function is formulated based on the maximum likelihood principle. Meanwhile, the outliers that frequently appear in practical processes are accommodated with the Student's t-distribution. The parameter vector, variance of noise, and the degree of freedom are recursively estimated. Finally, a numerical example, as well as a simulated continuous stirred tank reactor (CSTR) system, is performed to verify the effectiveness of the proposed recursive EM algorithm. [ABSTRACT FROM AUTHOR]

This paper focuses on the parameter estimation for radial basis function-based state-dependent autoregressive models with moving average noises (RBF-ARMA models). An extended projection algorithm is derived based on the negative gradient search. In order to reduce the sensitivity of the algorithm to noise and reduce the fluctuations of the parameter estimation errors, a modified extended stochastic gradient algorithm is proposed. By introducing a moving data window, a modified moving data window-based extended stochastic gradient algorithm is further developed to improve the parameter estimation accuracy. The simulation results show that the proposed algorithms can effectively estimate the parameters of the RBF-ARMA models. [ABSTRACT FROM AUTHOR]

For a multivariable Hammerstein controlled autoregressive moving average system (CARMA) system, the identification difficulty is hard to parameterize the system into an quasi auto-regression form to which the standard least square method can apply. By using an interactive maximum likelihood (IML) estimation method, this paper interactively maximizes the logarithmic likelihood function over multiple parameter vectors in a more general model, respectively. The details include: (1) reframe the system into a sum of some bilinear functions about the parameter vectors of the nonlinear part and the linear part; (2) interactively maximize the logarithmic likelihood function over each parameter vector to get their estimates; (3) when updating one parameter vector, substitute other parameter vectors or unknown information vectors by their estimates. The advantage of the IML algorithm is that it overcomes the limit on an autoregressive model form with one parameter vector. The IML method is simple to understand and easy to implement. Numerical simulations indicate that the explored IML algorithm is capable of generating accurate parameter estimates, and easy to implement on-line. [ABSTRACT FROM AUTHOR]

Abstract This paper focuses on the parameter estimation problem of multivariate output-error autoregressive systems. Based on the decomposition technique and the auxiliary model identification idea, we derive a decomposition based auxiliary model recursive generalized least squares algorithm. The key is to divide the system into two fictitious subsystems, the one including a parameter vector and the other including a parameter matrix, and to estimate the two subsystems using the recursive least squares method, respectively. Compared with the auxiliary model based recursive generalized least squares algorithm, the proposed algorithm has less computational burden. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Abstract This paper focuses on the parameter estimation problems of multivariate equation-error systems. A recursive generalized extended least squares algorithm is presented as a comparison. Based on the maximum likelihood principle and the coupling identification concept, the multivariate equation-error system is decomposed into several regressive identification models, each of which has only a parameter vector, and a coupled subsystem maximum likelihood recursive least squares identification algorithm is developed for estimating the parameter vectors of these submodels. The simulation example shows that the proposed algorithm is effective and has high estimation accuracy. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper concentrates on the identification problems of pseudo-linear autoregressive moving average systems. A least squares based iterative (LSI) algorithm is proposed using the data filtering technique and an LSI algorithm is developed for comparisons. The basic idea is to use a linear filter to filter the input–output data, to decompose a pseudo-linear autoregressive moving average system into a system model and a noise model. Finally, two examples are given to confirm the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]