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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 considers the parameter and order estimation for multiple-input single-output nonlinear systems. Since the orders of the system are unknown, a high-dimensional identification model and a sparse parameter vector are established to include all the valid inputs and basic parameters. Applying the data filtering technique, the input-output data are filtered and the original identification model with autoregressive noise is changed into the identification model with white noise. Based on the compressed sensing recovery theory, a data filtering-based orthogonal matching pursuit algorithm is presented for estimating the system parameters and the orders. The presented method can obtain highly accurate estimates from a small number of measurements by finding the highest absolute inner product. The simulation results confirm that the proposed algorithm is effective for recovering the model of the multiple-input single-output Hammerstein finite impulse response systems. [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]

Because of complex structures, the identification of nonlinear systems is very difficult, especially for closed-loop nonlinear systems (i.e., feedback nonlinear systems). This paper considers the parameter identification of a feedback nonlinear system where the forward channel is a controlled autoregressive model and the feedback channel is a static nonlinear function. Using the hierarchical identification principle decomposes a feedback nonlinear system into two subsystems, one contains the parameters of the linear dynamic block and the other contains the parameters of the nonlinear static block. A hierarchical least squares algorithm and a recursive least squares algorithm are presented for feedback nonlinear systems. The proposed algorithms are simple in principle and easy to implement on-line. [ABSTRACT FROM AUTHOR]

This paper focuses on the recursive parameter estimation methods for the exponential autoregressive (ExpAR) model. Applying the negative gradient search and introducing a forgetting factor, a stochastic gradient and a forgetting factor stochastic gradient algorithms are presented. In order to improve the parameter estimation accuracy and the convergence rate, the multi-innovation identification theory is employed to derive a forgetting factor multi-innovation stochastic gradient algorithm. A simulation example is provided to test 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]

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]

Mathematical models are basic for designing controller and system identification is the theory and methods for establishing the mathematical models of practical systems. This paper considers the parameter identification for Hammerstein controlled autoregressive systems. Using the key term separation technique to express the system output as a linear combination of the system parameters, the system is decomposed into several subsystems with fewer variables, and then a hierarchical least squares (HLS) algorithm is developed for estimating all parameters involving in the subsystems. The HLS algorithm requires less computation than the recursive least squares algorithm. The computational efficiency comparison and simulation results both confirm the effectiveness of the proposed algorithms. [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 studies the parameter estimation problem of Hammerstein output error autoregressive (OEAR) systems. According to the maximum likelihood principle and the Levenberg–Marquardt optimization method, a maximum likelihood Levenberg–Marquardt recursive (ML-LM-R) algorithm using the varying interval input–output data is proposed. Furthermore, a stochastic gradient algorithm is also derived in order to compare it with the proposed ML-LM-R algorithm. Two numerical examples are provided to verify the effectiveness of the proposed algorithms. [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]

This paper presents a data filtering based stochastic gradient algorithm for estimating the parameters of multivariable Hammerstein FIR-MA-like systems. By filtering the input and output data, the FIR-MA-like model is transformed into a controlled autoregressive model. The examples confirm that the proposed algorithm is more accurate and has a better performance than the stochastic gradient algorithm. [ABSTRACT FROM AUTHOR]