Least-Squares Based and Gradient Based Iterative Parameter Estimation Algorithms for a Class of Linear-in-Parameters Multiple-Input Single-Output Output Error Systems

The identification of a class of linear-in-parameters multiple-input single-output systems is considered. By using the iterative search, a least-squares based iterative algorithm and a gradient based iterative algorithm are proposed. A nonlinear example is used to verify the effectiveness of the algorithms, and the simulation results show that the least-squares based iterative algorithm can produce more accurate parameter estimates than the gradient based iterative algorithm

Data filtering-based least squares iterative algorithm for Hammerstein nonlinear systems by using the model decomposition

This paper focuses on the iterative identification problems for a class of Hammerstein nonlinear systems. By decomposing the system into two fictitious subsystems, a decomposition-based least squares iterative algorithm is presented for estimating the parameter vector in each subsystem. Moreover, a data filtering-based decomposition least squares iterative algorithm is proposed. The simulation results indicate that the data filtering-based least squares iterative algorithm can generate more accurate parameter estimates than the least squares iterative algorithm

Least Squares Based and Two-Stage Least Squares Based Iterative Estimation Algorithms for H-FIR-MA Systems

This paper studies the identification of Hammerstein finite impulse response moving average (H-FIR-MA for short) systems. A new two-stage least squares iterative algorithm is developed to identify the parameters of the H-FIR-MA systems. The simulation cases indicate the efficiency of the proposed algorithms

Two Identification Methods for Dual-Rate Sampled-Data Nonlinear Output-Error Systems

This paper presents two methods for dual-rate sampled-data nonlinear output-error systems. One method is the missing output estimation based stochastic gradient identification algorithm and the other method is the auxiliary model based stochastic gradient identification algorithm. Different from the polynomial transformation based identification methods, the two methods in this paper can estimate the unknown parameters directly. A numerical example is provided to confirm the effectiveness of the proposed methods

Combined state and parameter estimation for Hammerstein systems with time-delay using the Kalman filtering

This paper discusses the state and parameter estimation problem for a class of Hammerstein state space systems with time-delay. Both the process noise and the measurement noise are considered in the system. Based on the observable canonical state space form and the key term separation, a pseudo-linear regressive identification model is obtained. For the unknown states in the information vector, the Kalman filter is used to search for the optimal state estimates. A Kalman-filter based least squares iterative and a recursive least squares algorithms are proposed. Extending the information vector to include the latest information terms which are missed for the time-delay, the Kalman-filter based recursive extended least squares algorithm is derived to obtain the estimates of the unknown time-delay, parameters and states. The numerical simulation results are given to illustrate the effectiveness of the proposed algorithms

Least squares-based iterative identification methods for linear-in-parameters systems using the decomposition technique

By extending the least squares-based iterative (LSI) method, this paper presents a decomposition-based LSI (D-LSI) algorithm for identifying linear-in-parameters systems and an interval-varying D-LSI algorithm for handling the identification problems of missing-data systems. The basic idea is to apply the hierarchical identification principle to decompose the original system into two fictitious sub-systems and then to derive new iterative algorithms to estimate the parameters of each sub-system. Compared with the LSI algorithm and the interval-varying LSI algorithm, the decomposition-based iterative algorithms have less computational load. The numerical simulation results demonstrate that the proposed algorithms work quite well

Parameter and State Estimator for State Space Models

This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective

Least Squares Based Iterative Algorithm for the Coupled Sylvester Matrix Equations

By analyzing the eigenvalues of the related matrices, the convergence analysis of the least squares based iteration is given for solving the coupled Sylvester equations AX+YB=C and DX+YE=F in this paper. The analysis shows that the optimal convergence factor of this iterative algorithm is 1. In addition, the proposed iterative algorithm can solve the generalized Sylvester equation AXB+CXD=F. The analysis demonstrates that if the matrix equation has a unique solution then the least squares based iterative solution converges to the exact solution for any initial values. A numerical example illustrates the effectiveness of the proposed algorithm

Combined Parameter and State Estimation Algorithms for Multivariable Nonlinear Systems Using MIMO Wiener Models

This paper deals with the parameter estimation problem for multivariable nonlinear systems described by MIMO state-space Wiener models. Recursive parameters and state estimation algorithms are presented using the least squares technique, the adjustable model, and the Kalman filter theory. The basic idea is to estimate jointly the parameters, the state vector, and the internal variables of MIMO Wiener models based on a specific decomposition technique to extract the internal vector and avoid problems related to invertibility assumption. The effectiveness of the proposed algorithms is shown by an illustrative simulation example

Adaptive filtering-based multi-innovation gradient algorithm for input nonlinear systems with autoregressive noise

In this paper, by means of the adaptive filtering technique and the multi-innovation identification theory, an adaptive filtering-based multi-innovation stochastic gradient identification algorithm is derived for Hammerstein nonlinear systems with colored noise. The new adaptive filtering configuration consists of a noise whitening filter and a parameter estimator. The simulation results show that the proposed algorithm has higher parameter estimation accuracies and faster convergence rates than the multi-innovation stochastic gradient algorithm for the same innovation length. As the innovation length increases, the filtering-based multi-innovation stochastic gradient algorithm gives smaller parameter estimation errors than the recursive least squares algorithm