This paper considers the parameter estimation problems of two-input single-output Hammerstein finite impulse response systems. A hierarchical least squares algorithm is proposed for improving the computational efficiency through combining the hierarchical identification principle and the identification model decomposition, and a multi-innovation least squares algorithm is proposed for enhancing the parameter estimation accuracy based on the multi-innovation identification theory. The key is to derive two sub-identification models, each of which contains a set of merged parameter vectors. The proposed algorithm is effective and can generate highly accurate parameter estimates compared with the over-parametrization identification method, and can be easily extended to multi-input multi-output systems. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.

Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems

This study considers the parameter estimation of a multi-variable output-error-like system with autoregressive moving average noise. In order to solve the problem of the information vector containing unknown variables, a least squares-based iterative algorithm is proposed by using the iterative search. The original system is divided into several subsystems by using the decomposition technique. However, the subsystems contain the same parameter vector, which poses a challenge for the identification problem, the approach taken here is to use the coupling identification concept to cut down the redundant parameter estimates. In addition, the recursive least squares algorithm is provided for comparison. The simulation results indicate that the proposed algorithms are effective.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-cta.2019.0112

Partially-coupled least squares based iterative parameter estimation for multi-variable output-error-like autoregressive moving average systems

Maximum likelihood methods are based on the probability and statistics theory, and significant for parameter estimation and system modeling. This paper combines the maximum likelihood principle with the data filtering technique for parameter estimation of a class of bilinear systems. The input-output representation of a bilinear system is derived through eliminating the state variables in the model. Then, a filtering based maximum likelihood iterative least squares algorithm is proposed for identifying the parameters of bilinear systems with colored noises by filtering the input-output data with a filter. A least squares based iterative algorithm is given for comparison. The simulation results indicate that the proposed algorithm is effective for identifying bilinear systems. The filtering based maximum likelihood iterative least squares algorithm is more accurate under different noise variance, and has higher computational efficiency.

Maximum Likelihood Least Squares Based Iterative Estimation for a Class of Bilinear Systems Using the Data Filtering Technique

Parameter estimation for block‐oriented nonlinear systems using the key term separation

In this paper, we focus on the modeling problem of the multi-frequency signals which contain many different frequency components. Based on the Newton search and the measured data, a Newton recursive parameter estimation algorithm is developed to estimate the amplitude, the angular frequency and the phase of a multi-frequency signal. In order to improve the performance of the identification algorithm, a convergence factor is introduced in the Hessian matrix of the developed Newton recursive method. The numerical examples verify that the proposed algorithm is effective for modeling the multi-frequency sine signals.

https://link.springer.com/content/pdf/10.1007/s00034-020-01356-3.pdf

A Recursive Parameter Estimation Algorithm for Modeling Signals with Multi-frequencies

This paper considers the parameter identification problems of controlled autoregressive systems using observation information. According to the hierarchical identification principle, we decompose the controlled autoregressive system into two subsystems by introducing two fictitious output variables. Then a two-stage gradient-based iterative algorithm is proposed by means of the iterative technique. In order to improve the performance of the tracking the time-varying parameters, we derive a two-stage multi-innovation gradient-based iterative algorithm based on the multi-innovation identification theory. Finally, an example is provided to illustrate the effectiveness of the proposed algorithms.

Two-stage Gradient-based Iterative Estimation Methods for Controlled Autoregressive Systems Using the Measurement Data

This paper studies the parameter identification problems for multivariable output-error-like systems with colored noises. Based on the hierarchical identification principle, the original system is decomposed into several subsystems. However, each subsystem contains the same parameter vector, which leads to redundant computation. By taking the average of the parameter estimation vectors of each subsystem, a partially-coupled subsystem recursive generalized extended least squares (PC-S-RGELS) algorithm is presented to cut down the redundant parameter estimates. Furthermore, a partially-coupled recursive generalized extended least squares (PC-RGELS) algorithm is presented to further reduce the computational cost and the redundant estimates by using the coupling identification concept. Finally, an example indicates the effectiveness of the derived algorithms.

https://www.mdpi.com/2227-7390/7/6/558/pdf

Lei Lv

Papers

Two-stage Gradient-based Iterative Estimation Methods for Controlled Autoregressive Systems Using the Measurement Data

Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems