This article studies the parameter estimation to the system response from the discrete measurement data. By constructing the dynamical rolling cost functions and using the nonlinear optimization, t...

The parameter estimation algorithms based on the dynamical response measurement data

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 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 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

The parameter estimation problem for multi-input multi-output Hammerstein systems is considered. For the Hammerstein model to be identified, its dynamic time-invariant subsystem is described by a controlled autoregressive model with a communication delay. The modified Kalman filter (MKF) algorithm is derived to estimate the unknown intermediate variables in the system and the MKF-based recursive least squares (LS) algorithm is presented to estimate all the unknown parameters. Furthermore, the hierarchical identification is adopted to decompose the system into two fictitious subsystems: one containing the unknown parameters in the non-linear block and the other containing the unknown parameters in the linear subsystem. Then an MKF-based hierarchical LS algorithm is derived. The convergence analysis shows the performance of the presented algorithms. The numerical simulation results indicate that the proposed algorithms are effective.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-cta.2016.1033

Junxia Ma

Papers

Hierarchical identification for multivariate Hammerstein systems by using the modified Kalman filter