Data Filtering-Based Multi-innovation Stochastic Gradient Algorithm for Nonlinear Output Error Autoregressive Systems

Parameter identification algorithm for ship manoeuvrability and wave peak model based multi-innovation stochastic gradient algorithm use data filtering technique

This paper develops a multi-innovation stochastic gradient (MISG) algorithm for multi-input, multi-output systems. The convergence analysis using the martingale convergence theorem shows that the parameter estimates by the MISG algorithm consistently converge to the true parameters under the persistent excitation condition. The MISG algorithm uses not only the current innovation but also the past innovation at each iteration and repeatedly utilizes the available input-output data, thus the parameter estimation accuracy can be improved. The simulation example confirms the theoretical results.

Block-oriented nonlinear systems have attracted a considerable attention for their flexible structure and practicability. This study proposes a novel multi-innovation stochastic gradient (MISG) algorithm to address the identification problem in input nonlinear systems. This involves applying the inexact line search strategy to determine an appropriate convergence factor at each recursive step. The proposed algorithm tracks the nonlinear system dynamics faster than the conventional MISG algorithm. It is therefore suitable for online identification and can be applied to nonlinear time-varying systems. The concept of auxiliary model identification is also adopted for dealing with unmeasurable variables. The effectiveness of the proposed algorithm is verified through simulated examples.

In this paper, we discuss the identification problem of multi-input output-error moving average systems. A filtering based multi-innovation stochastic gradient algorithm with forgetting factors is derived by using the filtering technique with the multi-innovation identification theory, and a multi-innovation extended stochastic gradient algorithm is given for comparison. The simulation results confirm that the proposed algorithms can generate highly accurate parameter estimates compared with the multi-innovation stochastic gradient algorithm.

System identification provides many convenient and useful methods for engineering modelling. This study targets the parameter identification problems for multivariable equation-error autoregressive moving average systems. To reduce the influence of the coloured noises on the parameter estimation, the data filtering technique is adopted to filter the input and output data, and to transform the original system into a filtered system with white noises. Then the filtered system is decomposed into several subsystems and a filtering-based partially-coupled generalised extended stochastic gradient algorithm is developed via the coupling concept. In contrast to the multivariable generalised extended stochastic gradient algorithm, the proposed algorithm can give more accurate parameter estimates. Finally, the effectiveness of the proposed algorithm is well demonstrated by simulation examples.

SummaryIn 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.

This paper considers the parameter estimation for multi-input output error autoregressive (OEAR) systems. The main contribution of this paper is to propose iterative algorithms for multi-input OEAR systems using the data filtering technique. Firstly, a least squares iterative (LSI) identification algorithm is given for multi-input OEAR systems as a comparison. Secondly, we transform an OEAR system into two identification models and present a data filtering based least squares iterative (F-LSI) identification algorithm. Finally, an illustrative simulation example is provided to test the proposed algorithms, the simulation results indicate that the F-LSI identification algorithm can produce more accurate parameter estimates than the LSI identification algorithm.

This paper studies several identification methods for Hammerstein systems with piece-wise linearities. By using the key term separation technique, the model of the nonlinear Hammerstein systems be changed to an identification model, then based on the derived model, a stochastic gradient identification algorithm, a forgetting factor stochastic gradient algorithm and a modified stochastic gradient algorithm are used to estimate all the unknown parameters of the systems. An example is provided to show the effectiveness of the proposed algorithms.

This paper combines a missing outputs identification model with a stochastic gradient algorithm to estimate the parameters of dual-rate sampled data systems with a preload nonlinear input. A switching function is provided to turn the model of the nonlinear systems into an identification model. Based on the identification model, a missing outputs identification model is introduced to predict the unmeasurable outputs and a stochastic gradient algorithm is derived to identify the parameters of the identification model by all the inputs and all the outputs. The simulation results indicate that the proposed algorithm is effective.

The least mean square methods include two typical parameter estimation algorithms, which are the projection algorithm and the stochastic gradient algorithm, the former is sensitive to noise and the latter is not capable of tracking the time‐varying parameters. On the basis of these two typical algorithms, this study presents a generalised projection identification algorithm (or a finite data window stochastic gradient identification algorithm) for time‐varying systems and studies its convergence by using the stochastic process theory. The analysis indicates that the generalised projection algorithm can track the time‐varying parameters and requires less computational effort compared with the forgetting factor recursive least squares algorithm. The way of choosing the data window length is stated so that the minimum parameter estimation error upper bound can be obtained. The numerical examples are provided.

This paper mainly considers the fractional parameter identification algorithms of the bilinear-in-parameter autoregressive (AR-BIP) system. The data filtering technique is introduced to improve the parameter estimation accuracy of the AR-BIP system, which involves using a filter to filter the data of the identification model. The filtering-based hierarchical fractional least mean square algorithm (F-HFLMS) and the filtering-based multi-innovation hierarchical fractional least mean square algorithm (F-MHFLMS) are proposed for effective and accurate parameter estimation of the AR-BIP system. Using the multi-innovation theory and expanding the scalar innovation into the innovation vector, the F-MHFLMS could take full advantage of the input and output data information of the system. The performance of the F-MHFLMS algorithm is compared with the F-HFLMS strategy for the AR-BIP system using the values of the mean square error (MSE) and the average predicted output error. The effectiveness and accuracy of F-HFLMS and F-MHFLMS algorithms are demonstrated under the numerical experimentation based on different noise variances, fractional orders and innovation lengths. Compared with the F-HFLMS algorithm, the F-MHFLMS algorithm can acquire more accurate and robust parameter estimation.

SummaryThis paper focuses on the parameter estimation issues of multivariate equation‐error autoregressive moving average systems. By applying the gradient search and the multi‐innovation theory, we derive a multi‐innovation gradient based iterative (MI‐GI) algorithm. In order to improve the computational efficiency and the parameter estimation accuracy, a filtering and decomposition based gradient iterative (F‐D‐GI) algorithm is presented by using the data filtering technique and the decomposition technique. The key is to choose an appropriate filter to filter the input‐output data and to transform an original system into several subsystems. Compared with the MI‐GI algorithm, the F‐D‐GI algorithm can generate more accurate parameter estimates. Finally, an illustrative example is provided to indicate the effectiveness of the proposed algorithms.

This manuscript deals with parametric and state estimation problem of discrete-time nonlinear polynomials systems. In this respect, the aim is to design a Recursive State and Parametric Estimation (RSPE) algorithm, based on least square principle, polynomial adjustable models and Kalman filter theory. Our simulation results show the validity of the proposed algorithm.

This paper considers the parameter estimation problems of Hammerstein–Wiener systems by using the data filtering technique. In order to improve the estimation accuracy, the data filtering-based recursive generalized extended least squares algorithm is derived. In order to improve the computational efficiency, the data filtering-based generalized extended stochastic gradient algorithm is derived for estimating the system parameters. Finally, the computational efficiency of the proposed algorithms is analyzed and compared. The simulation results indicate that the proposed algorithms can effectively estimate the parameters of Hammerstein–Wiener systems.

Obtaining initial parameter estimates for chaotic dynamical systems using linear associative memories