英语论文网

荷兰埃因霍温理工大学电气工程论文定制Improve Recursive Identification using Multi-Iteration

Control Systems, Faculty of Electrical Engineering
Eindhoven University of Technology

Abstract: A multi-iteration recursive identification algorithm is proposed and studied. The algorithmperforms multiple iterations for each data sample in order to improve the accuracy of the estimate. Thealgorithm is worked out for an ARMAX model using Gauss Newton method and pseudo-linear regression.The convergence of the methods is proved by using stochastic process theory and martingale convergencetechnique. Simulation results show that the algorithm has higher accuracy in parameter estimation andfaster convergence than the conventional recursive method.

Keywords: Recursive identification, multi-iteration, ARMAX model, convergence

1. INTRODUCTION
Recursive or online identification is used in adaptivesystems such as adaptive control and adaptive signalprocessing. Many recursive identification methods are basedon the corresponding off-line methods such as recursiveleast-squares (ARX) method, see, e.g., Åström and Eykhoff(1971), recursive ARMAX method, see, e.g., Åström andBohlin (1965), recursive output error method , see, e.g.,Ljung (1978), and recursive Box-Jenkins method, see, e.g.,Ljung (1999). For a linear time-invariant system, the
recursive least-squares (ARX) method is equivalent to theoff-line least-squares (ARX) method because it has ananalytic solution. However, recursive ARMAX method,recursive output error method and recursive Box-Jenkinsmethod are only approximations of their off-linecounterparts because these off-line methods need nonlinearoptimization to obtain model parameters where iterations arenecessary. Traditional recursive identification methods useone sample and perform one iteration at each recursion; see,e.g., Ljung and Söderström (1983).
In this work, conventional recursive identification methodsare revised to improve the model accuracy and convergencerate. The idea is to perform, at each recursion, multipleiterations. This was motivated by a finding in Zhu (2001,Section 5.9) that an off-line output error method performedfar better than a recursive output error method. Comparedwith the conventional approach, multi-iteration needs more
computer memory and longer computing time. This is of aless concern due to the dramatic increase of computercapacity since the traditional recursive methods weredeveloped in the 1970s. In this paper, the idea of theapproach is worked out for the ARMAX model but can breadily generalized to other methods. Consider a timeinvariantstochastic system described by an ARMAX model:

5. CONCLUSION
A multi-iteration recursive identification algorithm for
ARMAX model is developed. In the method, multiple
iterations are applied to each data sample in order to obtain
more accurate parameter estimates and faster convergence.
The convergence of the algorithm is proved. Simulation
results show that the algorithm outperforms the conventional
single iteration method in accuracy and convergence rate.
The same technique has been applied to other recursive
identification methods with success such as recursive output
error method (Oruç, 2007) and recursive ARMA model
estimation of time series (Han et. al., 2008).
Acknowledgments
The work of Xiangping Zhang is supported by National
Natural Science Foundation of China (No. 60634020本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。