带噪声输入的ARMAX模型辨识：一种参数频域解

IF 4.6 2区工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC

IEEE Transactions on Signal Processing Pub Date : 2024-12-23 DOI:10.1109/TSP.2024.3522300

Shenglin Song;Erliang Zhang

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引用次数: 0

摘要

本文研究了输入信号受白噪声干扰时ARMAX模型的频域参数辨识问题。通过多元ARMA表示，采用连续两阶段方法识别变量误差（EIV）框架内的ARMAX模型，并利用输入输出数据的二阶统计量进一步联合调整动态EIV模型的所有参数估计，以实现无偏估计之间的方差最小。构造了EIV-ARMAX模型和多元ARMA过程的可辨识性的充分条件。分析了估计量的一致性，给出了估计量的不确定性界，并与cram - rao下界进行了比较。通过数值和实例验证了该方法的有效性。

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Identification of ARMAX Models With Noisy Input: A Parametric Frequency Domain Solution

This paper deals with frequency domain parametric identification of ARMAX models when the input is corrupted by white noise. By means of a multivariate ARMA representation, the ARMAX model within the errors-in-variables (EIV) framework is identified by a successive two-stage approach, and all the parameter estimates of the dynamic EIV model are further jointly tuned to achieve minimum variance among unbiased estimators using second-order statistics of input-output data. Sufficient conditions are constructed to obtain the identifiability of the EIV-ARMAX model as well as the multivariate ARMA process. The consistency of the estimator is analyzed, and the uncertainty bound of the estimate is also provided and compared with the Cramér-Rao lower bound. The performance of the proposed method is demonstrated via numerical and real examples.

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来源期刊

IEEE Transactions on Signal Processing 工程技术-工程：电子与电气

CiteScore

11.20

自引率

9.30%

发文量

310

审稿时长

3.0 months

期刊介绍： The IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals. The term “signal” includes, among others, audio, video, speech, image, communication, geophysical, sonar, radar, medical and musical signals. Examples of topics of interest include, but are not limited to, information processing and the theory and application of filtering, coding, transmitting, estimating, detecting, analyzing, recognizing, synthesizing, recording, and reproducing signals.