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System identification under saturated precise or set-valued measurements

Science China(Information Sciences) 2023年第1期66卷 224-243页

作者： Yanlong ZHAO Hang ZHANG Ting WANG Guolian KANG Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Institute of Artificial Intelligence University of Science and Technology Beijing Department of Biostatistics St.Jude Children's Research Hospital

This paper considers the system identification problem based on saturated precise or set-valued measurements, which is widely used in various fields and has essential difficulties. Since existing methodologies cannot make full use of the mixed data, this paper is aiming to fill the gap and build a unified framework in dealing with such problems rigorously and comprehensively. New algorithms are introduced and their properties are established. Most significantly, the cramécr-rao(Cr) lower bound based on the measurements is established, which consists of two parts with respect to the precise data and set-valued data, respectively. This prompts the idea of designing an estimation algorithm by grouping and combining the estimations under two classifications of data. As a result, a Cr lower bound-based algorithm(CrBA) is constructed. The convergence properties are theoretically analyzed in terms of consistency and asymptotic efficiency under periodic inputs. For general inputs, an algorithm based on the CrBA that combines the expectation maximization(EM) algorithm for set-valued subsystems and the gradient descent algorithm for precise subsystems is proposed. Numerical simulations validate the superiority of the proposed algorithms.

关键词： system identification cramér-rao lower bound truncated data precise measurement set-valued measurement

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robust Frequency Estimation Under Additive Mixture Noise

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Computers, Materials & Continua 2022年第7期72卷 1671-1684页

作者： Yuan Chen Yulu Tian Dingfan Zhang Longting Huang Jingxin Xu School of Computer and Communication Engineering University of Science&Technology BeijingBeijing100083China School of Automation Science and Electrical Engineering Beihang UniversityBeijing100191China School of Information Engineering Wuhan University of TechnologyWuhan430070China Department of Energy and Public Works Queensland4702Australia

In many applications such as multiuser radar communications and astrophysical imaging processing,the encountered noise is usually described by the finite sum ofα-stable(1≤αriables.In this paper,a new parameter estimator is developed,in the presence of this new heavy-tailed noise.Since the closed-formPDF of theα-stable variable does not exist exceptα=1 andα=2,we take the sum of the Cauchy(α=1)and Gaussian(α=2)noise as an example,namely,additive Cauchy-Gaussian(ACG)noise.The probability density function(PDF)of the mixed random variable,can be calculated by the convolution of the Cauchy’s PDF and Gaussian’s PDF.Because of the complicated integral in the PDF expression of the ACG noise,traditional estimators,e.g.,maximum likelihood,are analytically not tractable.To obtain the optimal estimates,a new robust frequency estimator is devised by employing the Metropolis-Hastings(M-H)algorithm.Meanwhile,to guarantee the fast convergence of the M-H chain,a new proposal covariance criterion is also devised,where the batch of previous samples are utilized to iteratively update the proposal covariance in each sampling process.Computer simulations are carried out to indicate the superiority of the developed scheme,when compared with several conventional estimators and the cramér-rao lower bound.

关键词： Frequency estimation additive cauchy-gaussian noise voigt profile metropolis-hastings algorithm cramér-rao lower bound

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