Linear time-invariant system identification is considered in the behavioral setting. Nonstandard features of the problem are specification of missing and exact variables and identification from ...multiple time series with different length. The problem is equivalent to mosaic Hankel structured low-rank approximation with element-wise weighted cost function. Zero/infinite weights are assigned to the missing/exact data points. The problem is in general nonconvex. A solution method based on local optimization is outlined and compared with alternative methods on simulation examples. In a stochastic setting, the problem corresponds to errors-invariables identification. A modification of the generic problem considered is presented that is a deterministic equivalent to the classical ARMAX identification. The modification is also a mosaic Hankel structured low-rank approximation problem.
The fault signal feature extraction and fault identification of the bearing has important scientific research significance in the mechanized production. Aiming at this, this paper puts forward ...bearing fault diagnosis method based on singular value decomposition (SVD) and Hidden Markov Model (HMM). To gain required fault feature information, firstly, it builds Hankel matrix, and conducts decomposition through SVD. SVD method is helpful for gaining effective fault feature information from the complex bearing fault signals, and then apply the achieved characteristic value to build the training model of Markov. The test result proves that the method of this paper has good practicability in the bearing fault identification.
This paper presents a new approach to estimate the unknown frequencies of the constituent sinusoids in a noiseless signal. The signal comprising of unknown number of sinusoids of unknown amplitudes ...and unknown phases is measured in the time domain. The Hankel matrix of measured samples is used as a basis for further analysis in the Pisarenko harmonic decomposition. A new constraint, the Existence Factor (EF), has been introduced in the methodology based on the relationship between the frequencies of the unknown sinusoids and the eigenspace of Hankel matrix of signal's samples. The accuracy of the method has been tested through multiple simulations on different signals with an unknown number of sinusoidal components. Results showed that the proposed method has efficiently estimated all the unknown frequencies. (4 pages)
This article proposes a Bayesian procedure for simultaneous identification of the Kronecker indices and model parameters of a multivariate linear system. The model parameters include the starting ...values and innovations of the system so that the series considered may be co-integrated or non-invertible. The procedure uses some recent developments in stochastic search variable selection in linear regression analysis and Markov chain Monte Carlo methods in statistical computing. It also takes into consideration the row structure of a vector model implied by the Kronecker indices. Comparison with other existing methods is discussed. Simulated and real examples are used to illustrate the proposed procedure.
In a recent paper, we proposed a new estimation method for the blind deconvolution of a linear system with discrete random input, when the observations may be noise perturbed. We give here asymptotic ...properties of the estimators in the parametric situation. With nonnoisy observations, the speed of convergence is governed by the l1-tail of the inverse filter, which may have an exponential decrease. With noisy observations, the estimator satisfies a limit theorem with known distribution, which allows for the construction of confidence regions. To our knowledge, this is the first precise asymptotic result in the noisy blind deconvolution problem with an unknown level of noise. We also extend results concerning Hankel's estimation to Toeplitz's estimation and prove a formula to compute Toeplitz forms that may have interest in itself.
In the present article, we are interested in the identification of canonical ARMA echelon form models represented in a “refined” form. An identification procedure for such models is given by Tsay (J. ...Time Ser. Anal.10(1989), 357-372). This procedure is based on the theory of canonical analysis. We propose an alternative procedure which does not rely on this theory. We show initially that an examination of the linear dependency structure of the rows of the Hankel matrix of correlations, with originkin Z (i.e., with correlation at lagkin position (1, 1)), allows us not only to identify the Kronecker indicesn1, …, nd, whenk=1, but also to determine the autoregressive ordersp1, …, pd, as well as the moving average ordersq1, …, qdof the ARMA echelon form model by settingk>1 andk<1, respectively. Successive test procedures for the identification of the structural parametersni,pi, andqiare then presented. We show, under the corresponding null hypotheses, that the test statistics employed asymptotically follow chi-square distributions. Furthermore, under the alternative hypothesis, these statistics are unbounded in probability and are of the formNδ{1+op(1)}, whereδis a positive constant andNdenotes the number of observations. Finally, the behaviour of the proposed identification procedure is illustrated with a simulated series from a given ARMA model.
In this paper, we present perturbation results for eigenvalues of a matrix pencil of Hankel matrices for which the elements are given by complex moments. These results are extended to the case that ...matrices have a block Hankel structure. The influence of quadrature error on eigenvalues that lie inside a given integral path can be reduced by using Hankel matrices of an appropriate size. These results are useful for discussing the numerical behavior of root finding methods and eigenvalue solvers which make use of contour integrals. Results from some numerical experiments are consistent with the theoretical results.
We develop a novel approach to estimate the n unknown constituent frequencies of a sinusoidal signal that comprises of unknown number, n, of sinusoids of unknown phases and unknown amplitudes. The ...approach has been applied to multiple sinusoidal signals in the presence of white Gaussian noise with varying signal to noise ratio (SNR). The approach is based on eigenspace analysis of Hankel matrix formed with the samples from averaged frequency spectrum of the signal obtained through multiple measurements. The eigenspace analysis is based on the newly developed 3M relationship which reflects and exploits the relationship between the consecutive sets of Maximum, Middle and Minimum eigenvalues of square symmetric matrix of the Hankel matrix. The 3M relationship exhibits a pattern in line with the order of the Hankel matrix and leads to parametric estimation of the constituent sinusoids. This paper also presents the relationship equation between the size of 3M relationship pattern and the dimensions of the Hankel matrix. The performance of the developed approach has been tested to correctly estimate multiple constituent frequencies within a noisy signal.
UWB (Ultra-Wideband, UWB) is a short-range wireless transmission technology. For its high speed, low power, low complexity and low power spectral density, UWB is considered as the most important one ...of future wireless communications development directions. This paper focuses on the synchronization and channel parameters in UWB, and proposes the efficient closed-form estimation. In this paper, it is studied that the Hankel Matrix is constructed with the optimal number of columns in order to obtain the minimum element redundancy rate. Finally, the corresponding algorithm is designed, which not only can bring about the closed-form estimation, but also can greatly reduce the computation.
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