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Exponential data fitting using multilinear algebra: the decimative case
Author(s) -
Papy JeanMichel,
De Lathauwer Lieven,
Van Huffel Sabine
Publication year - 2009
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.1212
Subject(s) - multilinear algebra , multilinear map , tensor (intrinsic definition) , aliasing , mathematics , exponential function , subspace topology , algorithm , hankel matrix , dimensionality reduction , curse of dimensionality , reduction (mathematics) , sequence (biology) , dimension (graph theory) , matrix (chemical analysis) , computational complexity theory , tensor algebra , algebra over a field , computer science , pure mathematics , mathematical analysis , artificial intelligence , geometry , statistics , current algebra , materials science , division algebra , biology , undersampling , jordan algebra , composite material , filtered algebra , genetics
This paper presents a high‐precision method for the estimation of the parameters of a signal, modelled as a finite sum of complex damped exponentials, whose poles may be close. It is well known that increasing the sampling rate increases the accuracy of traditional methods, like total least squares (TLSs)‐ESPRIT and HTLS, in the case of closely spaced exponentials. However, in the case of long sequences, the computational complexity makes these methods hard to apply. To overcome this problem, the HTLSDstack and the HTLSDsum methods make use of decimated sequences. In this paper, we propose a higher order counterpart of HTLSDstack, based on concepts from multilinear algebra. Basically, it consists of decimating an oversampled signal by a factor D , making sure that no aliasing occurs. Each sequence is arranged in a Hankel matrix and the D Hankel matrices are stacked in a third‐order tensor. A dimensionality reduction algorithm is applied to the tensor and the resulting subspace is used to retrieve the parameters of interest. The dimensionality reduction is possibly unsymmetric in the different modes of the tensor, which allows us to take into account ill conditioning when poles are close. The new method yields better results than HTLSDstack while its complexity stays fairly low compared to non‐decimative methods. Copyright © 2009 John Wiley & Sons, Ltd.