Exponential data fitting using multilinear algebra: the decimative case

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.