Exponential data fitting using multilinear algebra: the single‐channel and multi‐channel case

There is a wide variety of signal processing applications in which the data are assumed to be modelled as a sum of exponentially damped sinusoids. Many subspace‐based approaches (such as ESPRIT, matrix pencil, Prony, etc.) aim to estimate the parameters of this model. Typically, the data are arranged in Toeplitz or Hankel matrices and suitable parameter estimates are obtained via a truncated singular value decomposition (SVD) of the data matrix. It is shown that the parameter accuracy may be improved by arranging single‐channel or multi‐channel data in a higher‐order tensor and estimating the model parameters via a multilinear generalization of the SVD. The algorithm is presented and its performance is illustrated by means of simulations.