Higher Order Tensor-Based Method for Delayed Exponential Fitting

Abstract

We present subspace-based schemes for the estimation of the poles (angular frequencies and damping factors) of a sum of damped and delayed sinusoids. In our model, each component is supported over a different time frame, depending on the delay parameter. Classical subspace-based methods are not suited to handle signals with varying time supports. In this contribution, we propose solutions based on the approximation of a partially structured Hankel-type tensor on which the data are mapped. We show, by means of several examples, that the approach based on the best rank-(R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ,R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ,R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ) approximation of the data tensor outperforms the current tensor and matrix-based techniques in terms of the accuracy of the angular frequency and damping factor parameter estimates, especially in the context of difficult scenarios as in the low signal-to-noise ratio regime and for closely spaced sinusoids