Higher Order Tensor-Based Method for Delayed Exponential Fitting

Rmy Boyer, Lieven De Lathauwer, Karim Abed-Meraim
2007 IEEE Transactions on Signal Processing  
Meraim. Higher-order tensor-based method for delayed exponential fitting. IEEE Transactions on Signal Processing, Institute of Electrical and Electronics Engineers, 2007, 55 (6). hal-00575669 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
more » ... ted 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-( 1 2 3 ) 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. Index Terms-Conditional Cramér-Rao bound (CCRB), damped and delayed sinusoids, higher order tensor, rank reduction, singular value decomposition (SVD), subspace-based parameter estimation.
doi:10.1109/tsp.2007.893981 fatcat:5kuhqvxu3vcphkogjh7632t42a