From ESPRIT to ESPIRA: Estimation of Signal Parameters by Iterative Rational Approximation

TL;DR

The paper presents ESPIRA, a new signal parameter estimation method based on iterative rational approximation, which is more stable and efficient, especially with noisy data, compared to traditional methods like ESPRIT.

Contribution

Introduces ESPIRA, a novel algorithm combining AAA rational approximation with matrix pencil techniques for improved signal parameter estimation.

Findings

ESPIRA achieves similar accuracy to ESPRIT and matrix pencil methods on exact data.

ESPIRA outperforms traditional methods in noisy data scenarios.

ESPIRA requires less computational effort than existing methods.

Abstract

We introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm for rational approximation of the discrete Fourier transform of the given equidistant signal values. We show that ESPIRA can be interpreted as a matrix pencil method applied to Loewner matrices. These Loewner matrices are closely connected with the Hankel matrices which are usually employed for signal recovery. Due to the construction of the Loewner matrices via an adaptive selection of index sets, the matrix pencil method is stabilized. ESPIRA achieves similar recovery results for exact data as ESPRIT and the matrix pencil method but with less computational effort. Moreover, ESPIRA strongly outperforms ESPRIT and the matrix pencil method for noisy data and for signal approximation by short exponential sums.