VEXPA: Validated EXPonential Analysis through regular sub-sampling

TL;DR

VEXPA introduces a robust, reliable, and parallelizable exponential analysis method using uniform sub-Nyquist sampling and aliasing reconditioning, enhancing standard algorithms with automatic model order detection and outlier robustness.

Contribution

It presents VEXPA, a novel exponential analysis approach that leverages sub-sampling and aliasing to improve reliability, robustness, and computational efficiency over existing methods.

Findings

VEXPA achieves reliable exponential model estimation with automatic order detection.

The method demonstrates robustness against certain outliers.

VEXPA offers comparable accuracy to atomic norm minimization with lower computational cost.

Abstract

We present a procedure that adds a number of desirable features to standard exponential analysis algorithms, among which output reliability, a divide-and-conquer approach, the automatic detection of the exponential model order, robustness against some outliers, and the possibility to parallelize the analysis. The key enabler for these features is the introduction of uniform sub-Nyquist sampling through decimation of the dense signal data. We actually make use of possible aliasing effects to recondition the problem statement rather than that we avoid aliasing. In Section 2 the standard exponential analysis is described, including a sensitivity analysis. In Section 3 the ingredients for the new approach are collected, of which good use is made in Section 4 where we essentially bring everything together in what we call VEXPA. Some numerical examples of the new procedure illustrate in Section 5 that the additional features are indeed realized and that VEXPA is a valuable add-on to any stand-alone exponential analysis. While returning a lot of additional output, it maintains a favourable comparison to the CRLB of the underlying method, for which we here choose a matrix pencil method. Moreover, the output reliability of VEXPA is similar to that of atomic norm minimization, whereas its computational complexity is far less.