Regularized adaptive long autoregressive spectral analysis

TL;DR

This paper introduces a novel unsupervised spectral analysis method combining spectral smoothness and time continuity priors, optimized via Kalman smoothing, to improve results with limited data, demonstrated on meteorological radar.

Contribution

It synthesizes prior spectral smoothness and temporal continuity into a unified regularized criterion optimized by Kalman smoothing, with automatic hyperparameter adjustment via maximum likelihood.

Findings

Enhanced spectral analysis with limited data

Automatic hyperparameter tuning improves robustness

Significant improvements demonstrated on meteorological radar data

Abstract

This paper is devoted to adaptive long autoregressive spectral analysis when (i) very few data are available, (ii) information does exist beforehand concerning the spectral smoothness and time continuity of the analyzed signals. The contribution is founded on two papers by Kitagawa and Gersch. The first one deals with spectral smoothness, in the regularization framework, while the second one is devoted to time continuity, in the Kalman formalism. The present paper proposes an original synthesis of the two contributions: a new regularized criterion is introduced that takes both information into account. The criterion is efficiently optimized by a Kalman smoother. One of the major features of the method is that it is entirely unsupervised: the problem of automatically adjusting the hyperparameters that balance data-based versus prior-based information is solved by maximum likelihood. The improvement is quantified in the field of meteorological radar.