Line Spectrum Estimation with Probabilistic Priors

TL;DR

This paper introduces a probabilistic approach to line spectrum estimation using von Mises priors and an efficient optimization method, improving accuracy over traditional estimators.

Contribution

It develops a maximum a posteriori estimator incorporating circular von Mises priors for frequencies and proposes an alternating projections algorithm for optimization.

Findings

Estimator outperforms traditional methods in accuracy.

Numerical evaluations show close approach to Cramér-Rao bound.

Method effectively handles prior knowledge of frequency certainty.

Abstract

For line spectrum estimation, we derive the maximum a posteriori probability estimator where prior knowledge of frequencies is modeled probabilistically. Since the spectrum is periodic, an appropriate distribution is the circular von Mises distribution that can parameterize the entire range of prior certainty of the frequencies. An efficient alternating projections method is used to solve the resulting optimization problem. The estimator is evaluated numerically and compared with other estimators and the Cram\'er-Rao bound.