Sinusoidal Parameter Estimation from Signed Measurements via Majorization-Minimization Based RELAX

TL;DR

This paper introduces 1bMMRELAX, an efficient algorithm for sinusoidal parameter estimation from one-bit signed measurements, which significantly reduces computational complexity while maintaining high accuracy.

Contribution

The paper develops a majorization-minimization based version of 1bRELAX, called 1bMMRELAX, that uses FFT operations to improve computational efficiency in sinusoidal parameter estimation.

Findings

1bMMRELAX reduces computational time compared to 1bRELAX.

It maintains high estimation accuracy in both simulated and real data.

FFT-based implementation accelerates the iterative process.

Abstract

We consider the problem of sinusoidal parameter estimation using signed observations obtained via one-bit sampling with fixed as well as time-varying thresholds. In a previous paper, a relaxation-based algorithm, referred to as 1bRELAX, has been proposed to iteratively maximize the likelihood function. However, the exhaustive search procedure used in each iteration of 1bRELAX is time-consuming. In this paper, we present a majorization-minimization (MM) based 1bRELAX algorithm, referred to as 1bMMRELAX, to enhance the computational efficiency of 1bRELAX. Using the MM technique, 1bMMRELAX maximizes the likelihood function iteratively using simple FFT operations instead of the more computationally intensive search used by 1bRELAX. Both simulated and experimental results are presented to show that 1bMMRELAX can significantly reduce the computational cost of 1bRELAX while maintaining its excellent estimation accuracy.