Parameters estimation of a noisy sinusoidal signal with time-varying amplitude

TL;DR

This paper develops robust algebraic and modulating functions-based estimators for frequency, amplitude, and phase of noisy sinusoidal signals with time-varying amplitude, demonstrating their stability and robustness to noise and sampling issues.

Contribution

It introduces a novel application of algebraic and modulating functions techniques for parameter estimation in noisy, time-varying sinusoidal signals, with proven robustness and stability.

Findings

Estimators are robust to large sampling periods.

Estimators maintain accuracy with non-zero mean noise.

Convergence and stability are theoretically validated.

Abstract

In this paper, we give estimators of the frequency, amplitude and phase of a noisy sinusoidal signal with time-varying amplitude by using the algebraic parametric techniques introduced by Fliess and Sira-Ramirez. We apply a similar strategy to estimate these parameters by using modulating functions method. The convergence of the noise error part due to a large class of noises is studied to show the robustness and the stability of these methods. We also show that the estimators obtained by modulating functions method are robust to "large" sampling period and to non zero-mean noises.