Unexpected sine-fitting residual RMS bias on additive noise-corrupted data points

Authors

  • Francisco Alegria Universidade Técnica de Lisboa

DOI:

https://doi.org/10.21014/actaimeko.v14i4.2139

Keywords:

additive noise, estimation bias, estimation uncertainty, Monte Carlo methods, numerical validation, sinusoidal parameter estimation

Abstract

This work presents a novel result in signal processing theory, addressing the statistical properties of least squares estimation when fitting sinusoidal models to noise-corrupted data—a fundamental operation in numerous signal processing applications. We rigorously demonstrate the previously unrecognized estimation bias in the root mean square (RMS) of residuals when processing signals with additive Gaussian white noise, even when the sinusoidal frequency is known. Our theoretical framework derives a closed-form expression for this bias. The analytical derivations are validated through comprehensive Monte Carlo simulations. This work contributes to current trends in robust signal parameter estimation, uncertainty quantification, and performance analysis of signal processing algorithms under non-ideal conditions—essential considerations for applications in communications, radar, sonar, audio, biomedical signal processing, and measurement.

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Published

2025-12-22

Issue

Vol. 14 No. 4 (2025)

Section

Research Papers

License

Copyright (c) 2025 Francisco Alegria

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