A simple and robust method for noise variance estimation for time-varying signals

TL;DR

This paper introduces a straightforward and robust method for estimating noise variance in time-varying 1-D signals, improving accuracy especially amidst unmodelled dynamics and outliers.

Contribution

It presents a novel approach leveraging the relationship between noise variance and prediction error variance, enhancing robustness over existing methods.

Findings

More accurate noise variance estimates in noisy, dynamic signals

Robustness to outliers and unmodelled dynamics

Improved estimation stability compared to classic methods

Abstract

In this brief paper, we present a simple approach to estimate the variance of measurement noise with time-varying 1-D signals. The proposed approach exploits the relationship between the noise variance and the variance of the prediction errors (or innovation sequence) of a linear estimator, the idea that was pioneered by [9] and [2]. Compared with the classic and more recent methods in the same category, the proposed method can render more robust estimates with the presence of unmodelled dynamics and outliers in the measurement.