Effects of Correlated Noise on the Performance of Persistence Based Dynamic State Detection Methods

TL;DR

This paper investigates how correlated (colored) noise affects the accuracy of persistence-based methods for dynamic state detection, revealing increased false positives at lower SNRs for certain noise types.

Contribution

It extends previous work by analyzing the impact of colored noise on persistence-based detection, highlighting its vulnerabilities to non-white noise.

Findings

Colored noise causes false positives at lower SNRs for α<0

Persistence methods are robust to white Gaussian noise but sensitive to colored noise

Lower α values in 1/f^α noise increase detection errors

Abstract

The ability to characterize the state of dynamic systems has been a pertinent task in the time series analysis community. Traditional measures such as Lyapunov exponents are often times difficult to recover from noisy data, especially if the dimensionality of the system is not known. More recent binary and network based testing methods have delivered promising results for unknown deterministic systems, however noise injected into a periodic signal leads to false positives. Recently, we showed the advantage of using persistent homology as a tool for achieving dynamic state detection for systems with no known model and showed its robustness to white Gaussian noise. In this work, we explore the robustness of the persistence based methods to the influence of colored noise and show that colored noise processes of the form $1/f^{\alpha}$ lead to false positive diagnostic at lower signal to noise ratios for $\alpha<0$.