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

arXiv: https://arxiv.org/abs/2009.00494 · HTML: https://mlsanity.com/paper/2009.00494/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2020.

## Built on by (most cited first, 2 of 2)

- [Topological Signal Processing using the Weighted Ordinal Partition Network](https://mlsanity.com/paper/2205.08349/) (2022)
- [Topological Approach for Data Assimilation](https://mlsanity.com/paper/2411.18627/) (2024)

## Abstract (arXiv)

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/fα lead to false positive diagnostic at lower signal to noise ratios for α<0.