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Noise-level estimation of time series using coarse-grained entropy
Krzysztof Urbanowicz1, Janusz A Hołyst
1Faculty of Physics and Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland. urbanow@if.pw.edu.pl
Summary
We developed a novel noise-level estimation method effective even at high noise levels. This technique utilizes coarse-grained correlation entropy to accurately determine noise standard deviation in various systems.
Area of Science:
- Nonlinear dynamics
- Statistical physics
- Signal processing
Background:
- Accurate noise-level estimation is crucial for analyzing complex systems.
- Existing methods often fail under high noise conditions.
- Characterizing noise is essential for understanding system behavior.
Purpose of the Study:
- To introduce a robust noise-level estimation method applicable to high noise environments.
- To demonstrate the method's validity across different noise types and chaotic systems.
Main Methods:
- Utilizing the functional dependence of coarse-grained correlation entropy K2(epsilon) on the threshold parameter epsilon.
- Analyzing the characteristic relationship between K2(epsilon) and noise standard deviation (sigma).
- Numerical verification with Gaussian, uniform, and dynamical (Langevin) noise.
Main Results:
- The function K2(epsilon) exhibits a characteristic dependence on noise standard deviation sigma.
- The proposed method successfully estimates noise levels in various chaotic systems.
- Validation confirmed applicability to Gaussian, uniform, and dynamical noise sources.
Conclusions:
- The K2(epsilon) entropy provides a reliable metric for noise-level estimation.
- This method offers a significant advancement for analyzing noisy complex and chaotic systems.
- The technique is broadly applicable, including to the Chua electronic circuit.