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Estimation of Dynamical Noise Power in Unknown Systems
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  • Andrea Scarciglia ,
  • Fulvio Gini ,
  • Vincenzo Catrambone ,
  • Claudio Bonanno ,
  • Gaetano Valenza
Andrea Scarciglia
University of Pisa

Corresponding Author:[email protected]

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Fulvio Gini
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Vincenzo Catrambone
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Claudio Bonanno
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Gaetano Valenza
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Abstract

Noise can be modeled as a sequence of random variables defined on a probability space that may add to a given dynamical system T that is a map on a phase space. In the nontrivial case of dynamical noise {εn}n, where εn ∈ N(0, σ2) and the system output is xn = T(xn−1, xn−2, …, x0)+εn, without any specific knowledge/assumption on T, the quantitative estimation of noise power σ2 is a challenge. Here, we introduce a formal method, based on nonlinear entropy profile, to estimate the dynamical noise power σ2 without knowledge on the specific T function. Time-series generated from Logistic maps and Pomeau-Manneville systems under different conditions are used to test the correctness of the method. Results demonstrate that the proposed estimation algorithm properly discerns different noise levels with no a priori information.
Numerical simluations, including sereis generation, are performed with MATLAB.
2023Published in IEEE Signal Processing Letters volume 30 on pages 234-238. 10.1109/LSP.2023.3255170