Estimation of Dynamical Noise Power in Unknown Systems

Noise can be modeled as a sequence of random variables defined on a probability space that may be added to a given dynamical system T, which is a map on a phase space. In the non-trivial case of dynamical noise {e(n)}(n), where e(n) follows a Gaussian distribution N(0, s(2)) and the system output is x(n) = T (x(n-1); x(0)) + e(n), without any specific knowledge or assumption about T, the quantitative estimation of the noise power s(2) is a challenge. Here, we introduce a formal method based on the nonlinear entropy profile to estimate the dynamical noise power s(2) without requiring knowledge of the specific T function. We tested the correctness of the proposed method using time series generated from Logistic maps and Pomeau-Manneville systems under different conditions. Our results demonstrate that the proposed estimation algorithm can properly discern different noise levels without any a priori information.

Automated summary

This article proposes a method based on nonlinear entropy profile to estimate the power of dynamic noise s(2) without requiring knowledge of the specific T function. Testing with time series generated from Logistic maps and Pomeau-Manneville systems under different conditions, the results demonstrate that the proposed estimation algorithm can properly discern different noise levels without any a priori information.