ABSTRACT
Nonlinear Noise Estimation Coarse-grained Entropy Method Let { }, 1,2, ,ix i N= be a nonlinear time series. After selecting suitable time delay τ and embedded dimension m we reconstruct phase space, and then get m dimension vector sequence
where ( 1)M N m τ= − − . The correlated integral of embedded phase space is defi ned as the follows
(2)
where ( )H ⋅ is Heaviside function, and r is threshold and ⋅ is maximum norm. Therefore, coarse-grained entropy can be estimated as follows
where σ,,,, cbak are parameters under estimation, and the function ( )g z is defi ned as follows
= (5)
noise. After estimating the standard deviation of noise σ by the use of fi tting formula (4), fi nally we can calculate noise-to-signal ratio (NSR) of time series as follows
and we take it as a measurement of noise level of time series.
