Extracting strong measurement noise from stochastic time series: Applications to empirical data

Abstract

It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time series even in the case when the amplitudes of measurement noise and uncontaminated signal are of the same order of magnitude. Our approach is based on a recently developed method for a nonparametric reconstruction of Langevin processes. Minimizing a proper non-negative function, the procedure is able to correctly extract strong measurement noise and to estimate drift and diffusion coefficients in the Langevin equation describing the evolution of the original uncorrupted signal. As input, the algorithm uses only the two first conditional moments extracted directly from the stochastic series and is therefore suitable for a broad panoply of different signals. To demonstrate the power of the method, we apply the algorithm to synthetic as well as climatological measurement data, namely, the daily North Atlantic Oscillation index, shedding light on the discussion of the nature of its underlying physical processes.

The Langevin Approach: An R Package for Modeling Markov Processes

“…This coefficient is also useful for computing the numerical error of the diffusion coefficient [19].…”

Fatigue Load Estimation through a Simple Stochastic Model

“…It is worth mentioning that, as known in previous studies [16,17], the existence of an offset in the conditional moments indicates the presence of measurement noise in the data. As shown in Figure 4b,c, the linear interpolations cross the origin, and no offset seems to exist.…”

“…Though, when the measurements obey this Markov condition, the next step can be carried out, one advantage of this Langevin framework is that it also works in some cases where the Markov test fails. One such case is the presence of measurement noise [16,17], which opens a broad panoply of different practical situations where this framework is applicable. In the present case, though no measurement noise seems to be present, as reported below, the Markov condition is not perfectly fulfilled, as shown in Figure 4a.…”

New approach for optimizing energy by adjusting the trade-off coefficient in wind turbines

“…As mentioned in [22] and [23], 'it is a big challenge' and needs some deep experience on concepts like the Langevin and Ornstein-Uhlenbeck process. Figure 5 The simulation results for the best a = 0.0099 obtained from applying GA.…”