White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.

Should the classical variance be used as a basic measure in standards metrology

Abstract: Since a measurement is no better than its uncertainty, specifying the uncertainty is a very important part of metrology. One is inclined to believe that the fundamental constants in physics are invariant with time and that they are the foundation upon which to build internationl system (SI) standards and metrology. Therefore clearly specifying uncertainties for these physical invariants at state-of-the-art levels should be one of the principal goals of metrology. However, by the very act of observing some physical quantity we may perturb the standard, thus introducing uncertainties. The random deviations in a series of observations may be caused by the measurement system, by environmental coupling or by intrinsic deviations in the standard. For these reasons and because correlated random noise is as commonly occurring in nature as uncorrelated random noise, the universal use of the classical variance, and the standard deviation of the mean may cloud rather than clarify questions regarding uncertainties; i.e., these measures are well behaved only for random uncorrelated deviations (white noise), and white noise is typically a subset of the spectrum of observed deviations. The assumption that each measurement in a series is independent because the measurements are taken at different times should be called into question if, in fact, the series is not random and uncorrelated, i.e., does not have a white spectrum. In this paper, studies of frequency standards, standard-volt cells, and gauge blocks provide examples of long-term random-correlated time series which indicate behavior that is not “white” (not random and uncorrelated). This paper outlines and illustrates a straightforward time-domain statistical approach, which for power-law spectra yields an alternative estimation method for most of the important random power-law processes encountered. Knowing the spectrum provides for clearer uncertainty assessment in the presence of correlated random deviations, the statistical approach outlined also provides a simple test for a white spectrum, thus allowing a metrologist to know whether use of the classical variance is suitable or whether to incorporate better uncertainty assessment procedures, e.g., as outlined in the paper.

The Cramér-Rao estimation error lower bound computation for deterministic nonlinear systems

Abstract: For continuous-time nonlinear deterministic system models with discrete nonlinear measurements in additive Ganssian white noise, the extended Kalman filter (EKF) convariance propagation equations linearized about the true unknown trajectory provide the Cramer-Rao lower bound to the estimation error covariance matrix. A useful application is establishing the optimum filter performance for a given nonlinear estimation problem by developing a simulation of the nonlinear system and an EKF linearized about the true trajectory.

Nonlinear prediction as a way of distinguishing chaos from random fractal sequences

Abstract: NONLINEAR forecasting has recently been shown to distinguish between deterministic chaos and uncorrelated (white) noise added to periodic signals1, and can be used to estimate the degree of chaos in the underlying dynamical system2. Distinguishing the more general class of coloured (autocorrelated) noise has proven more difficult because, unlike additive noise, the correlation between predicted and actual values measured may decrease with time—a property synonymous with chaos. Here, we show that by determining the scaling properties of the prediction error as a function of time, we can use nonlinear prediction to distinguish between chaos and random fractal sequences. Random fractal sequences are a particular class of coloured noise which represent stochastic (infinite-dimensional) systems with power-law spectra. Such sequences have been known to fool other procedures for identifying chaotic behaviour in natural time series9, particularly when the data sets are small. The recognition of this type of noise is of practical importance, as measurements from a variety of dynamical systems (such as three-dimensional turbulence, two-dimensional and geostrophic turbulence, internal ocean waves, sandpile models, drifter trajectories in large-scale flows, the motion of a classical electron in a crystal and other low-dimensional systems) may over some range of frequencies exhibit power-law spectra.