Estimation Of Second-order Statistics Research Articles

Challenges and improvements in applying a particle image velocimetry (PIV) approach to granular flows

The particle image velocimetry (PIV) is a well-established non-invasive optical technique for measuring the velocity field in fluids. Recently, the PIV approach has been extended to granular flows, where the medium under investigation is composed of a discrete number of grains that are typically non-transparent and of super-millimetric size. Granular PIV (g-PIV) still represents a non-standard application, as some accuracy concerns arise. In particular, since granular flows can be highly sheared, the choice of appropriate interrogation windows for the PIV analysis is not trivial. As well, owing to the spatially-averaged nature of the PIV approach, the estimation of second-order statistics remains a very challenging task. Here, we report a laboratory investigation on dry granular flows composed of glass spheres in a rotating drum. The velocity measurements at the sidewall are obtained by using a window deformation multi-pass PIV approach, where the open-source code PIVlab has been specifically used. Different combinations of the number of PIV passes and of interrogation windows are investigated. A slightly modified version of PIVlab allowed us to carry out g-PIV calculations with an arbitrary number of passes (i.e. greater than 4). Comparisons among different analyses helped us to identify reliable settings for g-PIV applications.

Indicator-Based Geostatistical Models For Mapping Fish Survey Data

Marine research survey data on fish stocks often show a small proportion of very high-density values, as for many environmental data. This makes the estimation of second-order statistics, such as the variance and the variogram, non-robust. The high fish density values are generated by fish aggregative behaviour, which may vary greatly at small scale in time and space. The high values are thus imprecisely known, both in their spatial occurrence and order of magnitude. To map such data, three indicator-based geostatistical methods were considered, the top-cut model, min–max autocorrelation factors (MAF) of indicators, and multiple indicator kriging. In the top-cut and MAF approaches, the variable is decomposed into components and the most continuous ones (those corresponding to the low and medium values) are used to guide the mapping. The methods are proposed as alternatives to ordinary kriging when the variogram is difficult to estimate. The methods are detailed and applied on a spatial data set of anchovy densities derived from a typical fish stock acoustic survey performed in the Bay of Biscay, which show a few high-density values distributed in small spatial patches and also as solitary events. The model performances are analyzed by cross-validating the data and comparing the kriged maps. Results are compared to ordinary kriging as a base case. The top-cut model had the best cross-validation performance. The indicator-based models allowed mapping high-value areas with small spatial extent, in contrast to ordinary kriging. Practical guidelines for implementing the indicator-based methods are provided.

New second order cyclostationary analysis and application to the detection and characterization of a runner׳s fatigue

Cyclostationarity (CS), as characteristic of signals, is a technique that offers diagnostic advantages for the analysis of failures, faults and disturbances which are related to a system being examined. The aim of this paper is to introduce the concept of CS for signals and to present possibilities of statistical resampling procedures for the estimation of second order statistics of such signals. The resampling methods treated in this paper are referred to as subsampling and moving block bootstrap (MBB). A description of these methods is presented and their applicability to CS simulated data is proved. The comparison between those two procedures shows that subsampling seems to be more efficient and more relevant than MBB. The subsampling-based CS analysis of biomechanical ground reaction force signals (GRF signals), coming from a high level professional runner, proves the second order cyclostationary (CS2) nature of the GRF signals. Moreover, it enables us to distinguish successfully the CS2 cyclic frequencies of the signals under consideration. Some new indicators based on the subsampling procedure are also proposed. This allows a better characterization and a full innovative description of the different fatigue states of a runner.

Likelihood-Ratio-Based Verification in High-Dimensional Spaces

The increase of the dimensionality of data sets often leads to problems during estimation, which are denoted as the curse of dimensionality. One of the problems of second-order statistics (SOS) estimation in high-dimensional data is that the resulting covariance matrices are not full rank, so their inversion, for example, needed in verification systems based on the likelihood ratio, is an ill-posed problem, known as the singularity problem. A classical solution to this problem is the projection of the data onto a lower dimensional subspace using principle component analysis (PCA) and it is assumed that any further estimation on this dimension-reduced data is free from the effects of the high dimensionality. Using theory on SOS estimation in high-dimensional spaces, we show that the solution with PCA is far from optimal in verification systems if the high dimensionality is the sole source of error. For moderate dimensionality, it is already outperformed by solutions based on euclidean distances and it breaks down completely if the dimensionality becomes very high. We propose a new method, the fixed-point eigenwise correction, which does not have these disadvantages and performs close to optimal.

On the application of intervening variables for stochastic finite element analysis

This paper investigates the application of first order Taylor series expansion considering intervening variables for estimating second order statistics for problems of stochastic finite element analysis. In particular, two types of intervening variables are considered. The focus is on studying the response of linear elastic static structures whose properties are characterized by means of log-normal random fields. Results obtained indicate that the use of intervening variables can lead to improved estimation of second order statistics when compared with traditional approaches based on Taylor series while numerical efforts remain similar.

The Effect of a Voice Activity Detector on the Speech Enhancement Performance of the Binaural Multichannel Wiener Filter

A multimicrophone speech enhancement algorithm for binaural hearing aids that preserves interaural time delays was proposed recently. The algorithm is based on multichannel Wiener filtering and relies on a voice activity detector (VAD) for estimation of second-order statistics. Here, the effect of a VAD on the speech enhancement of this algorithm was evaluated using an envelope-based VAD, and the performance was compared to that achieved using an ideal error-free VAD. The performance was considered for stationary directional noise and nonstationary diffuse noise interferers at input SNRs from ?10 to +5?dB. Intelligibility-weighted SNR improvements of about 20?dB and 6?dB were found for the directional and diffuse noise, respectively. No large degradations (<1?dB) due to the use of envelope-based VAD were found down to an input SNR of 0?dB for the directional noise and ?5?dB for the diffuse noise. At lower input SNRs, the improvement decreased gradually to 15?dB for the directional noise and 3?dB for the diffuse noise.

Discrete-Time Estimation of Second-Order Statistics of Generalized Almost-Cyclostationary Processes

In this paper, the problem of estimating second-order statistics of continuous-time generalized almost-cyclostationary (GACS) processes is addressed. GACS processes in the wide sense have autocorrelation function almost-periodic in time whose generalized Fourier series expansion has both frequencies and coefficients that depend on the lag shifts. Almost-cyclostationary (ACS) processes are obtained as a special case when the frequencies do not depend on the lag shifts. ACS processes filtered by Doppler channels and communications signals with time-varying parameters are further examples. It is shown that continuous-time GACS processes do not have a discrete-time counterpart. The discrete-time cyclic cross-correlogram of the discrete-time ACS processes obtained by uniformly sampling GACS processes is considered as estimator of samples of the continuous-time cyclic cross-correlation function. The asymptotic performance analysis is carried out by resorting to the hybrid cyclic cross-correlogram which is partially continuous-time and partially discrete-time. Its mean-square consistency and asymptotic complex Normality as the number of data-samples approaches infinity and the sampling period approaches zero are proved under mild conditions on the regularity of the Fourier series coefficients and the finite or practically finite memory of the processes expressed in terms of summability of cumulants. It is shown that the asymptotic properties of the hybrid cyclic cross-correlogram are coincident with those of the continuous-time cyclic cross-correlogram. Hence, discrete-time estimation does not give rise to any loss in asymptotic performance with respect to continuous-time estimation.

On the Sensitivity of the Transmit MIMO Wiener Filter With Respect to Channel and Noise Second-Order Statistics Uncertainties

We consider the sensitivity of the transmit multiple-input multiple-output (MIMO) Wiener filter with respect to channel and noise second-order statistics (SOS) uncertainties. Using results from matrix perturbation theory, we derive second-order approximations to the excess mean-square error (EMSE) induced by using the channel or noise SOS estimates as if they were the true quantities. Assuming optimal training and sufficiently high signal-to-noise ratio (SNR), we develop simple and informative approximations to the EMSE, which indicate that the channel estimation errors are much more significant than the noise SOS estimation errors. Uncertainties due to channel time variations induce EMSE that increases with increasing SNR and asymptotically tends to a constant value.

On the robustness of the finite-length MMSE-DFE with respect to channel and second-order statistics estimation errors

The finite-length minimum mean square error decision-feedback equalizer (MMSE-DFE) is an efficient structure mitigating intersymbol interference (ISI) introduced by practically all communication channels at high-enough symbol rates. The filters constituting the MMSE-DFE, as well as related performance measures, can be computed by assuming perfect knowledge of the channel impulse response and the input and noise second-order statistics (SOS). In practice, we estimate the unknown quantities, and thus, inevitable estimation errors arise. We model the estimation errors as small perturbations, and we derive a second-order approximation to the excess MSE. Furthermore, we derive second-order approximations to the mean excess MSE in terms of the parameter estimation error covariance matrices and simple and informative bounds, revealing the factors that govern the behavior of MMSE-DFE under mismatch. Simulations confirm that the derived second-order approximations provide accurate estimates of the MMSE-DFE performance degradation due to mismatch.

On the robustness of the finite-length MMSE-DFE with respect to channel and second-order statistics estimation errors

The finite-length minimum mean square error decision-feedback equalizer (MMSE-DFE) is an efficient structure mitigating intersymbol interference (ISI) introduced by practically all communication channels at high-enough symbol rates. The filters constituting the MMSE-DFE, as well as related performance measures, can be computed by assuming perfect knowledge of the channel impulse response and the input and noise second-order statistics (SOS). In practice, we estimate the unknown quantities, and thus, inevitable estimation errors arise. We model the estimation errors as small perturbations, and we derive a second-order approximation to the excess MSE. Furthermore, we derive second-order approximations to the mean excess MSE in terms of the parameter estimation error covariance matrices and simple and informative bounds, revealing the factors that govern the behavior of MMSE-DFE under mismatch. Simulations confirm that the derived second-order approximations provide accurate estimates of the MMSE-DFE performance degradation due to mismatch.