Ensemble transform Kalman-Bucy filters

Two recent works have adapted the Kalman–Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman–Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.

Estimating correlated observation error statistics using an ensemble transform Kalman filter

For certain observing types, such as those that are remotely sensed, the observation errors are correlated and these correlations are state- and time-dependent. In this work, we develop a method for diagnosing and incorporating spatially correlated and time-dependent observation error in an ensemble data assimilation system. The method combines an ensemble transform Kalman filter with a method that uses statistical averages of background and analysis innovations to provide an estimate of the observation error covariance matrix. To evaluate the performance of the method, we perform identical twin experiments using the Lorenz ’96 and Kuramoto-Sivashinsky models. Using our approach, a good approximation to the true observation error covariance can be recovered in cases where the initial estimate of the error covariance is incorrect. Spatial observation error covariances where the length scale of the true covariance changes slowly in time can also be captured. We find that using the estimated correlated observation error in the assimilation improves the analysis.

Wavelet based detection of changes in the composition of RLC networks

The current work discusses the compositional analysis of spectra that may be related to amorphous materials that lack discernible Lorentzian, Debye or Drude responses. We propose to model such response using a 3-dimensional random RLC network using a descriptor formulation which is converted into an input-output transfer function representation. A wavelet identification study of these networks is performed to infer the composition of the networks. It was concluded that wavelet filter banks enable a parsimonious representation of the dynamics in excited randomly connected RLC networks. Furthermore, chemometric classification using the proposed technique enables the discrimination of dielectric samples with different composition. The methodology is promising for the classification of amorphous dielectrics.

On the application of optimal wavelet filter banks for ECG signal classification

This paper discusses ECG signal classification after parametrizing the ECG waveforms in the wavelet domain. Signal decomposition using perfect reconstruction quadrature mirror filter banks can provide a very parsimonious representation of ECG signals. In the current work, the filter parameters are adjusted by a numerical optimization algorithm in order to minimize a cost function associated to the filter cut-off sharpness. The goal consists of achieving a better compromise between frequency selectivity and time resolution at each decomposition level than standard orthogonal filter banks such as those of the Daubechies and Coiflet families. Our aim is to optimally decompose the signals in the wavelet domain so that they can be subsequently used as inputs for training to a neural network classifier.

Acoustic scattering : high frequency boundary element methods and unified transform methods

We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods. We also make connections to the unified transform method due to A. S. Fokas and co-authors, analysing particular instances of this method, proposed by J. A. De-Santo and co-authors, for problems of acoustic scattering by diffraction gratings.

Accurate delay analysis in prioritised wireless sensor networks for generalized packet arrival

This letter presents an accurate delay analysis in prioritised wireless sensor networks (WSN). The analysis is an enhancement of the existing analysis proposed by Choobkar and Dilmaghani, which is only applicable to the case where the lower priority nodes always have packets to send in the empty slots of the higher priority node. The proposed analysis is applicable for any pattern of packet arrival, which includes the general case where the lower priority nodes may or may not have packets to send in the empty slots of the higher priority nodes. Evaluation of both analyses showed that the proposed delay analysis has better accuracy over the full range of loads and provides an excellent match to simulation results.

Methane cross-validation between three Fourier Transform Spectrometers: SCISAT ACE-FTS, GOSAT TANSO-FTS, and ground-based FTS measurements in the Canadian high Arctic

We present cross-validation of remote sensing measurements of methane profiles in the Canadian high Arctic. Accurate and precise measurements of methane are essential to understand quantitatively its role in the climate system and in global change. Here, we show a cross-validation between three datasets: two from spaceborne instruments and one from a ground-based instrument. All are Fourier Transform Spectrometers (FTSs). We consider the Canadian SCISAT Atmospheric Chemistry Experiment (ACE)-FTS, a solar occultation infrared spectrometer operating since 2004, and the thermal infrared band of the Japanese Greenhouse Gases Observing Satellite (GOSAT) Thermal And Near infrared Sensor for carbon Observation (TANSO)-FTS, a nadir/off-nadir scanning FTS instrument operating at solar and terrestrial infrared wavelengths, since 2009. The ground-based instrument is a Bruker 125HR Fourier Transform Infrared (FTIR) spectrometer, measuring mid-infrared solar absorption spectra at the Polar Environment Atmospheric Research Laboratory (PEARL) Ridge Lab at Eureka, Nunavut (80° N, 86° W) since 2006. For each pair of instruments, measurements are collocated within 500 km and 24 h. An additional criterion based on potential vorticity values was found not to significantly affect differences between measurements. Profiles are regridded to a common vertical grid for each comparison set. To account for differing vertical resolutions, ACE-FTS measurements are smoothed to the resolution of either PEARL-FTS or TANSO-FTS, and PEARL-FTS measurements are smoothed to the TANSO-FTS resolution. Differences for each pair are examined in terms of profile and partial columns. During the period considered, the number of collocations for each pair is large enough to obtain a good sample size (from several hundred to tens of thousands depending on pair and configuration). Considering full profiles, the degrees of freedom for signal (DOFS) are between 0.2 and 0.7 for TANSO-FTS and between 1.5 and 3 for PEARL-FTS, while ACE-FTS has considerably more information (roughly 1° of freedom per altitude level). We take partial columns between roughly 5 and 30 km for the ACE-FTS–PEARL-FTS comparison, and between 5 and 10 km for the other pairs. The DOFS for the partial columns are between 1.2 and 2 for PEARL-FTS collocated with ACE-FTS, between 0.1 and 0.5 for PEARL-FTS collocated with TANSO-FTS or for TANSO-FTS collocated with either other instrument, while ACE-FTS has much higher information content. For all pairs, the partial column differences are within ± 3 × 1022 molecules cm−2. Expressed as median ± median absolute deviation (expressed in absolute or relative terms), these differences are 0.11 ± 9.60 × 10^20 molecules cm−2 (0.012 ± 1.018 %) for TANSO-FTS–PEARL-FTS, −2.6 ± 2.6 × 10^21 molecules cm−2 (−1.6 ± 1.6 %) for ACE-FTS–PEARL-FTS, and 7.4 ± 6.0 × 10^20 molecules cm−2 (0.78 ± 0.64 %) for TANSO-FTS–ACE-FTS. The differences for ACE-FTS–PEARL-FTS and TANSO-FTS–PEARL-FTS partial columns decrease significantly as a function of PEARL partial columns, whereas the range of partial column values for TANSO-FTS–ACE-FTS collocations is too small to draw any conclusion on its dependence on ACE-FTS partial columns.

VELOCITY FIELD OF COMPRESSIBLE MAGNETOHYDRODYNAMIC TURBULENCE: WAVELET DECOMPOSITION AND MODE SCALINGS

We study compressible magnetohydrodynamic turbulence, which holds the key to many astrophysical processes, including star formation and cosmic-ray propagation. To account for the variations of the magnetic field in the strongly turbulent fluid, we use wavelet decomposition of the turbulent velocity field into Alfven, slow, and fast modes, which presents an extension of the Cho & Lazarian decomposition approach based on Fourier transforms. The wavelets allow us to follow the variations of the local direction of the magnetic field and therefore improve the quality of the decomposition compared to the Fourier transforms, which are done in the mean field reference frame. For each resulting component, we calculate the spectra and two-point statistics such as longitudinal and transverse structure functions as well as higher order intermittency statistics. In addition, we perform a Helmholtz-Hodge decomposition of the velocity field into incompressible and compressible parts and analyze these components. We find that the turbulence intermittency is different for different components, and we show that the intermittency statistics depend on whether the phenomenon was studied in the global reference frame related to the mean magnetic field or in the frame defined by the local magnetic field. The dependencies of the measures we obtained are different for different components of the velocity; for instance, we show that while the Alfven mode intermittency changes marginally with the Mach number, the intermittency of the fast mode is substantially affected by the change.

Wavelet regression with correlated errors on a piecewise Holder class

This paper generalizes the methodology of Cat and Brown [Cai, T., Brown, L.D., 1998. Wavelet shrinkage for nonequispaced samples. The Annals of Statistics 26, 1783-1799] for wavelet shrinkage for nonequispaced samples, but in the presence of correlated stationary Gaussian errors. If the true function is a member of a piecewise Holder class, it is shown that, even for long memory errors, the rate of convergence of the procedure is almost-minimax relative to the independent and identically distributed errors case. (c) 2008 Elsevier B.V. All rights reserved.

ENO adaptive method for solving one-dimensional conservation laws

In this work an efficient third order non-linear finite difference scheme for solving adaptively hyperbolic systems of one-dimensional conservation laws is developed. The method is based oil applying to the solution of the differential equation an interpolating wavelet transform at each time step, generating a multilevel representation for the solution, which is thresholded and a sparse point representation is generated. The numerical fluxes obtained by a Lax-Friedrichs flux splitting are evaluated oil the sparse grid by an essentially non-oscillatory (ENO) approximation, which chooses the locally smoothest stencil among all the possibilities for each point of the sparse grid. The time evolution of the differential operator is done on this sparse representation by a total variation diminishing (TVD) Runge-Kutta method. Four classical examples of initial value problems for the Euler equations of gas dynamics are accurately solved and their sparse solutions are analyzed with respect to the threshold parameters, confirming the efficiency of the wavelet transform as an adaptive grid generation technique. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Computational aspects of harmonic wavelet Galerkin methods and an application to a precipitation front propagation model

This article is dedicated to harmonic wavelet Galerkin methods for the solution of partial differential equations. Several variants of the method are proposed and analyzed, using the Burgers equation as a test model. The computational complexity can be reduced when the localization properties of the wavelets and restricted interactions between different scales are exploited. The resulting variants of the method have computational complexities ranging from O(N(3)) to O(N) (N being the space dimension) per time step. A pseudo-spectral wavelet scheme is also described and compared to the methods based on connection coefficients. The harmonic wavelet Galerkin scheme is applied to a nonlinear model for the propagation of precipitation fronts, with the front locations being exposed in the sizes of the localized wavelet coefficients. (C) 2011 Elsevier Ltd. All rights reserved.

Nonstationary feature extraction techniques for automatic classification of impact acoustic signals

Condition monitoring of wooden railway sleepers applications are generallycarried out by visual inspection and if necessary some impact acoustic examination iscarried out intuitively by skilled personnel. In this work, a pattern recognition solutionhas been proposed to automate the process for the achievement of robust results. Thestudy presents a comparison of several pattern recognition techniques together withvarious nonstationary feature extraction techniques for classification of impactacoustic emissions. Pattern classifiers such as multilayer perceptron, learning cectorquantization and gaussian mixture models, are combined with nonstationary featureextraction techniques such as Short Time Fourier Transform, Continuous WaveletTransform, Discrete Wavelet Transform and Wigner-Ville Distribution. Due to thepresence of several different feature extraction and classification technqies, datafusion has been investigated. Data fusion in the current case has mainly beeninvestigated on two levels, feature level and classifier level respectively. Fusion at thefeature level demonstrated best results with an overall accuracy of 82% whencompared to the human operator.

Computerized identification of motor complications in Parkinson's disease

Objective: To investigate whether spirography-based objective measures are able to effectively characterize the severity of unwanted symptom states (Off and dyskinesia) and discriminate them from motor state of healthy elderly subjects. Background: Sixty-five patients with advanced Parkinson’s disease (PD) and 10 healthy elderly (HE) subjects performed repeated assessments of spirography, using a touch screen telemetry device in their home environments. On inclusion, the patients were either treated with levodopa-carbidopa intestinal gel or were candidates for switching to this treatment. On each test occasion, the subjects were asked trace a pre-drawn Archimedes spiral shown on the screen, using an ergonomic pen stylus. The test was repeated three times and was performed using dominant hand. A clinician used a web interface which animated the spiral drawings, allowing him to observe different kinematic features, like accelerations and spatial changes, during the drawing process and to rate different motor impairments. Initially, the motor impairments of drawing speed, irregularity and hesitation were rated on a 0 (normal) to 4 (extremely severe) scales followed by marking the momentary motor state of the patient into 2 categories that is Off and Dyskinesia. A sample of spirals drawn by HE subjects was randomly selected and used in subsequent analysis. Methods: The raw spiral data, consisting of stylus position and timestamp, were processed using time series analysis techniques like discrete wavelet transform, approximate entropy and dynamic time warping in order to extract 13 quantitative measures for representing meaningful motor impairment information. A principal component analysis (PCA) was used to reduce the dimensions of the quantitative measures into 4 principal components (PC). In order to classify the motor states into 3 categories that is Off, HE and dyskinesia, a logistic regression model was used as a classifier to map the 4 PCs to the corresponding clinically assigned motor state categories. A stratified 10-fold cross-validation (also known as rotation estimation) was applied to assess the generalization ability of the logistic regression classifier to future independent data sets. To investigate mean differences of the 4 PCs across the three categories, a one-way ANOVA test followed by Tukey multiple comparisons was used. Results: The agreements between computed and clinician ratings were very good with a weighted area under the receiver operating characteristic curve (AUC) coefficient of 0.91. The mean PC scores were different across the three motor state categories, only at different levels. The first 2 PCs were good at discriminating between the motor states whereas the PC3 was good at discriminating between HE subjects and PD patients. The mean scores of PC4 showed a trend across the three states but without significant differences. The Spearman’s rank correlations between the first 2 PCs and clinically assessed motor impairments were as follows: drawing speed (PC1, 0.34; PC2, 0.83), irregularity (PC1, 0.17; PC2, 0.17), and hesitation (PC1, 0.27; PC2, 0.77). Conclusions: These findings suggest that spirography-based objective measures are valid measures of spatial- and time-dependent deficits and can be used to distinguish drug-related motor dysfunctions between Off and dyskinesia in PD. These measures can be potentially useful during clinical evaluation of individualized drug-related complications such as over- and under-medications thus maximizing the amount of time the patients spend in the On state.

Assessment of PD Speech Anomalies @ Home

Background: Voice processing in real-time is challenging. A drawback of previous work for Hypokinetic Dysarthria (HKD) recognition is the requirement of controlled settings in a laboratory environment. A personal digital assistant (PDA) has been developed for home assessment of PD patients. The PDA offers sound processing capabilities, which allow for developing a module for recognition and quantification HKD. Objective: To compose an algorithm for assessment of PD speech severity in the home environment based on a review synthesis. Methods: A two-tier review methodology is utilized. The first tier focuses on real-time problems in speech detection. In the second tier, acoustics features that are robust to medication changes in Levodopa-responsive patients are investigated for HKD recognition. Keywords such as Hypokinetic Dysarthria , and Speech recognition in real time were used in the search engines. IEEE explorer produced the most useful search hits as compared to Google Scholar, ELIN, EBRARY, PubMed and LIBRIS. Results: Vowel and consonant formants are the most relevant acoustic parameters to reflect PD medication changes. Since relevant speech segments (consonants and vowels) contains minority of speech energy, intelligibility can be improved by amplifying the voice signal using amplitude compression. Pause detection and peak to average power rate calculations for voice segmentation produce rich voice features in real time. Enhancements in voice segmentation can be done by inducing Zero-Crossing rate (ZCR). Consonants have high ZCR whereas vowels have low ZCR. Wavelet transform is found promising for voice analysis since it quantizes non-stationary voice signals over time-series using scale and translation parameters. In this way voice intelligibility in the waveforms can be analyzed in each time frame. Conclusions: This review evaluated HKD recognition algorithms to develop a tool for PD speech home-assessment using modern mobile technology. An algorithm that tackles realtime constraints in HKD recognition based on the review synthesis is proposed. We suggest that speech features may be further processed using wavelet transforms and used with a neural network for detection and quantification of speech anomalies related to PD. Based on this model, patients' speech can be automatically categorized according to UPDRS speech ratings.