Presence Of Additive Noise Research Articles

A New Transmission Line Protection Approach Using Cumulants and Artificial Neural Networks

This article presents a new methodology for transmission line protection that uses higher-order statistics (HOS), cumulants, and artificial neural networks (ANNs). The main objective is to design a distance relay algorithm. Results for the fault-detection and -classification stages are presented, as well as for fault location. The proposed method combines a large number of samples of cumulants with different features and the capability of ANNs to discriminate different patterns. In summary, HOS are used for feature extraction in the protection scheme. The ANNs receive these statistics as inputs, and they are responsible for the logical functioning of the protection system, deciding if a trip is needed after detecting, classifying, and locating a fault. The results have shown that the proposed approach is suitable for protection purposes. For the fault-detection stage, results have shown to be immune to the high presence of additive noise and also to the power-system frequency deviation. Moreover, the fault-classification stage is computed without the need of current information from the power system. Finally, the preliminary results for fault location are precise for a correct estimation of fault distance and determination of the fault zone. It must be highlighted that this new distance protection approach is essentially based on voltage signals, using current signals only for determining the direction of the fault. This fact represents an innovation in distance relaying.

Coding schemes for multi‐level Flash memories that are intrinsically resistant against unknown gain and/or offset using reference symbols

Coding schemes for storage channels, such as optical recording and non-volatile memory (Flash), with unknown gain and offset are presented. In its simplest case, the coding schemes guarantee that a symbol with a minimum value (floor) and a symbol with a maximum (ceiling) value are always present in a codeword so that the detection system can estimate the momentary gain and the offset. The results of the computer simulations show the performance of the new coding and detection methods in the presence of additive noise.

Application of meshfree methods for solving the inverse one-dimensional Stefan problem

Abstract This work is motivated by studies of numerical simulation for solving the inverse one and two-phase Stefan problem. The aim is devoted to employ two special interpolation techniques to obtain space-time approximate solution for temperature distribution on irregular domains, as well as for the reconstruction of the functions describing the temperature and the heat flux on the fixed boundary x=0 when the position of the moving interface is given as extra specification. The advantage of applying the methods is producing the shape functions which provide the important delta function property to ensure that the essential conditions are fulfilled. Due to ill-posedness of the problem, the process is intractable numerically, so special optimization technique is used to obtain the regularized solution. Numerical results for the typical benchmark test examples, which have the input measured data perturbed by increasing amounts of noise and continuity to the input data in the presence of additive noise, are obtained, which present the efficiency of the proposed method.

M-estimator-based robust estimation of the number of components of a superimposed sinusoidal signal model

In this paper, we consider the problem of estimating the number of components of a superimposed nonlinear sinusoids model of a signal in the presence of additive noise. We propose and provide a detailed empirical comparison of robust methods for estimation of the number of components. The proposed methods, which are robust modifications of the commonly used information theoretic criteria, are based on various M-estimator approaches and are robust with respect to outliers present in the data and heavy-tailed noise. The proposed methods are compared with the usual non-robust methods through extensive simulations under varied model scenarios. We also present real signal analysis of two speech signals to show the usefulness of the proposed methodology.

A comparative study: the effect of the perturbation vector type in the differential evolution algorithm on the accuracy of robot pose and heading estimation

Evolutionary algorithms (EAs) belong to a group of classic optimizers these days, and can be used in many application areas. Autonomous mobile robotics is not an exception. EAs are utilized profusely for the purposes of localization and map building of unknown environment—SLAM. This paper concentrates on one particular class of EA, the so called differential evolution (DE). It addresses the problem of selecting a suitable set of parameter values for the DE algorithm applied to the task of continuous robot localization in a known environment under the presence of additive noise in sensorial data. The primary goal of this study is to find at least one type of perturbation vector from a set of known perturbation vector types, suitable to navigate a robot using 2D laser scanner (2DLS) sensorial system. The basic navigational algorithm used in this study uses a vector representation for both the data and the environment map, which is used as a reference data source for the navigation. Since the algorithm does not use a probability occupancy grid, the precision of the results is not limited by the grid resolution. The comparative study presented in this paper includes a relatively large amount of experiments in various types of environments. The results of the study suggest that the DE algorithm is a suitable tool for continuous robot localization task in an indoor environment, with or without moving objects, and under the presence of various levels of additive noise in sensorial data. Two perturbation vector types were found as the most suitable for this task on average, namely rand/1/exp and randtobest/1/bin.

Astronomical image denoising using dictionary learning

Astronomical images suffer a constant presence of multiple defects that are consequences of the intrinsic properties of the acquisition equipments, and atmospheric conditions. One of the most frequent defects in astronomical imaging is the presence of additive noise which makes a denoising step mandatory before processing data. During the last decade, a particular modeling scheme, based on sparse representations, has drawn the attention of an ever growing community of researchers. Sparse representations offer a promising framework to many image and signal processing tasks, especially denoising and restoration applications. At first, the harmonics, wavelets, and similar bases and overcomplete representations have been considered as candidate domains to seek the sparsest representation. A new generation of algorithms, based on data-driven dictionaries, evolved rapidly and compete now with the off-the-shelf fixed dictionaries. While designing a dictionary beforehand leans on a guess of the most appropriate representative elementary forms and functions, the dictionary learning framework offers to construct the dictionary upon the data themselves, which provides us with a more flexible setup to sparse modeling and allows to build more sophisticated dictionaries. In this paper, we introduce the Centered Dictionary Learning (CDL) method and we study its performances for astronomical image denoising. We show how CDL outperforms wavelet or classic dictionary learning denoising techniques on astronomical images, and we give a comparison of the effect of these different algorithms on the photometry of the denoised images.

Robust FHPD Features from Speech Harmonic Analysis for Speaker Identification

Speaker identification accuracy decreases significantly in the presence of additive noise. In this paper, we propose a robust speech feature extraction method, which is based on the harmonic structure of voiced segments. The robust features are composed of fundamental and harmonic peak data from short-time spectrum. These features are evaluated by thirty speaker data from TIMIT database and additive noise signals from NOISEX-92 database with clean training and noisy testing samples. Results reflect that under low SNR (signal-to-noise ratio) environments new features achieve better performance than conventional MFCC (Mel-Frequency Cepstral Coefficients) parameters.

Design and convergence analysis of stochastic frequency estimator using contraction theory

This study investigates the design and analysis of an estimator for unknown frequencies of a sinusoid in the presence of additive noise. A dynamic stochastic estimator is proposed to ensure simultaneous globally convergent estimation of the state and the frequencies of a sinusoid comprising multiple frequencies. Approach given in this study exploits the results of stochastic contraction theory and the observers. The concept of contraction theory related to semi-contracting systems is used to show the asymptotic convergence of the proposed non-linear estimator. The boundedness and convergence of the state and frequencies estimates for all initial conditions and frequency values has been shown analytically. The proposed estimator is generalised to estimate n-unknown frequencies of a given noisy sinusoid. Numerical simulations of estimator are presented for different combinations of frequencies to justify the claim.

Bifurcations of emerging patterns in the presence of additive noise

A universal description of the effects of additive noise on super- and subcritical spatial bifurcations in one-dimensional systems is theoretically, numerically, and experimentally studied. The probability density of the critical spatial mode amplitude is derived. From this generalized Rayleigh distribution we predict the shape of noisy bifurcations by means of the most probable value of the critical mode amplitude. Comparisons with numerical simulations are in quite good agreement for cubic or quintic amplitude equations accounting for stochastic supercritical bifurcation and for cubic-quintic amplitude equation accounting for stochastic subcritical bifurcation. Experimental results obtained in a one-dimensional Kerr-like slice subjected to optical feedback confirm the analytical expression prediction for the supercritical bifurcation shape.

High-Rate Self-Synchronizing Codes

Self-synchronization under the presence of additive noise can be achieved by allocating a certain number of bits of each codeword as markers for synchronization. Difference systems of sets are combinatorial designs which specify the positions of synchronization markers in codewords in such a way that the resulting error-tolerant self-synchronizing codes may be realized as cosets of linear codes. Ideally, difference systems of sets should sacrifice as few bits as possible for a given code length, alphabet size, and error-tolerance capability. However, it seems difficult to attain optimality with respect to known bounds when the noise level is relatively low. In fact, the majority of known optimal difference systems of sets are for exceptionally noisy channels, requiring a substantial amount of bits for synchronization. To address this problem, we present constructions for difference systems of sets that allow for higher information rates while sacrificing optimality to only a small extent. Our constructions utilize optimal difference systems of sets as ingredients and, when applied carefully, generate asymptotically optimal ones with higher information rates. We also give direct constructions for optimal difference systems of sets with high information rates and error-tolerance that generate binary and ternary self-synchronizing codes.

Time and frequency constrained sonar signal design for optimal detection of elastic objects

In this paper, the task of model-based transmit signal design for optimizing detection is considered. Building on past work that designs the spectral magnitude for optimizing detection, two methods for synthesizing minimum duration signals with this spectral magnitude are developed. The methods are applied to the design of signals that are optimal for detecting elastic objects in the presence of additive noise and self-noise. Elastic objects are modeled as linear time-invariant systems with known impulse responses, while additive noise (e.g., ocean noise or receiver noise) and acoustic self-noise (e.g., reverberation or clutter) are modeled as stationary Gaussian random processes with known power spectral densities. The first approach finds the waveform that preserves the optimal spectral magnitude while achieving the minimum temporal duration. The second approach yields a finite-length time-domain sequence by maximizing temporal energy concentration, subject to the constraint that the spectral magnitude is close (in a least-squares sense) to the optimal spectral magnitude. The two approaches are then connected analytically, showing the former is a limiting case of the latter. Simulation examples that illustrate the theory are accompanied by discussions that address practical applicability and how one might satisfy the need for target and environmental models in the real-world.

Multifractal analyses of response time series: A comparative study

Response time series with a non-Gaussian distribution and long-range dependent dynamics have been reported for several cognitive tasks. Conventional monofractal analyses numerically define a long-range dependency as a single scaling exponent, but they assume that the response times are Gaussian distributed. Ihlen and Vereijken (Journal of Experimental Psychology: General, 139, 436-463, 2010) suggested multifractal extensions of the conventional monofractal analyses that are more suitable when the response time has a non-Gaussian distribution. Multifractal analyses estimate a multifractal spectrum of scaling exponents that contain the single exponent estimated by the conventional monofractal analyses. However, a comparison of the performance of multifractal analyses with behavioral variables has not yet been addressed. The present study compares the performance of seven multifractal analyses. The multifractal analyses were tested on multiplicative cascading noise that generates time series with a predefined multifractal spectrum and with a structure of variation that mimics intermittent response time variation. Time series with 1,024 and 4,096 samples were generated with additive noise and multiharmonic trends of two different magnitudes (signal-to-noise/trend ratio; 0.33 and 1). The results indicate that all multifractal analysis has individual pros and cons related to sample size, multifractality, and the presence of additive noise and trends in the response time series. The summary of pros and cons of the seven multifractal analyses provides a guideline for the choice of multifractal analyses of response time series and other behavioral variables.

A Mixture Model Approach for Formant Tracking and the Robustness of Student's-t Distribution

We address the problem of robust formant tracking in continuous speech in the presence of additive noise. We propose a new approach based on mixture modeling of the formant contours. Our approach consists of two main steps: (i) Computation of a pyknogram based on multiband amplitude-modulation/frequency-modulation (AM/FM) decomposition of the input speech; and (ii) Statistical modeling of the pyknogram using mixture models. We experiment with both Gaussian mixture model (GMM) and Student's-t mixture model (tMM) and show that the latter is robust with respect to handling outliers in the pyknogram data, parameter selection, accuracy, and smoothness of the estimated formant contours. Experimental results on simulated data as well as noisy speech data show that the proposed tMM-based approach is also robust to additive noise. We present performance comparisons with a recently developed adaptive filterbank technique proposed in the literature and the classical Burg's spectral estimator technique, which show that the proposed technique is more robust to noise.

Statistical modeling and denoising Wigner–Ville distribution

Studying the properties of the Wigner-Ville distribution (wvd) and its smoothed versions such as smoothed pseudo-WVD (spwvd), we demonstrate that they have significantly non-Gaussian statistics. Also, we investigate the presence of two-dimensional heteroscedasticity in them for different signals based on employing Lagrange multiplier (LM) procedure. Therefore, we employ a heteroscedastic model called two-dimensional generalized autoregressive conditional heteroscedastic (2-D garch) for statistical modeling of these distributions. This modeling captures the characteristics of WVD and SPWVD, such as heavy tailed marginal distribution, and the dependencies among them. Since the performance of WVD and its smoothed versions degrade in the presence of additive noise, we design a novel Bayesian estimator for estimating the clean distributions based on garch modeling. Also, estimating the instantaneous frequency (if) curves of signals in presence of noise based on WVD and its smoothed versions is an interesting topic in the radar domain. So, we apply the denoised distributions for estimating the if. Experimental results demonstrate the efficiency of proposed method in denoising wvd and SPWVD and also performance improvement for if estimation in utilizing the denoised distributions.

Noise bias in weak lensing shape measurements

Weak lensing experiments are a powerful probe of cosmology through their measurement of the mass distribution of the universe. A challenge for this technique is to control systematic errors that occur when measuring the shapes of distant galaxies. In this paper we investigate noise bias, a systematic error that arises from second order noise terms in the shape measurement process. We first derive analytical expressions for the bias of general Maximum Likelihood Estimators (MLEs) in the presence of additive noise. We then find analytical expressions for a simplified toy model in which galaxies are modeled and fitted with a Gaussian with its size as a single free parameter. Even for this very simple case we find a significant effect. We also extend our analysis to a more realistic 6-parameter elliptical Gaussian model. We find that the noise bias is generically of the order of the inverse-squared signal-to-noise ratio (SNR) of the galaxies and is thus of the order of a percent for galaxies of SNR of 10, i.e. comparable to the weak lensing shear signal. This is nearly two orders of magnitude greater than the systematics requirements for future all-sky weak lensing surveys. We discuss possible ways to circumvent this effect, including a calibration method using simulations discussed in an associated paper.

Evaluation of a four-point sine wave frequency estimator for portable DSP based instrumentation

A recent frequency estimation method was proposed in a Measurement paper for use in portable DSP based instrumentation. This method is especially important due to its low computational effort making it suitable for fast and low cost instrumentation. It has been found that many parameters can affect the frequency estimation using the proposed method. In this paper, the performance of the method in the presence of additive noise is evaluated, and the influence of signal frequency, initial phase, additive noise and number of analog-to-digital converter bits on the estimator is studied. Some caveats of the practical use of the method are addressed. Detailed numerical simulations based on a Monte Carlo procedure are presented in order to highlight the range of applicability of the method and determine the estimation bias.

On the consensus protocol of conspecific agents

We present a class of consensus protocols over groups of agents with stochastically switching, directed, and weighted communication topologies. In this protocol, an agent’s traits, that is, the cardinality of its neighbor set and the weight assigned to its neighbors in the updating process, are given by two jointly distributed random variables and the neighbors of an agent are selected with equal probability. We provide closed form results for the asymptotic convergence rate and for the steady state mean square deviation in the presence of additive noise. These results are specialized to consensus protocols based on Erdős–Rényi and numerosity-constrained networks.

Generalized Robust Multichannel Frequency-Domain LMS Algorithms for Blind Channel Identification

Recently, several noise-robust adaptive multichannel LMS algorithms have been proposed based on the spectral flatness of the estimated channel coefficients in the presence of additive noise. In this work, we propose a general form for the algorithms that integrates the existing algorithms into a common framework. Computer simulation results are presented and demonstrate that a new proposed algorithm gives better performance compared to existing algorithms in noisy environments.

Generalized Robust Multichannel Frequency-Domain LMS Algorithms for Blind Channel Identification

Recently, several noise-robust adaptive multichannel LMS algorithms have been proposed based on the spectral flatness of the estimated channel coefficients in the presence of additive noise. In this work, we propose a general form for the algorithms that integrates the existing algorithms into a common framework. Computer simulation results are presented and demonstrate that a new proposed algorithm gives better performance compared to existing algorithms in noisy environments.

Amplitude–energy fluctuations of optical pulses and statistics of the exit distance

We consider the propagation of an isolated optical pulse in the presence of additive noise. We apply an approach based on the Fokker–Planck equation to determine the probability distribution functions of the propagation distance at which the pulse energy and the pulse amplitude leave a certain region.