The Limit Distribution of Stochastic Evolution Equations Driven by-Stable Non-Gaussian Noise

We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.

Using Pearson’s System of Curves to Approximate the Distributions of the Difference between Two Correlated Estimates of Signal-to-Noise Ratios: The Cases of Bivariate Normal and Bivariate Lognormal Distributions

Background: The signal-to-noise ratio (SNR) is recognized as an index of measurements reproducibility. We derive the maximum likelihood estimators of SNR and discuss confidence interval construction on the difference between two correlated SNRs when the readings are from bivariate normal and bivariate lognormal distribution. We use the Pearsons system of curves to approximate the difference between the two estimates and use the bootstrap methods to validate the approximate distributions of the statistic of interest. Methods: The paper uses the delta method to find the first four central moments, and hence the skewness and kurtosis which are important in the determination of the parameters of the Pearsons distribution. Results: The approach is illustrated in two examples;one from veterinary microbiology and food safety data and the other on data from clinical medicine. We derived the four central moments of the target statistics, together with the bootstrap method to evaluate the parameters of Pearsons distribution. The fitted Pearsons curves of Types I and II were recommended based on the available data. The R-codes are also provided to be readily used by the readers.

A NEW CORRENTROPY BASED TDE METHOD UNDER α-STABLE DISTRIBUTION NOISE ENVIRONMENT

This paper presents a robust time delay estimation algorithm for the α-Stable noise based on correntropy. Many time delay estimation algorithms derived for impulsive stable noise are based on the theory of Fractional Lower Order Statistics (FLOS). Unlike previously introduced FLOS-type algorithms, the new algorithm is proposed to estimate the time delay by maximizing the generalized correlation function of two observed signals needing neither prior information nor estimation of the numerical value of the stable noise's characteristic exponent. An interval for kernel selection is found for a wide range of characteristic exponent values of α-Stable distribution. Simulations show the proposed algorithm offers superior performance over the existing covariation time delay estimation, least mean p-norm time delay estimation and achieves slightly improved performance than fractional lower order covariance time delay estimation at lower signal to noise ratio when the noise is highly impulsive.

Reduction of Vibration Noise for Amorphous Metal Alloy Core Distribution Transformer

To understand the vibration noise behaviors of amorphous metal alloy core distribution transformer(AMACDT), a 10 k VA prototype was tested under no-load and short-circuit conditions, respectively. The vibration characteristics were described when rated voltage was applied to the secondary side, and the primary side was connected with different load resistances. The largest amplitude positions on the upper bracket and tank surfaces were recorded by vibration sensors arranged on the surface. A data-acquisition platform was set up for signal measurement. The vibration amplitude related to frequency was discussed, and experimental results indicated that the position with the largest amplitude accrued in the middle of the upper bracket and tank surface, at phases a and c, respectively. The experimental results suggest that magnetostrictive and electrodynamic forces play a major role in exciting the vibration noise. At the same time, some rib-reinforcements were welded on the upper bracket and tank surfaces to lessen the vibration energy, which reduced the noise.

Multi-user quantum key distribution with collective eavesdropping detection over collective-noise channels

A multi-user quantum key distribution protocol is proposed with single particles and the collective eavesdropping detection strategy on a star network. By utilizing this protocol, any two users of the network can accomplish quantum key distribution with the help of a serving center. Due to the utilization of the collective eavesdropping detection strategy, the users of the protocol just need to have the ability of performing certain unitary operations. Furthermore, we present three fault-tolerant versions of the proposed protocol, which can combat with the errors over different collective-noise channels.The security of all the proposed protocols is guaranteed by the theorems on quantum operation discrimination.

Effect of uneven noise source and/or station distribution on estimating the azimuth anisotropy of surface waves

With the development of the dense array,the surface wave velocity and azimuthal anisotropy under the array can be directly obtained by beamforming the noise cross-correlation functions(NCFs). However, the retrieval of the Green’s function by cross-correlating the seismic noise requires that the noise source has a uniform distribution. For the case with uneven noise source, the azimuthal dependence on the sources in the expression for the spatial coherence function, which corresponds to the NCF in the time domain,has the same form as the azimuthal dependence of the surface wave velocity in weakly anisotropic media. Therefore, the uneven noise source will affect the surface wave anisotropy extraction. In this study, three passive seismic methods, i.e.,beamforming, SPAC(spatial autocorrelation), and NCF, are compared to demonstrate that an uneven source distribution and uneven station distribution have equivalent effects on the outcome from each method. A beamforming method is proposed to directly extract the velocity and azimuthal anisotropy of surface waves. The effect of uneven noise source and/or station distribution on estimating the azimuth anisotropy of surface waves was investigated using data from the ChinArray Phase Ⅱ. A method for correcting the apparent anisotropy in beamforming results caused by an uneven station distribution is suggested.

Skew t Distribution-Based Nonlinear Filter with Asymmetric Measurement Noise Using Variational Bayesian Inference

This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise.The system states and the statistics of skew t noise distribution,including the shape matrix,the scale matrix,and the degree of freedom(DOF)are estimated jointly by employing variational Bayesian(VB)inference.The proposed method is validated in a target tracking example.Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.

Modeling random telegraph signal noise in CMOS image sensor under low light based on binomial distribution

The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random telegraph signal noise in the pixel source follower based on the binomial distribution is set up. The number of electrons captured or released by the oxide traps in the unit time is described as the random variables which obey the binomial distribution. As a result,the output states and the corresponding probabilities of the first and the second samples of the correlated double sampling circuit are acquired. The standard deviation of the output states after the correlated double sampling circuit can be obtained accordingly. In the simulation section, one hundred thousand samples of the source follower MOSFET have been simulated,and the simulation results show that the proposed model has the similar statistical characteristics with the existing models under the effect of the channel length and the density of the oxide trap. Moreover, the noise histogram of the proposed model has been evaluated at different environmental temperatures.

Investigation on Noise Pollution Comprehensive Treatment of Distribution Transformer in Living Area

In the current paper,which deals with the noise pollution excited by distribution transformers in the living area,a comprehensive treatment scheme is put forward for the purpose of reducing the sound pressure level emitting into the environment.In accordance with the associated test standard,the sound pressure levels of distribution transformer and surrounding environment are not only tested but analyzed as well.The measurements were carried out with the frequency analysis of the 1/3 octave resolution,with the center frequencies at 125 Hz,250 Hz,400 Hz,and 500 Hz.As illustrated,on the basis of the measurement results,the frequency of noise at 500 Hz of distribution transformer causes the major noise pollution in the surrounding environment.This measurement result is in line with the noise frequency characteristics of distribution transformer.There are two transmission routes of noise:(i)the noise excited by distribution transformer transmits by means of the wall of distribution room,and (ii)part of noise spreads through the ground of distribution room.Accordingly,acoustic shield and vibration isolation device are applied for the reduction of the low frequency noise emitted through the above two paths.Aimed at applying the appropriate acoustic material and vibration mounting,the evaluation of the noise reduction and vibration absorption is carried out in accordance with the sound and vibration insulation theory.Following the noise treatment,the transformer and environment noise are measured again.The corresponding findings shed light on the fact that the sound level satisfied the requirement of limits of the ordinance.The proposed noise treatment scheme can be applied to the existing power distribution facilities for controlling the sound levels that reach a point where it is comparatively more unobjectionable.

Intercept-resend attack on six-state quantum key distribution over collective-rotation noise channels

We investigate the effect of collective-rotation noise on the security of the six-state quantum key distribution. We study the case where the eavesdropper, Eve, performs an intercept-resend attack on the quantum communication between Alice, the sender, and Bob, the receiver. We first derive the collective-rotation noise model for the six-state protocol and then parameterize the mutual information between Alice and Eve. We then derive quantum bit error rate for three interceptresend attack scenarios. We observe that the six-state protocol is robust against intercept-resend attacks on collective rotation noise channels when the rotation angle is kept within certain bounds.

Noise temperature distribution of superconducting hot electron bolometer mixers

We report on the investigation of optimal bias region of a wide-band superconducting hot electron bolometer(HEB)mixer in terms of noise temperature performance for multi-pixel heterodyne receiver application in the 5-meter Dome A Terahertz Explorer(DATE5)telescope.By evaluating the double sideband(DSB)receiver noise temperature(Trec)across a wide frequency range from 0.2 THz to 1.34 THz and with a large number of bias points,a broad optimal bias region has been observed,illustrating a good bias applicability for multipixel application since the performance of the HEB mixer is uniquely determined by each bias point.The noise temperature of the HEB mixer has been analyzed by calibrating the noise contribution of all RF components,whose transmissions have been measured by a time-domain spectroscopy.The corrected noise temperature distribution shows a frequency independence relation.The dependence of the optimal bias region on the bath temperature of the HEB mixer has also been investigated,the bath temperature has limited effect on the lowest receiver noise temperature until 7 K,however the optimal bias region deteriorates obviously with increasing bath temperature.

Path integral solutions for n-dimensional stochastic differential equations underα-stable Lévy excitation

In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic processes.Then,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov equation.Besides,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.

Research on Noise Reduction Approach of Raman-Based Distributed Temperature Sensor Based on Nonlinear Filter

The accuracy of temperature measurement is often reduced due to random noise in Raman-based distributed temperature sensor (RDTS). A noise reduction method based on a nonlinear filter is thus proposed in this paper. Compared with the temperature demodulation results of raw signals, the proposed method in this paper can reduce the average maximum deviation of temperature measurement results from 4.1°C to 1.2°C at 40.0°C, 50.0°C and 60.0°C. And the proposed method in this paper can improve the accuracy of temperature measurement of Raman-based distributed temperature sensor better than the commonly used wavelet transform-based method. The advantages of the proposed method in improving the accuracy of temperature measurement for Raman-based distributed temperature sensor are quantitatively reflected in the maximum deviation and root mean square error of temperature measurement results. Therefore, this paper proposes an effective and feasible method to improve the accuracy of temperature measurement results for Raman-based distributed temperature sensor.

Global Dynamics of a Stochastic Two-Prey One-Predator Model with <i>S</i>-Type Distributed Delays and Lévy Noises

In this paper, a stochastic two-prey one-predator model with S-type distributed time delays and Lévy noises is considered. Using the comparison theorem and Ito’s formula, sufficient conditions of persistence in the mean and extinct for each population are established. Then, conditions of global attractivity and stability in distribution by Barbalat’s conclusion are also obtained. Furthermore, Euler numerical simulation method is given to demonstrate our conclusions.

DOA Estimation Based on Sparse Representation of the Fractional Lower Order Statistics in Impulsive Noise

This paper is mainly to deal with the problem of direction of arrival(DOA) estimations of multiple narrow-band sources impinging on a uniform linear array under impulsive noise environments. By modeling the impulsive noise as α-stable distribution, new methods which combine the sparse signal representation technique and fractional lower order statistics theory are proposed. In the new algorithms, the fractional lower order statistics vectors of the array output signal are sparsely represented on an overcomplete basis and the DOAs can be effectively estimated by searching the sparsest coefficients. To enhance the robustness performance of the proposed algorithms,the improved algorithms are advanced by eliminating the fractional lower order statistics of the noise from the fractional lower order statistics vector of the array output through a linear transformation. Simulation results have shown the effectiveness of the proposed methods for a wide range of highly impulsive environments.

PARAMETER ESTIMATION FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SMALL STABLE NOISES FROM DISCRETE OBSERVATIONS

We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small a-stable noises, observed at n regularly spaced time points ti = i/n, i = 1,...,n on [0, 1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator （LSE） when a small dispersion parameter ε→0 and n →∞ simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.

Steady-state analysis subject to a coloured and a white additive of a bistable system multiplicative noise noise with coloured cross-correlated noises

The steady-state properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different values of noise correlation times T1 and T2. After introducing a dimensionless parameter R（R = α/D, D is the intensity of the multiplicative noise and a is the intensity of the additive noise）, and performing the numerical computations, we find the following points： （1） For the case of R 〉 1, A （the intensity of correlation between additive and multiplicative noises）, T1 and T2 can induce the stationary probability distribution （SPD） transition from bimodal to unimodal in structure, but for the cases of R _〈 1, the bimodal structure is preserved; （2） a can also induce the SPD transition from bimodal to unimodal in structure; （3） the bimodal structure of the SPD exhibits a symmetrical structure as D increases.

Performance analysis of Turbo-Codes in communication channels with impulsive noise

Performance of Turbo-Codes in communication channels with impulsive noise is analyzed. First, mathematical model of impulsive noise is presented because it has non-Gaussian nature and is found in many wireless channels due to impulsive phenomena of radio-frequency interference. Then, with linear Log-MAP decoding algorithm for its low complexity, Turbo-Codes are adopted and analyzed in such communication channels. To confirm the performance of the proposed method, simulations on both static and fully interleaved flat Rayleigh fading channels with impulsive noise have been carried out. It is shown that Turbo-Codes have a better performance than the conventional methods （e.g. convolutionally coded system）.

GENERALIZED OPERATORS AND OPERATOR-VALUED DISTRIBUTIONS IN QUANTUM FIELD THEORY

The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.

Effects of geometric design of forest road and roadside vegetation on traffic noise reduction

Geometric design of forest roads and design of their landscapes can reduce noise pollution and its harmful effects on human health. We investigated the effects of technical and biological parameters such as geometric road design and various roadside tree stands on reducing noise pollution according to the tree density and distance from roadway in Darabkola Forests, Sari, Iran. We recorded the noise generated by a car （Land Rover） relative to changes in longitudinal slope, horizontal curve radius and type of road pavement. We also measured noise levels according to roadside tree density and stand type （coniferous and hardwood） in 40 rectangular plots of three widths （25, 100 and 300 m） and 50 m length that were randomly demar- cated along forest roads. The changes in noise level were recorded using a decibel meter with an accuracy of q-1.5 dB and resolution of 0.1 dB. Noise levels were higher alongside unpaved roads than alongside paved roads. There was an inverse relationship between the measured noise level and horizontal curve radius. The rate of noise level on horizontal curve with a radius less than 30, 30-45 m and more than 45 m were 64.8, 70.8 and 75.9 dB, respectively. The noise level increased with the increasing longitudinal slope of the road. There was a significant difference between the noise level on slopes less than 3 % （67 dB） and 3-8 % （71.2 dB） in comparison with slopes greater than 8 % （77.8 dB）, （p 〈 0.05）. Pinus brutia L. reduced the noise level more （about 6 dB） in stands of 1/3 density of mixed hardwoods within 25 m from middle of the road. Careful design of geometric properties of forest roads as well as planting coniferous trees with hardwoods is a suitable solution for reducing noise pollution.