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.

Recognition of multi-carrier OFDM and single-carrier with alpha-stable distribution noise

In order to identify the multi-carrier orthogonal frequency division multiplexing(OFDM) and the single-carrier signal in the non-Gaussian noise environment, different features of the two signals are analyzed in terms of five parameters: generalized normalized fourth-order cumulant, the maximum value of the instantaneous amplitude power spectral density, absolute standard deviation of instantaneous phase on the section with weak signals, and position and numbers of the generalized cyclic spectrum's peak. The recognition method of the multi-carrier OFDM and single-carrier signal is proposed in the environment with alpha-stable distribution noise. Simulation results show that the recognition rate of the multi-carrier OFDM can reach 100% when the mixed signal to noise ratio(MSNR) is greater than-5 dB and the recognition rate can reach 90% for the single-carrier when the MSNR is greater than 2 dB.

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.

Stochastic Resonance in an Asymmetric Mono-stable System Subject to Two Periodic Forces and Multiplicative and Additive Noise

在易于二外部周期的力量、趋于增加的一个不对称的单稳态的系统和添加剂噪音的随机的回声(SR ) 的现象被调查。为基本、更高的泛音的 signal-to-noise 比率(SNR ) 是紧张的一个非单调的函数，这被显示出趋于增加并且添加剂噪音，以及系统参数。而且，为基本泛音的 SNR 随系统不对称现象的增加减少，当为更高的泛音的 SNR 是 non-monotonically 表现时，系统不对称现象变化。

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.

Stochastic resonance in a time-delayed mono-stable system with correlated multiplicative and additive white noise

This paper considers the stochastic resonance for a time-delayed mono-stable system, driven by correlated multiplicative and additive white noise. It finds that the output signal-to-noise ratio （SNR） varies non-monotonically with the delayed times. The SNR varies non-monotonically with the increase of the intensities of the multiplicative and additive noise, with the increase of the correlation strength between the two noises, as well as with the system parameter.

Analysis of weak signal detection based on tri-stable system under Levy noise

Stochastic resonance system is an effective method to extract weak signal.However,system output is directly influenced by system parameters.Aiming at this,the Levy noise is combined with a tri-stable stochastic resonance system.The average signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon.The characteristics of tri-stable stochastic resonance under Levy noise is analyzed in depth.First,the method of generating Levy noise,the effect of tri-stable system parameters on the potential function and corresponding potential force are presented in detail.Then,the effects of tri-stable system parameters w,a,b,and Levy noise intensity amplification factor D on the resonant output can be explored with different Levy noises.Finally,the tri-stable stochastic resonance system is applied to the bearing fault detection.Simulation results show that the stochastic resonance phenomenon can be induced by tuning the system parameters w,a,and b under different distributions of Levy noise,then the weak signal can be detected.The parameter intervals which can induce stochastic resonances are approximately equal.Moreover,by adjusting the intensity amplification factor D of Levy noise,the stochastic resonances can happen similarly.In bearing fault detection,the detection effect of the tri-stable stochastic resonance system is superior to the bistable stochastic resonance system.

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.

New Blind Recognition Method of SCLD and OFDM in Alpha-Stable Noise

This paper deals with modulation classification under the alpha-stable noise condition. Our goal is to discriminate orthogonal frequency division multiplexing (OFDM) modulation type from single carrier linear digital (SCLD) modulations in this scenario. Based on the new results concerning the generalized cyclostationarity of these signals in alpha-stable noise which are presented in this paper, we construct new modulation classification features without any priori information of carrier frequency and timing offset of the received signals, and use support vector machine (SVM) as classifier to discriminate OFDM from SCLD. Simulation results show that the recognition accuracy of the proposed algorithm can be up to 95% when the mix signal to noise ratio (MSNR) is up to ?1 dB.

Estimating distribution of water uptake with depth of winter wheat by hydrogen and oxygen stable isotopes under different irrigation depths

Crop root system plays an important role in the water cycle of the soil-plant-atmosphere continuum. In this study, com- bined isotope techniques, root length density and root cell activity analysis were used to investigate the root water uptake mechanisms of winter wheat （Triticum aesfivum L.） under different irrigation depths in the North China Plain. Both direct inference approach and multisource linear mixing model were applied to estimate the distribution of water uptake with depth in six growing stages. Results showed that winter wheat under land surface irrigation treatment （Ts） mainly absorbed water from 10-20 cm soil layers in the wintering and green stages （66.9 and 72.0%, respectively）; 0-20 cm （57.0%） in the jointing stage; 0-40 （15.3%） and 80-180 cm （58.1%） in the heading stage; 60-80 （13.2%） and 180-220 cm （35.5%） in the filling stage; and 0-40 （46.8%） and 80-100 cm （31.0%） in the ripening stage. Winter wheat under whole soil layers irrigation treatment （Tw） absorbed more water from deep soil layer than Ts in heading, filling and ripening stages. Moreover, root cell activity and root length density of winter wheat under TW were significantly greater than that of Ts in the three stages. We concluded that distribution of water uptake with depth was affected by the availability of water sources, the root length density and root cell activity. Implementation of the whole soil layers irrigation method can affect root system distribution and thereby increase water use from deeper soil and enhance water use efficiency.

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.

Effects of Long-Term Fertilization on the Distribution of Carbon, Nitrogen and Phosphorus in Water-Stable Aggregates in Paddy Soil

We investigated the size distribution of water-stable aggregates and the soil carbon, nitrogen and phosphorus concentration over aggregate size fractions based on a long-term （1990-2006） fertilization experiment in a reddish paddy soil. The results showed that the largest water-stable aggregate （WSA） （〉5 mm） and the smallest WSA （〈0.25 mm） took up the first largest proportion （38.3%） and the second largest proportion （23.3%）, respectively. Application of organic materials increased the proportion of the large WSA （〉2 mm） and decreased the proportion of the small WSA （〈1 ram）, resulting in an increase in the mean weight diameter of WSA, whereas application of chemical fertilizer had little effect. Application of organic materials, especially combined with chemical fertilizers, increased total carbon, nitrogen and phosphorus concentrations in all sizes of WSA, and total carbon, nitrogen and phosphorus were prone to concentrate in the large WSA. Further more, application of organic materials improved the supply effectiveness of available phosphorus, whereas had little influence on the labile carbon in WSA. Application of chemical fertilizers improved concentrations of total and available phosphorus in all sizes of WSA, whereas had little influence on total carbon and nitrogen contents. Economical fertilization model maintained the soil fertility when compared with full dose of chemical fertilizers, indicating that using organic materials could reduce chemical fertilizers by about one third.

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.

ON THE TESTING FOR ALPHA-STABLE DISTRIBUTIONS OF ETHERNET NETWORK TRAFFIC

The modeling of network traffic is important for the design and application of networks, but little is known as to the characteristics of distribution of packets in network traffic. In this letter the distribution of packets in network traffic is explored.