Accurate frequency estimation in a wideband digital receiver using the FFT algorithm encounters challenges, such as spectral leakage resulting from the FFT’s assumption of signal periodicity. High-resolution FFTs pos...Accurate frequency estimation in a wideband digital receiver using the FFT algorithm encounters challenges, such as spectral leakage resulting from the FFT’s assumption of signal periodicity. High-resolution FFTs pose computational demands, and estimating non-integer multiples of frequency resolution proves exceptionally challenging. This paper introduces two novel methods for enhanced frequency precision: polynomial interpolation and array indexing, comparing their results with super-resolution and scalloping loss. Simulation results demonstrate the effectiveness of the proposed methods in contemporary radar systems, with array indexing providing the best frequency estimation despite utilizing maximum hardware resources. The paper demonstrates a trade-off between accurate frequency estimation and hardware resources when comparing polynomial interpolation and array indexing.展开更多
This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both ...This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.展开更多
Olkin [1] proposed a ratio estimator considering p auxiliary variables under simple random sampling. As is expected, Simple Random Sampling comes with relatively low levels of precision especially with regard to the f...Olkin [1] proposed a ratio estimator considering p auxiliary variables under simple random sampling. As is expected, Simple Random Sampling comes with relatively low levels of precision especially with regard to the fact that its variance is greatest amongst all the sampling schemes. We extend this to stratified random sampling and we consider a case where the strata have varying weights. We have proposed a Multivariate Ratio Estimator for the population mean in the presence of two auxiliary variables under Stratified Random Sampling with L strata. Based on an empirical study with simulations in R statistical software, the proposed estimator was found to have a smaller bias as compared to Olkin’s estimator.展开更多
应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝...应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。展开更多
The errors in radar quantitative precipitation estimations consist not only of systematic biases caused by random noises but also spatially nonuniform biases in radar rainfall at individual rain-gauge stations. In thi...The errors in radar quantitative precipitation estimations consist not only of systematic biases caused by random noises but also spatially nonuniform biases in radar rainfall at individual rain-gauge stations. In this study, a real-time adjustment to the radar reflectivity rainfall rates （Z R） relationship scheme and the gauge-corrected, radar-based, estimation scheme with inverse distance weighting interpolation was devel- oped. Based on the characteristics of the two schemes, the two-step correction technique of radar quantitative precipitation estimation is proposed. To minimize the errors between radar quantitative precipitation es- timations and rain gauge observations, a real-time adjustment to the Z R relationship scheme is used to remove systematic bias on the time-domain. The gauge-corrected, radar-based, estimation scheme is then used to eliminate non-uniform errors in space. Based on radar data and rain gauge observations near the Huaihe River, the two-step correction technique was evaluated using two heavy-precipitation events. The results show that the proposed scheme improved not only in the underestimation of rainfall but also reduced the root-mean-square error and the mean relative error of radar-rain gauge pairs.展开更多
In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.
The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a m...The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a method to calculate the Q-factor based on the prestack Q-factor inversion and the generalized S-transform. The proposed method specifies a standard primary wavelet and calculates the cumulative Q-factors; then, it finds the interlaminar Q-factors using the relation between Q and offset(QVO) and the Dix formula. The proposed method is alternative to methods that calculate interlaminar Q-factors after horizon picking. Because the frequency spectrum of each horizon can be extracted continuously on a 2D time–frequency spectrum, the method is called the continuous spectral ratio slope(CSRS) method. Compared with the other Q-inversion methods, the method offers nearly effortless computations and stability, and has mathematical and physical significance. We use numerical modeling to verify the feasibility of the method and apply it to real data from an oilfield in Ahdeb, Iraq. The results suggest that the resolution and spatial stability of the Q-profile are optimal and contain abundant interlaminar information that is extremely helpful in making lithology and fluid predictions.展开更多
In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error est...In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson＇s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds.展开更多
文摘Accurate frequency estimation in a wideband digital receiver using the FFT algorithm encounters challenges, such as spectral leakage resulting from the FFT’s assumption of signal periodicity. High-resolution FFTs pose computational demands, and estimating non-integer multiples of frequency resolution proves exceptionally challenging. This paper introduces two novel methods for enhanced frequency precision: polynomial interpolation and array indexing, comparing their results with super-resolution and scalloping loss. Simulation results demonstrate the effectiveness of the proposed methods in contemporary radar systems, with array indexing providing the best frequency estimation despite utilizing maximum hardware resources. The paper demonstrates a trade-off between accurate frequency estimation and hardware resources when comparing polynomial interpolation and array indexing.
基金supported by the National Science Foundations (DMS0504783 DMS0604207)National Science Fund for Distinguished Young Scholars of China (70825005)
文摘This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.
文摘Olkin [1] proposed a ratio estimator considering p auxiliary variables under simple random sampling. As is expected, Simple Random Sampling comes with relatively low levels of precision especially with regard to the fact that its variance is greatest amongst all the sampling schemes. We extend this to stratified random sampling and we consider a case where the strata have varying weights. We have proposed a Multivariate Ratio Estimator for the population mean in the presence of two auxiliary variables under Stratified Random Sampling with L strata. Based on an empirical study with simulations in R statistical software, the proposed estimator was found to have a smaller bias as compared to Olkin’s estimator.
文摘应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。
基金supported bythe Special Fund for Basic Research and Operation of the Chinese Academy of Meteorological Sciences (GrantNo. 2011Y004)the Research and Development Special Fund for Public Welfare Industry (Meteorology+2 种基金Grant No.GYHY201006042)the National Natural Science Foundation of China (Grant No. 40975014)the Open Research Fund for State Key Laboratory of Hydroscience and Engineering of Tsinghua University (the search of basin QPE and QPF based on new generation of weather and numerical models)
文摘The errors in radar quantitative precipitation estimations consist not only of systematic biases caused by random noises but also spatially nonuniform biases in radar rainfall at individual rain-gauge stations. In this study, a real-time adjustment to the radar reflectivity rainfall rates （Z R） relationship scheme and the gauge-corrected, radar-based, estimation scheme with inverse distance weighting interpolation was devel- oped. Based on the characteristics of the two schemes, the two-step correction technique of radar quantitative precipitation estimation is proposed. To minimize the errors between radar quantitative precipitation es- timations and rain gauge observations, a real-time adjustment to the Z R relationship scheme is used to remove systematic bias on the time-domain. The gauge-corrected, radar-based, estimation scheme is then used to eliminate non-uniform errors in space. Based on radar data and rain gauge observations near the Huaihe River, the two-step correction technique was evaluated using two heavy-precipitation events. The results show that the proposed scheme improved not only in the underestimation of rainfall but also reduced the root-mean-square error and the mean relative error of radar-rain gauge pairs.
基金supported by the National Natural Science Foundation of China(11571104)the Hunan Provincial Innovation Foundation for Postgraduate(CX2017B220)Supported by the Construct Program of the Key Discipline in Hunan Province
文摘In this article, the authors give a typical integral＇s bidirectional estimates for allcases. At the same time, several equivalent characterizations on the F（p, q, s, k） space in theunit ball of Cn are given.
基金supported by The National Key Research and Development Program Plane(No.2017YFC0601505)National Natural Science Foundation(No.41672325)Science&Technology Department of Sichuan Province Technology Project(No.2017GZ0393)
文摘The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a method to calculate the Q-factor based on the prestack Q-factor inversion and the generalized S-transform. The proposed method specifies a standard primary wavelet and calculates the cumulative Q-factors; then, it finds the interlaminar Q-factors using the relation between Q and offset(QVO) and the Dix formula. The proposed method is alternative to methods that calculate interlaminar Q-factors after horizon picking. Because the frequency spectrum of each horizon can be extracted continuously on a 2D time–frequency spectrum, the method is called the continuous spectral ratio slope(CSRS) method. Compared with the other Q-inversion methods, the method offers nearly effortless computations and stability, and has mathematical and physical significance. We use numerical modeling to verify the feasibility of the method and apply it to real data from an oilfield in Ahdeb, Iraq. The results suggest that the resolution and spatial stability of the Q-profile are optimal and contain abundant interlaminar information that is extremely helpful in making lithology and fluid predictions.
基金supported by National Natural Science Foundation of China (11071226 11201122)
文摘In this article, we study the explicit expressions of the constants in the error estimate of the nonconforming finite element method. We explicitly obtain the approximation error estimate and the consistency error estimate for the Wilson＇s element without the regular assumption, respectively, which implies the final finite element error estimate. Such explicit a priori error estimates can be used as computable error bounds.
