A New Class of Biased Linear Estimators in Deficient-rank Linear Models

In this paper, we define a new class of biased linear estimators of the vector of unknown parameters in the deficient_rank linear model based on the spectral decomposition expression of the best linear minimun bias estimator. Some important properties are discussed. By appropriate choices of bias parameters, we construct many interested and useful biased linear estimators, which are the extension of ordinary biased linear estimators in the full_rank linear model to the deficient_rank linear model. At last, we give a numerical example in geodetic adjustment.

用于航空电磁数据调平处理的导数突变点统计法

航空电磁数据中经常存在条带状误差,为消除这种误差,通常采用窗口滤波。但是,窗口参数及滤波参数要求极为严格,且不能区分调平误差和其类似大小的地质异常,需要操作者多次尝试以寻求合适的处理参数。这里提出了导数突变点统计法,该方法首先在沿伪切割线方向(垂直飞行方向),对网格化的航空电磁数据求取伪切割线的导数,采用高通滤波方法滤掉幅值比较小的导数突变点;然后统计每条航线上的突变点个数,根据预设的阈值,确定出存在条带误差的航线;再针对这条航线上的数据,采用均值滤波得到调平结果。导数突变点统计法能自动找出存在误差的航线,并只针对误差线进行滤波,能有效消除条带状误差,极大地保留真实地质异常。导数突变点统计方法算法简单,输入参数少,数据处理速度快,为航空电磁数据调平提供了一种新思路。

DESCRIPTIONS OF THE CYLINDRICAL HELIX WITH NURBS

The representation of a cylindrical helix by Non-Uniform Rational B-Spline (NURBS) curves is presented in this paper. A method is proposed to assess the influences produced by different ways to determine the control ver-texes positions of helix. The error distribution cases between the helix approximated by NURBS curves and the original theoretical one are also analyzed. Meanwhile a computational method that guarantees the precision requirements is presented.

Rice condition numbers of QR and Cholesky factorizations

A condition number is an amplification coefficient due to errors in computing. Thus the theory of condition numbers plays an important role in error analysis. In this paper, following the approach of Rice, condition numbers are defined for factors of some matrix factorizations such as the Cholesky factorization of a symmetric positive definite matrix and QR factorization of a general matrix. The condition numbers are derived by a technique of analytic expansion of the factor dependent on one parameter and matrix-vector equation. Condition numbers of the Cholesky and QR factors are different from the ones previously introduced by other authors, but similar to Chang's results. In Cholesky factorization, corresponding with the condition number of the factor matrix L , K _L is a low bound of Stewart's condition number K .

An Existent Condition of Error Bounds for Abstract Linear Inequality System

We consider the abstract linear inequality system （A, C, b） and give a sufficient condition for the system （A, C, b） to have an error bound, which extends the previous result.

Error Estimate of the Fourier Collocation Method for the Benjamin-Ono Equation

In this paper,the Fourier collocation method for solving the generalized Benjamin-Ono equation with periodic boundary conditions is analyzed.Stability of the semi-discrete scheme is proved and error estimate in H^(1/2)-norm is obtained.

用于频率域航电数据调平的区域控制法

消除航空电磁数据中的条带状误差最通用的方法是结合手工调平和以窗口滤波为主要手段的计算机自动调平技术。为解决窗口参数的选取问题,提出了区域控制法。该方法首先利用2D-DDNL(data dpendent nonlinear)滤波器原理将整个网格化的航电数据矩阵作为一个窗口,得到整个区域的背景值,作为总区域背景场控制点值,用其对这个区域进行小窗口2D-DDNL滤波得到的局部背景值进行调节,即自动改变窗口参数,使局部背景场适应总区域背景场控制点值;这样得到的背景场与原始场相减,便得到一个包含局部地质异常和条带误差的中间量;对这个中间量采用一维改进的中值滤波,分离出条带误差,进而得到最终调平结果。该方法能自动调节窗口参数大小,减少了人为干扰,自动化程度高,较好地保留了有用地质信息,为航电数据调平提供了一种新方法。

Analysis of Error for a Rotating Strap-down Inertial Navigation System with Fibro Gyro

The error equation of a rotating inertial navigation system was introduced. The effect of the system's main error source (constant drift of gyro and zero bias of accelerometer) under rotating conditions for the system was analyzed. Validity of theoretical analysis was shown via simulation, and that provides a theoretical foundation for a rotating strap-down inertial navigation system during actual experimentation and application.

A Class of High Accuracy Explicit Difference Schemes for Solving the Heat-conduction Equation of High-dimension

In this paper, a class of explicit difference schemes with parameters for solving five-dimensional heat-conduction equation are constructed and studied.the truncation error reaches O（τ^2＋ h%4）, and the stability condition is given. Finally, the numerical examples and numerical results are presented to show the advantage of the schemes and the correctness of theoretical analysis.

深刻认识“在误差允许范围内”——以电火花打点计时器测速度为例

本文利用误差分析理论定量计算了打点计时器测物体速度时误差,把高中常用的"在误差允许范围内"这句术语进行了深刻剖析,旨在表明如何才能有理有据地说出"在误差允许范围内",本文所涉及的基础误差理论和方法对高中物理实验中的误差分析有一定的参考价值.

基于最小二乘支持向量机算法的小地锚抗拔承载力研究（英文）

目的:基于最小二乘支持向量机算法预测小地锚的抗拔承载力。方法:最小二乘支持向量机算法中的输入参数包括等效地锚直径,地锚埋置深度,平均顶椎阻力,平均椎套摩擦力以及安装工艺。使用现场试验的119组数据中的83组数据进行最小二乘支持向量机回归模型分析,并使用剩余的36组数据测试模型的拟合良好性;同时用敏感度分析研究每个输入参数的作用。结论:通过与人工神经网络模型的对比,发现最小二乘支持向量机的性能表现优异。

A correction method of color projection fringes in 3D contour measurement

In the three-dimensional(3D) contour measurement,the phase shift profilometry(PSP) method is the most widely used one.However,the measurement speed of PSP is very low because of the multiple projections.In order to improve the measurement speed,color grating stripes are used for measurement in this paper.During the measurement,only one color sinusoidal fringe is projected on the measured object.Therefore,the measurement speed is greatly improved.Since there is coupling or interference phenomenon between the adjacent color grating stripes,a color correction method is used to improve the measurement results.A method for correcting nonlinear error of measurement system is proposed in this paper,and the sinusoidal property of acquired image after correction is better than that before correction.Experimental results show that with these correction methods,the measurement errors can be reduced.Therefore,it can support a good foundation for the high-precision 3D reconstruction.

Long-term semi-autonomous orbit determination supported by a few ground stations for navigation constellation

In view of the present technology of autonomous orbit determination for navigation satellite constellation(NSC) and the geographical conditions of China,we propose a long-term semi-autonomous orbit determination scheme supported by a few ground stations for NSC in this paper.Since the effect of rotation and translation of the entire constellation relative to the inertial reference frame can bring large errors to the autonomous orbit determination using only cross-link range measurement,a few ground stations(such as 1-3) are supposed to construct the connection between the NSC and the ground.Supported by such a few ground stations,the NSC can realize long-term orbit determination called semi-autonomous orbit determination.The simulation results based on the IGS ephemeris indicate that,for a certain degree of measurement errors,the NSC can maintain its semi-autonomous orbit determination in a period of 240 days within 5 meters of URE.

Influence of Ice on Soil Elemental Characterization via Portable X-Ray Fluorescence Spectrometry

Field portable X-ray fluorescence （PXRF） spectrometry has become an increasingly popular technique for in-situ elemental characterization of soils. The technique is fast, portable, and accurate, requiring minimal sample preparation and no consumables. However, soil moisture 〉 20% has been known to cause fluorescence denudation and error in elemental reporting and few studies have evaluated the presence of soil moisture in solid form as ice. Gelisols （USDA Soil Taxonomy）, permafrost-affected soils, cover a large amount of the land surface in the northern and southern hemispheres. Thus, the applicability of PXRF in those areas requires further investigation. PXRF was used to scan the elemental composition （Ba, Ca, Cr, Fe, K, Mn, Pb, Rb, Sr, Ti, Zn, and Zr） of 13 pedons in central and northern Alaska, USA. Four types of scans were completed： 1） in-situ frozen soil, 2） re-frozen soil in the laboratory, 3） melted soil/water mixture in the laboratory, and 4） moisture-corrected soil. All were then compared to oven dry soil scans. Results showed that the majority of PXRF readings from in-situ, re-frozen, and melted samples were significantly underestimated, compared to the readings on oven dry samples, owing to the interference expected by moisture. However, when the moisture contents were divided into 〉 40% and 〈 40〈 groups, the PXRF readings under different scanning conditions performed better in the group with 〈 40% moisture contents. Most elements of the scans on the melted samples with 〈 40% moisture contents acceptably compared to those of the dry samples, with R2 values ranging from 0.446 （Mn） to 0.930 （St）. However, underestimation of the melted samples was still quite apparent. Moisture-corrected sample PXRF readings provided the best correlation to those of the dry, ground samples as indicated by higher R2 values, lower root mean square errors （RMSEs）, and slopes closer to 1 in linear regression equations. However, the in-situ （frozen） sample scans did not differ appreciably from the melted sample scans in their correlations to dry sample scans in terms of R2 values （0.81 vs. 0.88）, RMSEs （1.06 vs. 0.85）, and slopes （0.88 vs. 0.92）. Notably, all of those relationships improved for the group with moisture contents 〈 40%.

MAXIMUM SCORE CHANGE-POINT ESTIMATION IN BINARY RESPONSE MODEL

This paper is concerned with the estimation of change-point in a binary response model with the assumption that the conditional median of the error term, given the explanatory variable, is zero. We construct an estimation of change-point based on the maximum score function and give its exponential convergence rate under some mild conditions.

Comparison of Synchronization Ability of Four Types of Regular Coupled Networks

We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of null solution of error equations, further, into the negative definiteness of some symmetric matrices, thus we get the sufficient synchronization stability conditions. To test the valid of the results, we take the Chua's circuit as an example. Although the theoretical synchronization thresholds appear to be very conservative, they provide new insights about the influence of topology and scale of networks on synchronization, and that the theoretical results and our numerical simulations are consistent.

Leak detection in pipelines by exclusively frequency domain method

A further development of exclusively inverse frequency domain method for leak detection in pipelines is presented and validated.The location and leakage can be determined by analyzing the difference of transient water head response between the simulated and measured data in frequency domain.The transient signals are generated by portion sharp closure of a valve from the small constant opening and it needs only a few meters of water.The discrete boundary conditions and observation data are both transformed in frequency domain by Laplace transform.Example in numerical simulation is studied for demonstration of this approach.The application of the method to an experimental pipeline confirms the analysis and illustrates successful detection of the single pipeline leak.The precalibration approach is presented to minimize the effect of data and model error and it splits the method into two parts.One uses data from a known state to fit the parameters of the model and the other uses data from the current state for the fitting of leak parameters using the now calibrated model.Some important practical parameters such as wave speed,friction in steady and unsteady state and the adaptability of the method are discussed.It was found that the nonlinearity errors associated with valve boundary condition could be prevented by consideration of the induced flow perturbation curve shape.

A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids

A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k 4.The main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup condition.In particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each tetrahedron.The optimal error estimate is proved,verified by numerical examples.

Asymptotic properties of Lasso in high-dimensional partially linear models

We study the properties of the Lasso in the high-dimensional partially linear model where the number of variables in the linear part can be greater than the sample size.We use truncated series expansion based on polynomial splines to approximate the nonparametric component in this model.Under a sparsity assumption on the regression coefficients of the linear component and some regularity conditions,we derive the oracle inequalities for the prediction risk and the estimation error.We also provide sufficient conditions under which the Lasso estimator is selection consistent for the variables in the linear part of the model.In addition,we derive the rate of convergence of the estimator of the nonparametric function.We conduct simulation studies to evaluate the finite sample performance of variable selection and nonparametric function estimation.