Is Newton's iteration faster than simple iteration for transformation between geocentric and geodetic coordinates?

Summary Two iterative algorithms for transformation from geocentric to geodetic coordinates are compared for numerical efficiency: the well known Bowring's algorithm of 1976, which employs the method of simple iteration, and the recent (1989) algorithm by Borkowski, which employs the Newton-Raphson method. The results of numerical tests suggest that the simple iteration method implemented in Bowring's algorithm executes approximately 30% faster than the Newton-Raphson method implemented in Borkowski's algorithm. Only two iterations of each algorithm are considered. Two iterations are sufficient to produce coordinates accurate to the comparable level of 1E-9 m, which exceeds the requirements of any practical application. Therefore, in the class of iterative methods, the classical Bowring's algorithm should be the method of choice.     

Fast transform from geocentric to geodetic coordinates

 A new iterative procedure to transform geocentric rectangular coordinates to geodetic coordinates is derived. The procedure solves a modification of Borkowski's quartic equation by the Newton method from a set of stable starters. The new method runs a little faster than the single application of Bowring's formula, which has been known as the most efficient procedure. The new method is sufficiently precise because the resulting relative error is less than 10⁻¹⁵, and this method is stable in the sense that the iteration converges for all coordinates including the near-geocenter region where Bowring's iterative method diverges and the near-polar axis region where Borkowski's non-iterative method suffers a loss of precision. Received: 13 November 1998 / Accepted: 27 August 1999     

多元线性回归算法在井下三角高程测量中的应用研究

通过对井下三角高程测量的原理、误差来源及精度分析,指出钢尺量取仪器高和棱镜高的误差对三角高程测量结果的影响,提出一种利用多元线性回归减小该误差影响的算法,并通过实例对三角高程测量结果进行改正,验证该算法用于提高井下三角高程测量精度是可行的,并基本达到四等水准的要求.     

基于差分技术的悬索桥主缆高程测量误差修正方法

悬索桥基准索股是主缆架设的重要部分,基准索股垂直度测量主要采用三角高程测量法,而大气垂直折光差是影响三角高程测量的主要误差源。本文以等影响原则为前提,对差分技术的原理进行分析,利用基准点已知信息,对三角高程测量中的大气垂直折光差进行修正,从而提高基准索股垂直度测量的精度。上述方法能够满足主缆架设精度要求,并且在实际应用中得到了较好的结果,可为类似桥梁工程提供指导。     

Generation of differential GPS corrections along with performance of quality control

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Generation of differential GPS corrections along with performance of quality control

The DGPS technique can provide considerably better relative positioning accuracy than the stand-alone GPS positioning, but the improvement depends on the distance between the user and the reference station (spatial correlation), the latency of differential corrections (temporal correlation), and the quality of differential corrections. Therefore, how to correctly generate differential corrections as well as their pricision is very important to the DGPS positioning technique. This paper presents a new algorithm for generating differential GPS corrections. This algorithm directly uses code and carrier observations in the measurement model of a Kalman filter, so that it is possible to use a simple stochastic model and to use the standard algorithm of the Kalman filter. The algorithm accounts for biases like multipath errors and instrumental delays in code observations and it shows how differential corrections are differently affected by code biases when dual or single frequency data is used. In addition, the algorithm can be integrated with a real time quality control procedure. As a result, the quality of differential corrections can be guaranteed with a certain probability.     

基于单位四元数的数码相机检校

相机检校是航测工作中的基本组成部分,尤其在使用普通数码相机进行测量工作时,检校工作更为重要。本文将单位四元数引入共线方程进行空间后方交会,用单位四元数替代欧拉角,避免了三角函数运算的复杂性,也避免了三角函数存在奇异性的问题,同时也使得相机检校功能得到了扩展,在地面坐标与像空间坐标存在大旋转角的情况下,亦能正确地解决出相机内方位和畸变参数。     

三角高程测量及其新方法

介绍了传统三角高程测量的基本原理,并针对全站仪在测绘领域的普遍使用,总结出一种新的三角高程测量方法。     

三角高程测量在基坑监测中的研究及应用

采用一种新的三角高程测量方法进行变形监测,该方法可以使全站仪在任意点设站,减少了工作量,在测量中,不用量取仪器高、棱镜高,减少了三角高程测量中的误差来源,提高了精度。通过分析三角高程测量的精度,验证了精密三角高程测量代替几何水准测量的可行性与可靠性,结合基坑监测实例,将三角高程测量的数据与几何水准测量的数据进行比较,比较的结果显示,该三角测量方法结合精密全站仪可以替代几何水准测量,在实际工作中具有一定的适用性和参考价值。     

基于精密三角高程测量的基坑变形监测方法研究

传统的基坑监测中,几何水准测量工作效率低,任务量大。针对这些不足,本文采用一种新的三角高程测量方法进行变形监测,该方法可以使全站仪在任意点设站,减少了工作量,在测量中,不用量取仪器高、棱镜高,减少了三角高程测量中的误差来源,提高了精度。通过分析三角高程测量的精度,验证了精密三角高程测量代替几何水准测量的可行性与可靠性,结合基坑监测实例,将三角高程测量的数据与几何水准测量的数据进行比较．比较的结果显示,该三角测量方法结合精密全站仪可以替代几何水准测量,在实际工作中具有一定的适用性和参考价值。     

Independent Base Vector Representation to Address Endmember Variability in Hyperspectral Unmixing

The normal compositional model (NCM) is a well-known and powerful model in hyperspectral unmixing which represents endmembers as independent Gaussian vectors to capture endmember variability. However, the assumption of independent endmembers diminishes the model accuracy because the high degree of correlation between endmembers of a scene and identical sources of variability demonstrate that the endmembers are dependent. This paper proposes a new hyperspectral unmixing algorithm which represents endmembers using dependent Gaussian vectors to estimate abundance fractions. To overcome the higher complexity caused by dependence assumption, this algorithm introduces new independent Gaussian vectors named Base Vectors to represent different endmembers by a weighted linear combination. Also, the proposed unmixing algorithm uses maximum likelihood method to estimate weight coefficients of Base Vectors which are used to represent mixed pixel. Finally, abundance estimation can be done using the new representation for endmembers and mixed pixel. The proposed algorithm is evaluated and compared with other state-of-the-art unmixing algorithms using simulated and real hyperspectral images. Experimental results demonstrate that the proposed unmixing algorithm can unmix pixels composed of correlated endmembers in hyperspectral images in the presence of spectral variability more accurately than previous methods.     

基于FPGA的P-H法星上解算卫星相对姿态

针对目前星上遥感图像实时处理只能实现低级别算法的情况,提出了基于现场可编程门阵列（field-programmable gate array,FPGA）的P-H法星上相对姿态实时解算模型。该模型不仅避免了传统基于欧拉角的复杂三角函数计算与初值估算,还降低了迭代次数。试验选用FPGA（V7 xc7vx1140t）作为实时解算的硬件平台。在FPGA实现中,采用64位的浮点数据结构和串行/并行相结合策略;并采用LU（Lower-Upper）分解-分块算法实现矩阵求逆。试验结果表明,该模型的迭代次数比基于欧拉角的少了13次。该模型在FPGA和计算机的实现结果相差仅为5.0×10-14,加速度比为10。另外,该模型可广泛适用于实时性要求高的图像处理领域。     

自适应变异粒子群优化灰色模型在变形分析中的应用

标准灰色模型GM(1,1)以序列第一个分量作为初始条件进行灰色微分建模,未能充分利用序列中的新信息;其背景值的构造本质上采用了数值积分中的梯形法,精度不高。针对上述缺点,提出一种基于粒子群算法的灰色预测模型,即PSOGM(1,1)模型,对初始值和背景值参数进行优化,并将模型应用于岩体变形分析中。计算结果表明,PSOGM(1,1)模型具有较高的预测精度,可作为变形分析的一种新方法。     

边缘约束下的分形网络分割算法

分形网络演化算法（fractal net evolution approach,FNEA）是一种有效的多尺度影像分割算法,但对于具有斑点噪声、局部区域对比度低等特点的高分辨率合成孔径雷达（synthetic aperture radar,SAR）图像,直接应用FNEA算法得到的分割结果难以用于后续的面向对象影像分析。提出了基于边缘约束的FNEA（edge restricted FNEA,eFNEA）算法,通过加入边缘信息和构建异质性规则来为分割融入更多信息,提高分割效果。实验结果表明,对于微弱边缘和噪声污染严重等情形,eFNEA算法的分割结果均优于FNEA算法。     

Increasing GNSS RTK availability with a new single-epoch batch partial ambiguity resolution algorithm

GPS Single-epoch Real-Time Kinematic positioning is immune to cycle slips and can be immediately re-initialized after loss-of-lock, providing high availability. This technique requires reliable ambiguity resolution: incorrect ambiguities can cause position errors of several meters, and failed ambiguity resolution reduces availability. However, a bias or inaccuracy in a single phase observation can prevent successful resolution of the whole set of ambiguities. Partial ambiguity resolution allows a subset of ambiguities to be resolved with greater probability of success than the full set. A new algorithm for resolving a subset of ambiguities with validation from previous epochs is described. If normal ambiguity resolution fails, all ambiguity subsets are generated and ordered with the best subsets first. Each subset is then resolved in turn. Fixed subsets are validated against values from previous epochs; this validation procedure greatly reduces the proportion of epochs with incorrect ambiguities. An additional algorithm is described that uses the fixed ambiguities as precise ranges to resolve the remaining unfixed ambiguities. In order to test these new algorithms, GPS data were collected from static and ship-based GPS receivers around Harwich harbor and processed from reference stations at distances up to 111 km. In the static tests the distance over which a 90% ambiguity resolution success rate for dual-frequency data was achieved was increased from 15 to 76 km. However, in some cases, the processing time was too long for this algorithm to be practical without a time-based cut-off. There is also a risk of incorrect ambiguities being propagated, particularly for single-frequency processing. In a ship-based test, the distance over which sufficient availability to support harbor navigation was achieved using single-epoch dual-frequency RTK was increased from 1 to 66 km.     

全站仪中间设站法三角高程测量方法及精度研究

水准测量作业简单、精度高,成为高程控制测量的主要方法,但在高山地区因高差大,精度难以保证。现在用三角高程测量代替水准测量得到了广泛应用。本文从三角高程的测量原理出发,根据误差传播定律,推导出全站仪中间法三角高程测量的中误差。最后以云南曲靖市某路段为例,将全站仪中间法三角高程测量和水准测量的数据进行了对比,结果表明:全站仪中间法三角高程测量的精度完全可以达到三等水准测量的要求。     

引潮位的Doodson规格化展开及其精度评定

基于引潮位Doodson规格化展开的基本原理以及ELP/MPP02月球历表、Newcomb太阳历表的结构,设计了一个用以代表三角函数的数据结构;并由此自定义了三角函数的乘法与加法算法,将月球、太阳引潮位分别展开至5阶、3阶,振幅绝对值截断阈值为10-7,在展开过程中对"伪波"进行"滤波"处理后,最终得到包含4 686项展开式的引潮位展开表(其中振幅绝对值超过10-6的展开式有2 441项)。以德国BFO(Black Forest Observatory)测站为例,基于DE431历表,通过天球参考系变换计算得到1950—2050年间时间间隔为1 h的法向引潮力基准序列BFDE431;并根据各个引潮位展开表计算得到相应的法向引潮力序列;通过与BFDE431基准序列求差,得到各个差值序列的统计值。计算结果表明,文中给出的展开表对应的差值序列数值在±58×10~(-11)m·s~(-2)(nGal)以内,均方差为12.5×10~(-11)m·s~(-2),与XI89展开表的精度相当。但由于没有考虑行星及地球扁率的影响,仍未达到HW95和RATGP95展开表的精度水平。     

Curvature correction in electronic distance measurement

The usual methods for curvature correction, which consist of a geometric and a velocity component, are based on standard atmospheric conditions and thus take no account of variable refraction. A formula has been developed expressing the correction as a function of atmospheric refraction: K=(1-k_² S²/(24 R²) whereS is the measured distance, R is the radius of the earth, and k is the coefficient of refraction. This formula leads to a practical procedure employing trigonometric levelling in the determination of curvature correction for long-range geodimeter measurements.     

离散目标群的边界搜索

搜索离散目标群的边界是地理信息系统(GIS)和地图学中一个重要问题,传统的算法是基于矢量数据的。本文提出了基于栅格数据搜索离散目标群的边界的新方法,并用两个点群算例介绍了用闭运算搜索边界的方法与流程,为数字高程模型生成、地图学等提供一种新的边界搜索方法。