用基于Givens变换的QR分解计算类GPS广播星历参数

分析研究类GPS广播星历参数拟合算法的必要性,来介绍可用于解最小二乘问题的Givens变换,讨论使用Givens变换计算MEO和小倾角GEO卫星的类GPS广播星历参数的适用性,并用模拟数据进行验证。     

基于3D+-TPR-tree的点目标全时段移动索引设计

在经典3D R-tree基础上提出新的3D R-tree索引,通过改变待索引数据项的结构并重新设计查询处理算法,减少包容矩形死区,提高查询效率;为了满足全时段查询要求,设计一种称为3D -TPR-tree的联合索引结构,并对其中TPR-tree的参数包容矩形的调整算法进行优化。通过测试,证明3D R-tree的查询效率明显高于普通3D R-tree;此外,测试结果也表明经过优化的参数包容矩形的调整算法也部分提升了TPR-tree的查询性能。     

数字地图合并的平差原理与方法

提出了一种基于最小二乘平差的数字地图合并方法,采用平差原理以求得实体调整合并后的空间位置。实验表明,与其他方法相比,该方法具有较高的精度,且较好地保持了原有实体的特征。     

An Aggregate Constraint Method for Inequality-constrained Least Squares Problems

The inequality-constrained least squares (ICLS) problem can be solved by the simplex algorithm of quadratic programming. The ICLS problem may also be reformulated as a Bayesian problem and solved by using the Bayesian principle. This paper proposes using the aggregate constraint method of non-linear programming to solve the ICLS problem by converting many inequality constraints into one equality constraint, which is a basic augmented Lagrangean algorithm for deriving the solution to equality-constrained non-linear programming problems. Since the new approach finds the active constraints, we can derive the approximate algorithm-dependent statistical properties of the solution. As a result, some conclusions about the superiority of the estimator can be approximately made. Two simulated examples are given to show how to compute the approximate statistical properties and to show that the reasonable inequality constraints can improve the results of geodetic network with an ill-conditioned normal matrix.     

GPS高程拟合方法的研究

本文在76个拥有GPS大地高和正常高的已知的公共点作为原始数据的基础上,采用二次曲面拟合法、二次曲面加权法、二次曲面多面函数法、二次曲面最小二乘法来建立研究区的似大地水准面,通过实例发现,二次曲面加权法、二次曲面多面函数法、二次曲面最小二乘配置法与二次曲面拟合法进行比较,外检验点中误差的精度得到提高,并且二次曲面拟合所得到的残差值比较大的点精度有明显的提高,同时改善了模型,证明这种组合方法在GPS水准拟合方面有效、可行。     

基于大视场光学测量设备的多星观测和解算天文经纬度研究

本文提出了一种新的基于大视场光学测量设备和GPS测量点位天文坐标的方法,即测量多个星体方位角相对于主光轴方位角的增量,然后通过非线性最小二乘法解算出点位的天文坐标。采用该方法不仅可以避免讨论大气蒙气差的修正问题,而且能够满足高精度天文坐标的测量要求。     

一次范数最小估计的无偏性

理论上一次范数最小 ( L1 )估计的唯一性不存在 ,其唯一性主要取决于解算方法 ,大量算例验证其唯一性存在。本文作者基于算法来保证其唯一性 ,进而首次从理论上验证 L1估计的无偏性。利用初始反对称估计 ,设计了两个等价的线性规划问题 ,由此来解算得到 L1估计 ,根据误差分布为对称分布 ,便可证明 L1 估计的无偏性     

卫星重力梯度向下延拓的频域最小二乘配置法

本文深入研究频域最小二乘配置法的基本原理及其在求解卫星重力梯度向下延拓问题中的应用。与一般空域最小二乘配置法相比，该方法具有高效稳定的特点，特别适合于大规模重力场数据处理，并为利用卫星重力梯度数据精化局部重力场提供了可供参考的方法。     

A Least-squares Window Curves Method for Interpretation of Magnetic Anomalies Caused by Dipping Dikes

We have developed a least-squares method to determine simultaneously the depth and the width of a buried thick dipping dike from residualized magnetic data using filters of successive window lengths. The method involves using a relationship between the depth and the half-width of the source and a combination of windowed observations. The relationship represents a family of curves (window curves). For a fixed window length, the depth is determined for each half-width value by solving one nonlinear equation of the form f (z) = 0 using the least-squares method. The computed depths are plotted against the width values representing a continuous curve. The solution for the depth and the width of the buried dike is read at the common intersection of the window curves. The method involves using a dike model convolved with the same moving average filter as applied to the observed data. As a result, this method can be applied to residuals as well as to measured magnetic data. Procedures are also formulated to estimate the amplitude coefficient and the index parameter. The method is applied to theoretical data with and without random errors. The validity of the method is tested on airborne magnetic data from Canada and on a vertical component magnetic anomaly from Turkey. In all cases examined, the model parameters obtained are in good agreement with the actual ones and with those given in the published literature.