Increased accuracy of computations in the main satellite problem through linearization methods

The set of canonical redundant variables previously introduced by the first author is derived from Cartesian coordinates in a simplified form which allows the reduction of the Kepler problem to four harmonic oscillators with unit frequency. The coordinates are defined to be the direction cosines of the position of the particle along with the inverse of its distance. True anomaly is the new independent variable. The behavior of this new transformation is studied when applied to the numerical integrations of the main problem in satellite theory. In particular, computation time and accuracy of orbits in the new variables are compared with those in K-S and Cartesian variables. It is noteworthy that for high eccentricities the new variables require the least computation time for comparable accuracy, regardless of the integration scheme.     

Ejection-collision orbits with the more massive primary in the planar elliptic restricted three body problem

The main goal of this paper is to give an approximation to initial conditions for ejection-collision orbits with the more massive primary, in the planar elliptic restricted three body problem when the mass parameter µ and the eccentricity e are small enough. The proof is based on a regularization of variables and a perturbation of the two body problem.This work was partially supported by DGICYT grant number PB90-0695.     

BDS/GPS组合单历元基线解算方法

阐述了BDS/GPS单历元解算函数模型的相关理论,并进行了相应的公式推导。在此基础上,利用基于正则化的载波相位解算模型,解算宽巷模糊度。首先将BDS卫星宽巷模糊度值作为约束固定出IGSO和MEO卫星的模糊度;然后再将IGSO和MEO卫星模糊度值作为约束来固定GEO卫星模糊度。通过实测数据对该方法进行测试和分析,结果表明:BDS/GPS组合系统单历元宽巷模糊度成功率为100%;基频模糊度成功率90%以上;N、E、U方向定位精度达到了毫米至厘米级。     

改进的果蝇优化与Tikhonov正则化相结合的病态问题稳健解法

在对基本果蝇优化算法的优化流程进行深入分析的基础上,通过改变其随机搜索方向与增加搜索半径调整系数,给出了一种改进的果蝇优化算法(IFOA)。并在IFOA算法的目标函数中引入正则化项,提出了将IFOA算法与Tikhonov正则化方法进行结合以进行病态问题解算的方法。通过实例分析表明:该方法的解算精度要优于遗传算法和单一的Tikhonov正则化方法;在观测值含有粗差时,使用最小二乘法进行求解,其结果与真值的偏差会迅速增大,而此时本文方法的解算结果具有一定的稳健性。与以遗传算法为代表的智能搜索方法相比,本文方法具有参数设置少、计算速度快、寻优过程简单等特点,在病态问题解算中更具有实用性。     

Spectral analysis of nonlocal regularization in two‐dimensional finite element models

Strain‐softening in geomaterials often leads to ill‐posed boundary‐valued problems (BVP), which cannot be solved with finite element methods without introducing some kind of regularization such as nonlocal plasticity. Hereafter we propose to apply spectral analysis for testing the performance of nonlocal plasticity in regularizing ill‐posed BVP and producing mesh‐independent solutions when local plasticity usually fails. The spectral analysis consists of examining the eigenvalues and eigenvectors of the global tangential stiffness matrix of the incremental equilibrium equations. Based on spectral analysis, we propose a criterion for passing or failing the test of constitutive regularization in the context of BVP. If the eigenvalues of the tangential operator are all positive then the regularization succeeds, otherwise it fails and may not prevent artificial mesh‐dependent solutions from appearing. The approach is illustrated in the particular case of a biaxial compression with strain‐softening plasticity. In this particular case, local softening plasticity is found to produce negative eigenvalues in the tangential stiffness matrix, which indicates ill‐posed BVP. In contrast, nonlocal softening plasticity always produces positive eigenvalues, which regularizes ill‐posed BVP. The dominant eigenvectors, which generate localized deformation patterns, have a bandwidth independent of mesh size, provided that the mesh is fine enough to capture localization. These mesh‐independent eigenmodes explain why nonlocal plasticity produces numerical solutions that are mesh‐independent. Copyright © 2011 John Wiley & Sons, Ltd.     

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半参数模型在平面坐标转换中的应用

坐标转换在测绘领域一直起着至关重要的作用,而模型的选取又直接制约着转换的精度,通常在坐标转换中采用相似变换（Hermert）的方法,在平面坐标转换过程中一般采用4参数模型。然而当系统误差不可忽略时,该模型处理得到的结果并不理想。本文将半参数模型应用到平面坐标转换中,分别采用4参数模型和半参数模型两种方法对实验数据进行了处理,并进行了对比与分析。实验结果表明：在处理带有系统误差的平面坐标数据时,半参数模型比传统的参数模型更加精确。     

基于非局部总变差的消除不规则采样遥感图像复原方法

提出一种消除不规则采样的遥感图像复原方法,该方法结合了ACT算法和总变差（TV）图像复原模型以达到同时去除多种图像退化因素的目的,并且结合非局部均值（NLM）算子给出了基于NLTV的消除不规则采样遥感图像复原模型,最后使用算子分裂与扩展的坎贝尔投影算法求解模型。实验结果表明,该方法能够有效减少复原图像的阶梯效应并提高复原图像的纹理细节信息。     

基于ALR的Hopfield神经网络在高程拟合中的应用

运用具有正规化项的增广拉格朗日函数作为神经网络的能量函数,辅助二次曲面拟合,进一步探索Hopfield神经网络在高程拟合中的应用。实际算例表明,该方法可以大大提高神经网络的计算效率和可靠性。     

带线约束的摄影测量网格变分精化算法

针对城市场景三维重建模型在有线特征的边缘区域过于平滑的问题,提出一种带线约束的摄影测量网格变分精化方法。算法以初始重建网格模型为基础,引入3个能量项,将网格精化问题转化成能量下降问题。首先结合所有的影像信息构建影像一致性约束项,然后对网格表面顶点附加正则化约束,最后引入三维线特征约束,将3个能量项加权相加后离散化到每个顶点,得到梯度变化值。采用梯度下降法,使顶点沿着梯度方向移动,当能量不再下降或迭代一定次数时,即得到了精化后的网格模型。试验结果表明,本文算法能较好地保持边缘特征,与现有的泊松重建算法相比,网格的质量更高,视觉效果更好。