一类小波基函数的构造及其在测量数据处理中的应用探讨

Shannon函数有很好的滤波性能,但向两端衰减速度缓慢;Gauss“窗”函数有很好的控制小波衰减的特性,但其低通滤波效果较差。根据这两个函数各自的优点构造了一类新的小波基函数,分别为满足低通的父小波和带通的一阶、二阶母小波,讨论了它们的正交性、完备性和紧支集性等性质,以GPS资料为例,分析其信号平滑和压缩效应、边缘效应和奇异点检测,得出一些有益的结论,为大地测量数据处理提供一种小波分析方法。     

On the Distance Function Between Two Keplerian Elliptic Orbits

The problem of finding critical points of the distance function between two Keplerian elliptic orbits is reduced to the determination of all real roots of a trigonometric polynomial of degree 8. The coefficients of the polynomial are rational functions of orbital parameters. Using computer algebra methods we show that a polynomial of a smaller degree with such properties does not exist. This fact shows that our result cannot be improved and it allows us to construct an optimal algorithm to find the minimal distance between two Keplerian orbits. This revised version was published online in July 2006 with corrections to the Cover Date.     

地球磁场偶极子和非偶极子分量变化特征及其相关的地球深部过程

通过分析１９００年以来每５ａ地球磁场各阶球谐系数的相关系数发现,地球磁场偶极子分量的ρ值在１９０５-１９７０年基本保持不变,１９７０-１９８５年下降,１９８５-１９９５年又上升,呈Ｖ字型变化。而非偶极子分量的　值则具有周期性变化,在１９１５年、１９４５年和１９８０年出现峰值,在１９３５年和１９６５年则处于低谷,变化周期约为３０ａ。通过分析地球磁场非偶极子分量　值周期变化与日长周期变化的相关性,得出两点新的认识：１．非偶极子分量的周期性变化与核幔边界耦合过程相关,而偶极子分量的变化对应外核的深部过程;２．外核顶部流体具有周期性的变化,其变化周期与日长及非偶极子分量的变化周期一致。     

遥感图像准无损压缩技术的研究

提出了一种基于图像恢复技术的遥感图像压缩技术,在提高遥感图像压缩比的同时,使压缩后的重建图像质量达到准无损的技术要求。对SRTF、TM图像的试验结果表明,该技术是可行的。     

污染分布下的Lp估计抗差测度

观测数据中含有粗差或异常值扰动的误差分布可视为污染分布。根据M估计理论,导出了Lp估计的影响函数,分析了Lp估计的抗差能力,并用效率来测度估计的优劣、综合抗差能力和效率,指出观测数据中含有粗差的扰动,应用p为[1．2．1．5]的Lp估计来进行处理。     

Band-limited functions on a bounded spherical domain: the Slepian problem on the sphere

The Slepian problem consists of determining a sequence of functions that constitute an orthonormal basis of a subset of ℝ (or ℝ²) concentrating the maximum information in the subspace of square integrable functions with a band-limited spectrum. The same problem can be stated and solved on the sphere. The relation between the new basis and the ordinary spherical harmonic basis can be explicitly written and numerically studied. The new base functions are orthogonal on both the subspace and the whole sphere. Numerical tests show the applicability of the Slepian approach with regard to solvability and stability in the case of polar data gaps, even in the presence of aliasing. This tool turns out to be a natural solution to the polar gap problem in satellite geodesy. It enables capture of the maximum amount of information from non-polar gravity field missions. Received: 10 June 1998 / Accepted: 20 May 1999     

The Correlation Bias for Two-Dimensional Simulations by Turning Bands

The turning bands method (TBM) generates realizations of isotropic Gaussian random fields by summing contributions from line processes. We consider two-dimensional simulations and study the correlation bias attributable to the use of only a finite number L of lines. Our analytical and numerical results confirm that the maximal bias is of order 1/L, and that L = 64 lines suffice for excellent covariance reproduction. The notorious banding observed in simulations with an insufficient number of lines is a related but different phenomenon and depends strongly on the choice of the line simulation technique. Clear-cut recommendations for the number of lines necessary to avoid the effect can only be based on practical experience with the specific code at hand.     

利用干涉图确定成像质量

从像质的概念出发,导出了像质评定的简单公式。在干涉图的每个选定点上测量条纹间的间隔和角度来计算几何光线的斜率误差,然后把这些角度误差画在一张图纸上用以表示几何点扩散函数的角度大小,可以方便而简洁地评定成像质量,避免了复杂的计算。