用Landweber法求解GPS定位参数

在GPS定位中,由于观测结构不好等原因存在病态问题,常常造成GPS定位参数的最小二乘解不稳定.针对求解病态可题在参数估计中的影响,本文提出采用Landweber迭代正则化求解整周模糊度;在实施过程中,提出了迭代次数的确定方法;根据计算实例验证了Landweber迭代正则化方法求解GPS定位参数的有效性.     

Global chaoticity in the Pythagorean three-body problem

The effects of small changes in the initial conditions of the Pythagorean three-body problem are investigated by computer simulations. This problem consists of three interacting bodies with masses 3, 4 and 5 placed with zero velocities at the apices of a triangle with sides 3, 4 and 5. The final outcome of this motion is that two bodies form a binary and the third body escapes. We attempt to establish regions of the initial positions which give regular and chaotic motions. The vicinity of a small neighbourhood around the standard initial position of each body defines a regular region. Other regular regions also exist. Inside these regions the parameters of the triple systems describing the final outcome change continuously with the initial positions. Outside the regular regions the variations of the parameters are abrupt when the initial conditions change smoothly. Escape takes place after a close triple approach which is very sensitive to the initial conditions. Time-reversed solutions are employed to ensure reliable numerical results and distinguish between predictable and non-predictable motions. Close triple approaches often result in non-predictability, even when using regularization; this introduces fundamental difficulties in establishing chaotic regions.     

Global Regularization of the Restricted Problem of Three Bodies

The global regularizing transformations of the planar, circular restricted problem of three bodies are studied. It is shown that all these transformations can be written in the same general form which is the solution of a first order ordinary differential equation. This revised version was published online in July 2006 with corrections to the Cover Date.     

不适定方程正则化算法的谱分解式

从观测方程系数矩阵的谱分解着手探讨不适宜方程的正则化算法。利用谱分解式阐明了正则化的主要作用是平滑对参数估值比较敏感的观测误差的高频分量，完整给出了最小二乘平差、秩亏平差和病态方程正则化解的谱分解公式，证明了正则化解参数估值偏离真值的二次范数的期望值与均方误差是等价的。     

The planar Hill problem with oblate primary

The regularized equations of motion of the planar Hill problem which includes the effect of the oblateness of the larger primary body, is presented. Using the Levi-Civita coordinate transformation as well as the corresponding time transformation, we obtain a simple regularized polynomial Hamiltonian of the dynamical system that corresponds to that of two uncoupled harmonic oscillators perturbed by polynomial terms. The relations between the synodic and regularized variables are also given. The convenient numerical computations of the regularized equations of motion, allow derivation of a map of the group of families of simple-periodic orbits, free of collision cases, of both the classical and the Hill problem with oblateness. The horizontal stability of the families is calculated and we determine series of horizontally critical symmetric periodic orbits of the basic families g and g'. This revised version was published online in July 2006 with corrections to the Cover Date.     

Quaternions and the perturbed Kepler problem

Quaternions, introduced by Hamilton (Philos. Mag. 25, 489–495, 1844) as a generalization of complex numbers, lead to a remarkably simple representation of the perturbed three-dimensional Kepler problem as a perturbed harmonic oscillator. The paper gives an overview of this technique, including an outlook to applications in perturbation theories.     

A Regularized Image Restoration Algorithm for Lossy Compression in Astronomy

Astronomical images currently provide large amounts of data. Lossy compression algorithms have recently been developed for high compression ratios. These compression technique introduce distortion in the compressed images and for high compression ratios, a blocking effect appears. We propose a modified compression algorithm based on the hcompress scheme, and we introduce a new decompression method based on the regularization theory The image is restored scale by scale in a multiresolution scheme and the information lost during the compression is recovered by applying a Tikhonov regularization constraint. The experimental results show that the blocking effect is reduced and some measurements made on a simulated image show that the astrometric and the photometric properties of the restored images are improved.     

Diagnostics of the shape and orientation of a rock failure zone based on electrical measurements as an inverse problem of geophysics

Exploration geophysics is concerned with the development of methods and techniques for remote search for mineral deposits, solution of various engineering and geological problems, mining monitoring, and diagnostics of zones of rock bursts and natural and technogenic tectonic earthquakes. In this paper, we consider the diagnostic problem of exploration geophysics related to the determination of the shape and inclination angle of a plane source of natural geoelectric field, which, under certain conditions, simulates a rock failure zone, e.g., during the preparation of rock bursts at the sites of developed mineral deposits. This approach may also be useful in determining the shape and size of ore shoots by electrical measurements on the ground surface. Evaluation of the parameters of a rock failure zone is required in the case of accumulation of multiple fractures having charges of the same sign before a catastrophic failure. This problem is formulated as a Fredholm-Urysohn integral equation of the first kind. The solution of the integral equation is sought using the Tikhonov regularization method of the second order.     

Spectral-spatial classification of hyperspectral images using wavelet transform and hidden Markov random fields

This paper proposes a spectral–spatial method for classification of hyperspectral images. The proposed method, called SSC, consists of two steps. In the first step, to overcome the computation complexity, a wavelet-based classifier is designed. In the second step, to enhance the classification accuracy, a novel hidden Markov random field called NHMRF technique in spatial domain is suggested. In NHMRF, we convert two-dimensional energies of traditional hidden Markov random field to three-dimensional energies and then we apply edge preserving regularization terms on each two-dimensional energy of this cube. The class label of each test pixel is fixed based on minimum three-dimensional energy achieved by edge preserving regularization terms. Experimental results show that the classification accuracy of the proposed approach based on three-dimensional energies and edge preserving regularization terms is effectively improved in comparison with the state-of-the-art methods.     

基于偏差矫正的有偏估计及其在GPS快速定位中的应用

基于偏差矫正的一般理论提出了不适定问题的新的有偏估计。在病态条件下,Gauss-Markov模型参数的最优线性无偏估计,即LS估计是不稳健的,所得估值方差较大,严重偏离真值。因此,文中放弃了对参数估计无偏性的限制,考虑有偏估计的偏差,结合偏差矫正的正则化解法的一般理论提出了一种新的基于偏差矫正的有偏估计;结合岭估计中参数的选择方法确定了替代矩阵。最后通过GPS动态定位算例,验证了新估计的稳定性和有效性。