共查询到20条相似文献，搜索用时 421 毫秒
1.
G. Blaha 《Journal of Geodesy》1977,51(3):177-202
This paper is intended to demonstrate the usefulness of array algebra techniques in certain multilinear least squares problems.
A typical restriction of array algebra is the need for a gridded observational structure; however, the grid does not have
to be uniform and in general is not limited to any particular coordinate system nor to two- or three-dimensional spaces. Another
restriction comes to light when dealing with weighted multilinear least squares adjustments. The a—priori variance-covariance
matrix cannot be completely arbitrary but must be expressible in terms of certain matrix products. There exist various practical
ways (not discussed herein) to bridge these restrictions. The reward for using the array algebra technique when it is appropriate
lies in the great computational savings.
From the theoretical point of view, the backbone of most derivations are the “R-matrix multiplications” and a simple tool,
demonstrated herein, called “fundamental transformation”. It follows that the least squares solution of “array observation
equations” does not have to be sought by some new and complex mathematical means. The fundamental transformation allows such
an adjustment problem to be rewritten in a conventional (monolinear) form; the familiar least squares solution is then written
down and transformed back to the array form using the same tool. The statistical properties of the results (e.g. minimum variance)
are known from the conventional approach and do not have to be rederived in the array case. 相似文献
2.
F. Sansò 《Journal of Geodesy》1990,64(4):313-330
To apply the least squares method for the interpolation of harmonic functions is a common practice in Geodesy. Since the method
of least squares can be applied only to overdetermined problem, the interpolation problem which is always under-determined,
is often reduced to an overdetermined form by truncating a series of spherical harmonics. When the data points are the knots
of a regular grid it is easy to see that the estimated harmonic coefficients converge to the correct theoretical values, but
when the observation density is not constant a significant bias is introduced. The result is obtained by assuming that the
number of observations tends to infinity with points sampled from a given distribution. Under the same conditions it is shown
that quadrature and “collocation-like” formulas displays a statistically consistent behaviour. 相似文献
3.
复数域最小二乘平差及其在POLInSAR植被高反演中的应用 总被引：2，自引：1，他引：1
传统的测量观测值都是实数,因此测量平差都是在实数空间中进行的。然而,随着科学技术的快速发展,现代测绘领域中出现了一些用复数表示的观测数据。与实数数据一样,这些复数数据同样面临着如何从带有误差的观测值中找出未知量的最佳估计值的问题。但目前涉及复数观测的数据处理时,主要还是依据观测过程,分步或直接解算,不能考虑观测误差、多余观测信息等。针对这一情况,本文介绍了复数域中数据处理的最小二乘方法,试图将测量平差从实数域推广到复数域,并定量研究了两种平差准则的优劣性。为了了解复数域最小二乘的有效性,本文以极化干涉SAR植被高反演为例,建立复数域平差函数模型和随机模型,构建复数域最小二乘法反演植被高。结果表明该算法反演的植被高结果可靠,其精度优于经典植被高反演算法,且计算简单,易于实现。 相似文献
4.
现代测量技术多依赖于各种连续对地观测系统。有色噪声在影响参数估计的同时,还蕴含了地球科学研究所需的大量有用信息。本文讨论了连续平差模型及最小二乘解,将有限维空间中的测量平差问题推广至无穷维空间,从信号分析角度讨论了观测有色噪声的消除方法。研究表明,连续观测方程的最小二乘解可由经典最小二乘解的极限导出;有色噪声对解的影响是系统性的,然而通过合理的观测方案设计可以实现参数的无偏估计 相似文献
5.
FENG Wenhao LI Xin 《地球空间信息科学学报》2001,4(1):28-36
1 ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｏｕｒｃｏｕｎｔｒｙ ,ｔｈｅｓｕｒｖｅｙｉｎｇｗｏｒｋｏｎｉｎｄｕｓｔｒｉａｌｏｂｊｅｃｔｓｈａｖｅ ｇｒａｄｕａｌｌｙｉｎｃｒｅａｓｅｄ .Ｔｈｏｓｅｉｎｄｕｓｔｒｉａｌｏｂｊｅｃｔｓｉｎｃｌｕｄｅｒａｉｌｗａｙａｎｄｈｉｇｈｗａｙｔｕｎｎｅｌｓ,ｖａｒｉ ｏｕｓｏｉｌａｎｄｇａｓｃａｎｓ ,ｖａｒｉｏｕｓａｉｒｃｒａｆｔ,ｓｈｅｌｌｏｆｃａｒｓ,ｌａｒｇｅｍｉｌｉｔａｒｙａｎｔｅｎｎａｕｓｅｄｆｏｒｓｃｏｕｔｉｎｇｓｔｅａｌｔｈｐｌａｎｅ ,ｓｈｉｐ ,ｉｎｔｅｒｎａｌｓｔ… 相似文献
6.
Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm 总被引：4，自引：0，他引：4
Erik W. Grafarend 《GPS Solutions》2000,4(2):31-44
In order to achieve to GPS solutions of first-order accuracy and integrity, carrier phase observations as well as pseudorange
observations have to be adjusted with respect to a linear/linearized model. Here the problem of mixed integer-real valued
parameter adjustment (IRA) is met. Indeed, integer cycle ambiguity unknowns have to be estimated and tested. At first we review
the three concepts to deal with IRA: (i) DDD or triple difference observations are produced by a properly chosen difference
operator and choice of basis, namely being free of integer-valued unknowns (ii) The real-valued unknown parameters are eliminated
by a Gauss elimination step while the remaining integer-valued unknown parameters (initial cycle ambiguities) are determined
by Quadratic Programming and (iii) a RA substitute model is firstly implemented (real-valued estimates of initial cycle ambiguities)
and secondly a minimum distance map is designed which operates on the real-valued approximation of integers with respect to
the integer data in a lattice. This is the place where the integer Gram-Schmidt orthogonalization by means of the LLL algorithm (modified LLL algorithm) is applied being illustrated by four examples. In particular, we prove
that in general it is impossible to transform an oblique base of a lattice to an orthogonal base by Gram-Schmidt orthogonalization where its matrix enties are integer. The volume preserving Gram-Schmidt orthogonalization operator constraint to integer entries produces “almost orthogonal” bases which, in turn, can be used to produce the integer-valued
unknown parameters (initial cycle ambiguities) from the LLL algorithm (modified LLL algorithm). Systematic errors generated
by “almost orthogonal” lattice bases are quantified by A. K. Lenstra et al. (1982) as well as M. Pohst (1987). The solution point of Integer Least Squares generated by the LLL algorithm is = (L')−1[L'◯] ∈ ℤ
m
where L is the lower triangular Gram-Schmidt matrix rounded to nearest integers, [L], and = [L'◯] are the nearest integers of L'◯, ◯ being the real valued approximation of z ∈ ℤ
m
, the m-dimensional lattice space Λ. Indeed due to “almost orthogonality” of the integer Gram-Schmidt procedure, the solution point is only suboptimal, only close to “least squares.” ? 2000 John Wiley & Sons, Inc. 相似文献
7.
The affection caused by the colored noises should be taken into account to the adjustment model. As useful signals, these colored noises should be accurately identified and extracted by Fourier analysis. A continuous adjustment model is introduced with respect to the colored noises, and then it can be generalized from the finite space to the infinite space so called as Hilbert space. This extension is to provide a new technique to perform the continuous observational system design, Fourier analysis as well as the parameter estimation. It shows that the Gramer’s determinant provides maximization criteria in the system optimization design as well as a rule in diagnosing the adjustment model. Related with the definition of the integral, the least squares solution of the continuous adjustment model becomes the limit of the traditional least squares solution in finite space. Moreover, the influence caused by the colored noises is systematic, but it can be eliminated or compensated by optimally designing the observational system. 相似文献
8.
G. Blaha 《Journal of Geodesy》1977,51(4):265-286
This presentation is a follow-up of the paper “A Few Basic Principles and Techniques of Array Algebra”, published previously
in theBulletin Géodésique. The attention is focused on the use of array algebra in the problem area of multilinear least squares prediction and filtering.
The prediction mathematical models are treated using the concept of the covariance function and node points. In the latter
part of the paper, efficient prediction formulas in two dimensions are developed and solved through the least squares filtering
process, upon specializing the results derived previously for any dimensions. (Errata Sheet for the previous paper is added).
Formerly of DBA Systems, Inc. P.O. Drawer 550 Melbourne, Florida 32901. 相似文献
9.
P. Schwintzer C. Reigber A. Bode Z. Kang S. Y. Zhu F.-H. Massmann J. C. Raimondo R. Biancale G. Balmino J. M. Lemoine B. Moynot J. C. Marty F. Barlier Y. Boudon 《Journal of Geodesy》1997,71(4):189-208
Summary. GFZ Potsdam and GRGS Toulouse/Grasse jointly developed a new pair of global models of the Earth's gravity field to satisfy
the requirements of the recent and future geodetic and altimeter satellite missions. A precise gravity model is a prerequisite
for precise satellite orbit restitution, tracking station positioning and altimeter data reduction. According to different
applications envisaged, the new model exists in two parallel versions: the first one being derived exclusively from satellite
tracking data acquired on 34 satellites, the second one further incorporating satellite altimeter data over the oceans and
terrestrial gravity data. The most recent “satellite-only” gravity model is labelled GRIM4-S4 and the “combined” gravity model
GRIM4-C4. The models are solutions in spherical harmonics and have a resolution up to degree and order 60 plus a few resonance
terms in the case of GRIM4-S4, and up to degree/order 72 in the case of GRIM4-C4, corresponding to a spatial resolution of
555 km at the Earth's surface. The gravitational coefficients were estimated in a rigorous least squares adjustment simultaneously
with ocean tidal terms and tracking station position parameters, so that each gravity model is associated with a consistent
ocean tide model and a terrestrial reference frame built up by over 300 optical, laser and Doppler tracking stations. Comprehensive
quality tests with external data and models, and test arc computations over a wide range of satellites have demonstrated the
state-of-the-art capabilities of both solutions in long-wavelength geoid representation and in precise orbit computation.
Received 1 February 1996; Accepted 17 July 1996 相似文献
10.
Luc M. A. Jeudy 《Journal of Geodesy》1986,60(4):288-296
Principles of North determination using suspended gyrocompasses are reviewed. Accuracy is evaluated and a procedure with two
series of measurements symmetrical with respect to the zero torsion tape position is mathematically proven to be the “best”
(minimum variance). Our purpose is to prove that a 20″ accuracy (1 σ) instrument was brought to a level of accuracy four times
better by using multiple transit times and least squares fit. Over a total of 15 North determinations based on more than a
thousand transit times, an external standard error of 4″.4 was obtained using a WildGAK-1. 相似文献
11.
12.
LIQi CAOJian 《地球空间信息科学学报》2004,7(2):101-103
This paper is to construct a “digital local, regional, region“ information framework based on the technology of “SIG“ and its significance and application to the regional sustainable development evaluation system. First, the concept of the “grid computing“ and “SIG“ is interpreted and discussed, then the relationship between the “grid computing“ and “digital region“ is analyzed, and the framework of the “digital region“ is put forward. Finally, the significance and application of “grid computing“ to the “region sustainable development evaluation system“ are discussed. 相似文献
13.
Parametric least squares collocation was used in order to study the detection of systematic errors of satellite gradiometer
data. For this purpose, simulated data sets with a priori known systematic errors were produced using ground gravity data
in the very smooth gravity field of the Canadian plains. Experiments carried out at different satellite altitudes showed that
the recovery of bias parameters from the gradiometer “measurements” is possible with high accuracy, especially in the case
of crossing tracks. The mean value of the differences (original minus estimated bias parameters) was relatively large compared
to the standard deviation of the corresponding second-order derivative component at the corresponding height. This mean value
almost vanished when gravity data at ground level were combined with the second-order derivative data set at satellite altitude.
In the case of simultaneous estimation of bias and tilt parameters from ∂2
T/∂z
2“measurements”, the recovery of both parameters agreed very well with the collocation error estimation.
Received: 10 October 1996 / Accepted 25 May 1998 相似文献
14.
复数域总体最小二乘平差 总被引：1，自引：1，他引：0
在复数域最小二乘的基础上提出了复数域总体最小二乘平差方法,推导了复数域总体最小二乘和复数混合总体最小二乘的相关公式。通过算例比较分析了复数观测值的残差的模的平方和最小(平差准则1)下及残差的实部和虚部的平方和分别最小(平差准则2)下的复数最小二乘、复数观测值和系数矩阵的残差的模的平方和最小(平差准则3)下及残差的实部和虚部的平方和分别最小(平差准则4)下的复数总体最小二乘方法的优劣。试验结果表明:平差准则1下复数最小二乘较平差准则2下得到的结果更加合理,平差准则3下复数总体最小二乘较平差准则4下得到的结果更为准确;当顾及系数矩阵误差时,平差准则3下复数总体最小二乘要优于平差准则1下复数最小二乘。 相似文献
15.
The Doppler effect is the apparent shift in frequency of an electromagnetic signal that is received by an observer moving relative to the source of the signal. The Doppler frequency shift relates directly to the relative speed between the receiver and the transmitter, and has thus been widely used in velocity determination. A GPS receiver-satellite pair is in the Earth’s gravity field and GPS signals travel at the speed of light, hence both Einstein’s special and general relativity theories apply. This paper establishes the relationship between a Doppler shift and a user’s ground velocity by taking both the special and general relativistic effects into consideration. A unified Doppler shift model is developed, which accommodates both the classical Doppler effect and the relativistic Doppler effect under special and general relativities. By identifying the relativistic correction terms in the model, a highly accurate GPS Doppler shift observation equation is presented. It is demonstrated that in the GPS “frequency” or “velocity” domain, the relativistic effect from satellite motion changes the receiver-satellite line-of-sight direction, and the measured Doppler shift has correction terms due to the relativistic effects of the receiver potential difference from the geoid, the orbit eccentricity, and the rotation of the Earth. 相似文献
16.
17.
机载LiDAR技术作为一种新型的主动式空间观测技术,在快速获取空间三维地理信息方面具有不可估量的前景。然而,机载LiDAR系统获得的相邻航带点云数据在重叠区存在"漂移"问题,需要采用航带平差的方法实现不同航带点云数据之间的"无缝"拼接。针对LiDAR点云数据难以获取同名特征点来进行航带平差迭代初始值计算的问题,文中在总结航带平差迭代初始值求解方法的基础上,提出一种基于点与平面约束关系的最小二乘求解方法,提高初始值求解的准确性,并通过具体实例数据进行验证分析。 相似文献
18.
V. Ashkenazi 《Journal of Geodesy》1981,55(1):49-58
Doppler derived geocentric and relative geodetic positions are now widely used for detecting and controlling systematic scale
and orientation errors in large classical terrestrial triangulation networks. However, the combined adjustment of terrestrial
and space data raises several theoretical problems, including the choice of appropriate reference systems, the a priori weighting
of the various types of observations, the modelling of systematic errors and the conditioning of the network in terms of internal
and external rank deficiencies. Tests with large national networks show conclusively that, without correct modelling, systematic
errors will largely be unaffected by “higher order” observations. 相似文献
19.
顾及像点观测方程的系数矩阵中存在随机误差,提出了基于总体最小二乘的线阵卫星遥感影像光束法平差模型。在假定像点观测误差和系数矩阵误差均为独立、等精度分布的基础上,利用拉格朗日条件极值法推导了包含外方位元素虚拟观测方程和控制点误差方程的总体最小二乘光束法平差算法的具体公式和计算方法。该方法利用方差分量估计确定各类虚拟观测值的方差,可求解包含多类虚拟观测量的平差问题,并可用先验信息或岭迹法确定系数矩阵观测值的权比例系数,从而克服了现有总体最小二乘虚拟观测方法不能处理多类虚拟观测值的不足,确保了光束法平差可正确有效求解。分别利用模拟算例与两组真实影像进行了试验验证。结果表明,相比于常规最小二乘虚拟观测法以及现有总体最小二乘虚拟观测方法,本文方法具有更高的求解精度与适应性。相较于传统线阵卫星遥感影像光束法平差方法,本文方法可以获得更高的平差计算精度。 相似文献
20.
The upward-downward continuation of a harmonic function like the gravitational potential is conventionally based on the direct-inverse
Abel-Poisson integral with respect to a sphere of reference. Here we aim at an error estimation of the “planar approximation”
of the Abel-Poisson kernel, which is often used due to its convolution form. Such a convolution form is a prerequisite to
applying fast Fourier transformation techniques. By means of an oblique azimuthal map projection / projection onto the local
tangent plane at an evaluation point of the reference sphere of type “equiareal” we arrive at a rigorous transformation of
the Abel-Poisson kernel/Abel-Poisson integral in a convolution form. As soon as we expand the “equiareal” Abel-Poisson kernel/Abel-Poisson
integral we gain the “planar approximation”. The differences between the exact Abel-Poisson kernel of type “equiareal” and
the “planar approximation” are plotted and tabulated. Six configurations are studied in detail in order to document the error
budget, which varies from 0.1% for points at a spherical height H=10km above the terrestrial reference sphere up to 98% for points at a spherical height H = 6.3×106km.
Received: 18 March 1997 / Accepted: 19 January 1998 相似文献