共查询到20条相似文献,搜索用时 15 毫秒
1.
Georges Blaha 《Journal of Geodesy》1982,56(4):281-299
The present paper deals with the least-squares adjustment where the design matrix (A) is rank-deficient. The adjusted parameters \(\hat x\) as well as their variance-covariance matrix ( \(\sum _{\hat x} \) ) can be obtained as in the “standard” adjustment whereA has the full column rank, supplemented with constraints, \(C\hat x = w\) , whereC is the constraint matrix andw is sometimes called the “constant vector”. In this analysis only the inner adjustment constraints are considered, whereC has the full row rank equal to the rank deficiency ofA, andAC T =0. Perhaps the most important outcome points to the three kinds of results
- A general least-squares solution where both \(\hat x\) and \(\sum _{\hat x} \) are indeterminate corresponds tow=arbitrary random vector.
- The minimum trace (least-squares) solution where \(\hat x\) is indeterminate but \(\sum _{\hat x} \) is detemined (and trace \(\sum _{\hat x} \) corresponds tow=arbitrary constant vector.
- The minimum norm (least-squares) solution where both \(\hat x\) and \(\sum _{\hat x} \) are determined (and norm \(\hat x\) , trace \(\sum _{\hat x} \) corresponds tow?0
2.
在大地测量数据处理中,很多情况下可根据先验知识建立合理的不等式约束,能够改善平差结果,提高精度。首先简要总结了附不等式约束平差的各种方法及存在的问题。根据有效约束和库恩塔克条件,提出了解决不等式约束平差的新算法,把不等式约束平差转化为等式约束平差问题,从而得到解的显示表达。最后用一数值算例证明了该算法的可行性。 相似文献
3.
On weighted total least-squares adjustment for linear regression 总被引:11,自引:5,他引:11
The weighted total least-squares solution (WTLSS) is presented for an errors-in-variables model with fairly general variance–covariance
matrices. In particular, the observations can be heteroscedastic and correlated, but the variance–covariance matrix of the
dependent variables needs to have a certain block structure. An algorithm for the computation of the WTLSS is presented and
applied to a straight-line fit problem where the data have been observed with different precision, and to a multiple regression
problem from recently published climate change research. 相似文献
4.
The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation 总被引:71,自引:26,他引:71
P. J. G. Teunissen 《Journal of Geodesy》1995,70(1-2):65-82
The GPS double difference carrier phase measurements are ambiguous by an unknown integer number of cycles. High precision relative GPS positioning based on short observational timespan data, is possible, when reliable estimates of the integer double difference ambiguities can be determined in an efficient manner. In this contribution a new method is introduced that enables very fast integer least-squares estimation of the ambiguities. The method makes use of an ambiguity transformation that allows one to reformulate the original ambiguity estimation problem as a new problem that is much easier to solve. The transformation aims at decorrelating the least-squares ambiguities and is based on an integer approximation of the conditional least-squares transformation. This least-squares ambiguity decorrelation approach, flattens the typical discontinuity in the GPS-spectrum of ambiguity conditional variances and returns new ambiguities that show a dramatic improvement in correlation and precision. As a result, the search for the transformed integer least-squares ambiguities can be performed in a highly efficient manner. 相似文献
5.
This paper presents a typification method for linear pattern in urban building generalization. The proposed method includes two processes. Firstly, structural knowledge in terms of linear pattern is detected using a two-step algorithm taking the advantages of Gestalt visual perception, computational geometry and graph theory. Spatial neighbourhood is captured using interpolated constrained Delaunay triangulation and the resulting proximity graph is pruned to be heterogeneous to get acceptable linear patterns with regard to Gestalt visual perception. Then, a typification strategy is proposed, in which typification is regarded as a progressive and iterative process consisting of elimination, exaggeration and displacement. The typification strategy iteratively executes eliminating the building with minimum overall effect, exaggerating remaining buildings considering key location and spatial characteristics and displacing them to preserve the linear pattern until elimination quantity is satisfied. Experiments show that this proposed strategy is effective and linear patterns are guaranteed with correctness and completeness. 相似文献
6.
Dan Sharni 《Journal of Geodesy》1972,46(1):25-30
The linear regression of one variable on the other is reviwed, together with its statistical analysis.
The adjustment of both variables is reduced to the previous regression. The mathematical form of the straight line is independent
of the relative weight of the two variables. Only the adjusted coordinates vary, along the line, in proportion to that weight. 相似文献
7.
B. Kasietczuk 《Journal of Geodesy》1997,71(3):131-136
This paper presents an extension of the geodetic network adjustment model. The proposed extension makes possible the estimation
of the 3-rd and 4-th central moments for the vector of measurement errors in the process of network adjustment by the least-squares
method with application of orthogonal matrices. It allows to estimate the asymmetry and kurtosis of the measurement errors
distribution.
Received 13 April 1993; Accepted 8 July 1996 相似文献
8.
An iterative solution of weighted total least-squares adjustment 总被引:9,自引:0,他引:9
Total least-squares (TLS) adjustment is used to estimate the parameters in the errors-in-variables (EIV) model. However, its
exact solution is rather complicated, and the accuracies of estimated parameters are too difficult to analytically compute.
Since the EIV model is essentially a non-linear model, it can be solved according to the theory of non-linear least-squares
adjustment. In this contribution, we will propose an iterative method of weighted TLS (WTLS) adjustment to solve EIV model
based on Newton–Gauss approach of non-linear weighted least-squares (WLS) adjustment. Then the WLS solution to linearly approximated
EIV model is derived and its discrepancy is investigated by comparing with WTLS solution. In addition, a numerical method
is developed to compute the unbiased variance component estimate and the covariance matrix of the WTLS estimates. Finally,
the real and simulation experiments are implemented to demonstrate the performance and efficiency of the presented iterative
method and its linearly approximated version as well as the numerical method. The results show that the proposed iterative
method can obtain such good solution as WTLS solution of Schaffrin and Wieser (J Geod 82:415–421, 2008) and the presented numerical method can be reasonably applied to evaluate the accuracy of WTLS solution. 相似文献
9.
Some theory problems affecting parameter estimation are discussed in this paper. Influence and transformation between errors of stochastic and functional models is pointed out as well. For choosing the best adjustment model, a formula, which is different from the literatures existing methods, for estimating and identifying the model error, is proposed. On the basis of the proposed formula, an effective approach of selecting the best model of adjustment system is given. 相似文献
10.
Some theory problems affecting parameter estimation are discussed in this paper. Influence and transformation between errors
of stochastic and functional models is pointed out as well. For choosing the best adjustment model, a formula, which is different
from the literatures existing methods, for estimating and identifying the model error, is proposed. On the basis of the proposed
formula, an effective approach of selecting the best model of adjustment system is given.
Project supported by the Open Research Fund Program of the Key Laboratory of Geospace Environment and Geodesy, Ministry of
Education, Wuhan University (No. 905276031-04-10). 相似文献
11.
秩亏自由网平差能够处理控制网中没有足够起始数据的问题,在测量数据处理中得到广泛的应用。平差参数间存在等式约束的情形下,一般采用广义逆法。它需要计算法方程系数的M—P逆,计算比较烦琐。针对这一问题,提出附加等式约束秩亏自由网平差的虚拟观测值法,给出解向量及其统计性质。 相似文献
12.
Georges Blaha 《Journal of Geodesy》1982,56(3):209-219
The main goal of this paper is to show that the solution obtained by adjusting a free network via the inner adjustment constraint
method is the minimum norm solution. The latter is a special case of the class of “minimum trace” solutions, where the trace
of the variance-covariance matrix for the adjusted parameters is a minimum. The derivations are carried out in terms of pseudo-inverses,
the various other forms of generalized inverses having been left out of consideration. 相似文献
13.
14.
T. Vincenty 《Journal of Geodesy》1980,54(1):37-43
The principles of three-dimensional geodesy are used in the adjustment of horizontal networks with heights and astronomic
coordinates held fixed. The proposed method is simpler and faster than any conventional method, as it uses measurements on
the terrain without any reductions to a computational surface. There are no restrictions on the lengths of the lines. 相似文献
15.
A. Perelmuter 《Journal of Geodesy》1979,53(4):291-295
This paper deals with a method for adjustment of free networks, without application of singular matrices, instead, specific
constraints are applied leading to a minimum trace of the variance-covariance matrix of the parameters. 相似文献
16.
The least-squares ambiguity Decorrelation (LAMBDA) method has been widely used in GNSS for fixing integer ambiguities. It
can also solve any integer least squares (ILS) problem arising from other applications. For real time applications with high
dimensions, the computational speed is crucial. A modified LAMBDA (MLAMBDA) method is presented. Several strategies are proposed
to reduce the computational complexity of the LAMBDA method. Numerical simulations show that MLAMBDA is (much) faster than
LAMBDA. The relations between the LAMBDA method and some relevant methods in the information theory literature are pointed
out when we introduce its main procedures. 相似文献
17.
18.
Georges BLAHA 《Journal of Geodesy》1984,58(1):1-30
The geometrical approach to the least-squares, based on differential geometry with tensor structure and notations, describes
the adjustment theory in a simple and plausible manner. The development relies heavily on orthonormal space and surface vectors,
and on the extrinsic properties of surfaces linking the two kinds of vectors. In order to relate geometry to adjustments,
the geometrical concepts are extended to an n-dimensional space and u- or r-dimensional surfaces, where n is the number of
observations, u is the number of parameters in the parametric method and r is the number of conditions in the condition method,
with n=u+r. Connection is made to Hilbert spaces by demonstrating that the tensor approach to the least-squares is a classical
case of the Hilbert-space approach. 相似文献
19.
卫星光学遥感影像的几何畸变是制约其定位精度的重要原因。采用一般系统误差补偿模型难以从根本上消除影像复杂畸变。本文在有理函数模型RFM平差方案基础上,根据傅里叶级数的逼近特性,提出用二元傅里叶多项式代替一般多项式作为系统误差补偿项,以适用符合连续条件的任意形式畸变。仿真和实际数据平差试验结果表明,本文方法能够有效补偿由于影像内外方位元素误差造成的像方定位系统误差及不同大小的畸变。在控制点充足的条件下,附加3阶傅里叶补偿项的RFM平差定位精度显著优于附加一般多项式补偿项的常规方法,其中SPOT-5异轨立体像对平差后平面和高程定位精度可分别达到3.34 m和2.48 m,QuickBird同轨立体像对平差后平面和高程定位精度分别达到0.77 m和0.54 m,均达到了子像素精度水平。二元傅里叶多项式可作为一种通用的影像系统误差补偿模型,拓展应用于航空和近景影像的畸变校正。 相似文献
20.
E. Mysen 《Journal of Geodesy》2014,88(10):917-926
A realization of a height system covering the south of Norway has been performed, based on least-squares collocation applied to differences between geometric and gravimetric quasigeoid heights, inhomogeneous and isotropic covariance modelling, and without prior information on the error sources of the involved data types. As a result, the derived normal heights were biased by the systematic errors of the GPS-levelling network. The important covariance properties were determined at every location from spatially differenced observations, and made it straightforward to evaluate the uncertainties of the biased height reference. The distribution of predictions followed a Gaussian shape, but extreme realizations were overrepresented. 相似文献