共查询到20条相似文献，搜索用时 31 毫秒
1.
Helmut Moritz 《Journal of Geodesy》1987,61(1):21-40
The paper treats the problem of averaging two independent determinations of the same function (curve, surface, etc.). Starting from the simple arithmetic mean, the problem is successively generalized to scalar and vector functions, arriving at an integral equation of Wiener-Hopf type. Aspects of least-squares collocation are also included. Finally the problem of determining transformation parameters and other systematic deviations is treated, furnishing a simple example of continuous least-squares adjustment. 相似文献
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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
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Success probability of integer GPS ambiguity rounding and bootstrapping 总被引：26，自引：7，他引：19
P. J. G. Teunissen 《Journal of Geodesy》1998,72(10):606-612
Global Positioning System ambiguity resolution is usually based on the integer least-squares principle (Teunissen 1993).
Solution of the integer least-squares problem requires both the execution of a search process and an ambiguity decorrelation
step to enhance the efficiency of this search. Instead of opting for the integer least-squares principle, one might also want
to consider less optimal integer solutions, such as those obtained through rounding or sequential rounding. Although these
solutions are less optimal, they do have one advantage over the integer least-squares solution: they do not require a search
and can therefore be computed directly. However, in order to be confident that these less optimal solutions are still good
enough for the application at hand, one requires diagnostic measures to predict their rate of success. These measures of confidence
are presented and it is shown how they can be computed and evaluated.
Received: 24 March 1998 / Accepted: 8 June 1998 相似文献
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本文从二次型的期望公式出发，推导了经典最小二乘平差、最小二乘滤波、最小二乘推估和最小二乘配置的验后单位权方差的估计公式。 相似文献
9.
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
10.
Klaus-Peter Schwarz 《Journal of Geodesy》1974,48(2):171-186
When combining satellite and terrestrial networks, covariance matrices are used which have been estimated from previous data.
It can be shown that the least-squares estimator of the unknown parameters using such an estimated covariance matrix is not
necessarily the best. There are a number of cases where a more efficient estimator can be obtained in a different way. The
problem occurs frequently in geodesy, since in least-squares adjustment of correlated observations estimated covariance matrices
are often used.
If the general structure of the covariance matrix is known, results can often be improved by a method called covariance adjustment.
The statistical model used in least-squares collocation leads to a type of covariance matrix which fits into this framework.
It is shown in which way improvements can be made using a modified approach of principal component analysis.
As a numerical example the combination of a satellite and a terrestrial network has been computed with varying assumptions
on the covariance matrix. It is shown which types of matrices are critical and where the usual least-squares approach can
be applied without hesitation. Finally, a simplified representation of covariances for spatial networks by means of a suitable
covariance function is suggested.
Paper presented at the International Symposium on Computational Methods in Geometrical Geodesy-Oxford, 2–8 September, 1973. 相似文献
11.
针对短基线集形变模型反演中法方程系数矩阵呈病态的问题,提出一种正则化稳健解算方法。该方法基于Tikhonov正则化理论,将形变速率求解问题转化为极小化问题,根据L-曲线法选取正则化参数,考虑最小二乘残差各个分量间的关系选取正则化矩阵,实现短基线集形变模型反演的稳健解算。分别采用LS法、岭估计法和Tikhonov正则化法对覆盖北京地区的29景ENVISAT ASAR数据进行处理,反演出研究区沉降速率图。通过对代表不同沉降情况的21个点的均方误差值和时间相干值、整个研究区的均方误差图等的对比分析,表明本文提出的短基线集形变模型反演的正则化稳健解算方法可获取更可靠的形变监测结果。 相似文献
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二维直角坐标变换模型在工程领域中应用非常广泛,该模型是一个非线性模型,对于多公共点的二维直角坐标变换需要进行模型的线性化,计算待求参数的近似值,再利用间接平差原理计算各待求参数最或然值。本文在非线性模型基础上推导出一个线性模型,利用该模型进行二维直角坐标变换,无需计算待求参数近似值,对于涉及到二维直角坐标变换的问题,可以简化其解算过程。 相似文献
13.
Precision, volume and eigenspectra for GPS ambiguity
estimation based on the time-averaged satellite geometry 总被引：1，自引：1，他引：1
P. J. G. Teunissen 《Journal of Geodesy》1997,71(5):290-301
In this contribution we consider the
time-averaged GPS single-baseline model and study in a qualitative sense its
relation with the geometry-free model and the geometry-based model. The
least-squares estimators of the model are derived and their properties
discussed. Special attention is given to the ambiguity search space, since it
plays such a crucial role in the problem of integer ambiguity estimation and
validation. Easy-to-evaluate, closed-form expressions are presented for the
volumes of the ambiguity search spaces that belong to the geometry-free model,
the single-epoch geometry-based model and the time-averaged model. By means of
an eigenvalue analysis, the geometry of the ambiguity search spaces is revealed
and its impact on the search for the integer least-squares ambiguities
discussed.
Received: 3 April 1996; Accepted: 6 January 1997 相似文献
14.
A closed-form of Newton method for solving over-determined pseudo-distance equations 总被引：3，自引：0，他引：3
The Newton method has been widely used for solving nonlinear least-squares problem. In geodetic adjustment, one would prefer to use the Gauss–Newton method because of the parallel with linear least-squares problem. However, it is proved in theory as well as in practice that the Gauss–Newton method has slow convergence rate and low success rate. In this paper, the over-determined pseudo-distance equations are solved by nonlinear methods. At first, the convergence of decent methods is discussed after introducing the conditional equation of nonlinear least squares. Then, a compacted form of the Hessian matrix from the second partial derivates of the pseudo-distance equations is given, and a closed-form of Newton method is presented using the compacted Hessian matrix to save the computation and storage required by Newton method. At last, some numerical examples to investigate the convergence and success rate of the proposed method are designed and performed. The performance of the closed-form of Newton method is compared with the Gauss–Newton method as well as the regularization method. The results show that the closed-form of Newton method has good performances even for dealing with ill-posed problems while a great amount of computation is saved. 相似文献
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A weighted total least-squares (WTLS) approach with linear and quadratic constraints is developed. This method is according to the traditional Lagrange approach to optimize the target function of this problem. The WTLS and constrained total least-squares (CTLS) approach had been distinctively investigated, however, these two problems have not been simultaneously considered yet; furthermore, among the contributions on the CTLS problem, only Schaffrin and Felus considered linear and quadratic constraints together; nevertheless, in many practical examples, some elements of the design/coefficient matrix are fixed and should not be modified and this approach cannot deal with these cases. The main necessity of this research appears after the desirable property of the WTLS approach in preserving the structure of the design matrix was proven by Mahboub. In other words, currently, the WTLS approach is one of the most efficient methods for solving the so-called errors-in-variables model and an attempt for equipping it with constraints seems necessary. Also it is demonstrated that the additional constraints have a ’regularization role’ for ill-conditioned problems and the unconstrained solution suffers from ill-conditioning effects which give it an added advantage over the unconstrained WTLS algorithm. Four geodetic applications indicate the significant of this problem in the presence of colored and white noise in the data. 相似文献
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针对抗差估计的选权迭代法(IRLS)对迭代初值敏感的问题,提出了将抗差估计问题看作求全局最优化问题,利用具有全局收敛性和局部搜索能力的遗传算法(GA)进行求解;并对遗传算法的变异算子步长进行改进。最后通过实例验算,证明了GA抗差估计法的有效性和优越性。 相似文献
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On weighted total least-squares adjustment for linear regression 总被引：16，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
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Calibration of the clock-phase biases of GNSS networks: the closure-ambiguity approach 总被引：2，自引：2，他引：0
In global navigation satellite systems (GNSS), the problem of retrieving clock-phase biases from network data has a basic rank defect. We analyse the different ways of removing this rank defect, and define a particular strategy for obtaining these phase biases in a standard form. The minimum-constrained problem to be solved in the least-squares (LS) sense depends on some integer vector which can be fixed in an arbitrary manner. We propose to solve the problem via an undifferenced approach based on the notion of closure ambiguity. We present a theoretical justification of this closure-ambiguity approach (CAA), and the main elements for a practical implementation. The links with other methods are also established. We analyse all those methods in a unified interpretative framework, and derive functional relations between the corresponding solutions and our CAA solution. This could be interesting for many GNSS applications like real-time kinematic PPP for instance. To compare the methods providing LS estimates of clock-phase biases, we define a particular solution playing the role of reference solution. For this solution, when a phase bias is estimated for the first time, its fractional part is confined to the one-cycle width interval centred on zero; the integer-ambiguity set is modified accordingly. Our theoretical study is illustrated with some simple and generic examples; it could have applications in data processing of most GNSS networks, and particularly global networks using GPS, Glonass, Galileo, or BeiDou/Compass satellites. 相似文献
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A Bayesian method for linear, inequality-constrained adjustment and its application to GPS positioning 总被引：7，自引：0，他引：7
One of the typical approaches to linear, inequality-constrained adjustment (LICA) is to solve a least-squares (LS) problem subject to the linear inequality constraints. The main disadvantage of this approach is that the statistical properties of the estimate are not easily determined and thus no general conclusions about the superiority of the estimate can be made. A new approach to solving the LICA problem is proposed. The linear inequality constraints are converted into prior information on the parameters with a uniform distribution, and consequently the LICA problem is reformulated into a Bayesian estimation problem. It is shown that the LS estimate of the LICA problem is identical to the Bayesian estimate based on the mode of the posterior distribution. Finally, the Bayesian method is applied to GPS positioning. Results for four field tests show that, when height information is used, the GPS phase ambiguity resolution can be improved significantly and the new approach is feasible. 相似文献
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基于先验求权的虚拟观测值法及其在线阵影像定向中的应用 总被引：1，自引：0，他引：1
航天线阵列遥感影像定向参数之间存在强相关性,参数解算不稳定,难以得到准确结果。较为常见的解决方法是将定向参数处理成虚拟观测值或用岭估计代替最小二乘估计。本文首先分析了这两种方法的联系与区别,提出利用原始外方位元素精度等先验知识给定虚拟观测值权,进一步提高定向结果的可靠性。对SPOT-5与QuickBird两种高分辨率线阵影像的定向试验结果表明,在使用6个分布良好的地面控制点情况下,影像对地目标定位精度可达到2~4个像素的水平。 相似文献