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1.
Fabio Crosilla 《Journal of Geodesy》1983,57(1-4):226-239
This paper proposes an original method of constructing a criterion matrix for the optimal design of control networks by means
of the contraction of the eigenvalues and the rotation of the eigenvectors of a covariance matrix. The rotation of the eigenvectors
is carried out by two different methods, that is through independent rotations of the pairs of the eigenvector matrix components
and through a procrustean transfomation of the same matrix. The required criterion is that the “essential eigenvector components”
must be as orthogonal as possible to the predicted direction of deformation. A Second Order Design problem is then resolved,
that is the optimization of the precision of the observations of a local free distance network to be constructed for the study
of recent crustal movements in the seismogenetic area of Friuli (Italy). The results obtained show a high degree of correspondence
for the two proposed methods of rotation if limited rotations of the eigenvectors are considered. 相似文献
2.
工业测量中一种二次曲面的拟合方法 总被引：4，自引：0，他引：4
王解先 《武汉大学学报(信息科学版)》2007,32(1):47-50
针对工业测量中二次曲面的拟合问题，阐述了二次多项式的标准化、二次项系数矩阵的特征值和特征向量求取、测量坐标与标准坐标之间的转换关系、特征向量与旋转角的关系等问题，提出了按特征值、旋转角和平移量为参数拟合二次曲面的拟舍方法。算例表明了模型的准确性。 相似文献
3.
On the multivariate total least-squares approach to empirical coordinate transformations. Three algorithms 总被引：2，自引：1，他引：1
The multivariate total least-squares (MTLS) approach aims at estimating a matrix of parameters, Ξ, from a linear model (Y−E
Y
= (X−E
X
) · Ξ) that includes an observation matrix, Y, another observation matrix, X, and matrices of randomly distributed errors, E
Y
and E
X
. Two special cases of the MTLS approach include the standard multivariate least-squares approach where only the observation
matrix, Y, is perturbed by random errors and, on the other hand, the data least-squares approach where only the coefficient matrix
X is affected by random errors. In a previous contribution, the authors derived an iterative algorithm to solve the MTLS problem
by using the nonlinear Euler–Lagrange conditions. In this contribution, new lemmas are developed to analyze the iterative
algorithm, modify it, and compare it with a new ‘closed form’ solution that is based on the singular-value decomposition.
For an application, the total least-squares approach is used to estimate the affine transformation parameters that convert
cadastral data from the old to the new Israeli datum. Technical aspects of this approach, such as scaling the data and fixing
the columns in the coefficient matrix are investigated. This case study illuminates the issue of “symmetry” in the treatment
of two sets of coordinates for identical point fields, a topic that had already been emphasized by Teunissen (1989, Festschrift
to Torben Krarup, Geodetic Institute Bull no. 58, Copenhagen, Denmark, pp 335–342). The differences between the standard least-squares
and the TLS approach are analyzed in terms of the estimated variance component and a first-order approximation of the dispersion
matrix of the estimated parameters. 相似文献
4.
The mixed spherical map projections of equiareal, cylindric type are based upon the Lambert projection and the sinusoidal
Sanson–Flamsteed projection. These cylindric and pseudo-cylindric map projections of the sphere are generalized to the ellipsoid
of revolution (biaxial ellipsoid). They are used in consequence by two lemmas to generate a horizontal and a vertical weighted
mean of equiareal cylindric map projections of the ellipsoid of revolution. Its left–right deformation analysis via further
results leads to the left–right principal stretches/eigenvalues and left–right eigenvectors/eigenspace, as well as the maximal
left–right angular distortion for these new mixed cylindric map projections of ellipsoidal type. Detailed illustrations document
the cartographic synergy of mixed cylindric map projections.
Received: 23 April 1996 / Accepted: 19 April 1997 相似文献
5.
Ionospheric variation may be considered as a stationary time series under quiet conditions. However, the disturbance of a
stationary random process from stationarity results in the bias of corresponding samples from the stationary observations,
and in the change of statistical model parameters of the process. From a general mathematical aspect, a new method is presented
for monitoring ionospheric variations, based on the characteristic of time-series observation of GPS, and an investigation
of the statistical properties of the estimated auto-covariance of the random ionospheric delay when changing the number of
samples in the time series is carried out. A preliminary scheme for monitoring ionospheric delays is proposed.
Received: 18 August 2000 / Accepted: 12 April 2001 相似文献
6.
Exploring gravity field determination from orbit perturbations of the European Gravity Mission GOCE 总被引：5，自引：0，他引：5
A comparison was made between two methods for gravity field recovery from orbit perturbations that can be derived from global
positioning system satellite-to-satellite tracking observations of the future European gravity field mission GOCE (Gravity
Field and Steady-State Ocean Circulation Explorer). The first method is based on the analytical linear orbit perturbation
theory that leads under certain conditions to a block-diagonal normal matrix for the gravity unknowns, significantly reducing
the required computation time. The second method makes use of numerical integration to derive the observation equations, leading
to a full set of normal equations requiring powerful computer facilities. Simulations were carried out for gravity field recovery
experiments up to spherical harmonic degree and order 80 from 10 days of observation. It was found that the first method leads
to large approximation errors as soon as the maximum degree surpasses the first resonance orders and great care has to be
taken with modeling resonance orbit perturbations, thereby loosing the block-diagonal structure. The second method proved
to be successful, provided a proper division of the data period into orbital arcs that are not too long.
Received: 28 April 2000 / Accepted: 6 November 2000 相似文献
7.
Urho A. Rauhala 《Journal of Geodesy》1981,55(2):159-166
A least squares solution of sequential array algebra observation equations is derived using spectral decomposition of the
normal equation matrix in terms of array algebra. A new direct solution for computation of eigenvectors is derived using the
theory of general matrix inverses. 相似文献
8.
Modeling network autocorrelation within migration flows by eigenvector spatial filtering 总被引：8，自引：5，他引：3
Yongwan Chun 《Journal of Geographical Systems》2008,10(4):317-344
Although the assumption of independence among interaction flows frequently is engaged in spatial interaction modeling, in
many circumstances it leads to misspecified models and incorrect inferences. An informed approach is to explicitly incorporate
an assumed relationship structure among the interaction flows, and to explicitly model the network autocorrelation. This paper
illustrates such an approach in the context of U.S. interstate migration flows. Behavioral assumptions, similar to those of
the intervening opportunities or the competing destinations concepts, exemplify how to specify network flows that are related
to particular origin–destination combinations. The stepwise incorporation of eigenvectors, which are extracted from a network
link matrix, captures the network autocorrelation in a Poisson regression model specification context. Spatial autocorrelation
in Poisson regression is measured by the test statistic of Jacqmin-Gadda et al. (Stat Med
16(11):1283–1297, 1997). Results show that estimated regression parameters in the spatial filtering interaction model become
more intuitively interpretable.
相似文献
| Yongwan ChunEmail: |
9.
Daniel A. Griffith 《Journal of Geographical Systems》2002,4(1):43-51
As either the spatial resolution or the spatial scale for a geographic landscape increases, both latent spatial dependence
and spatial heterogeneity also will tend to increase. In addition, the amount of georeferenced data that results becomes massively
large. These features of high spatial resolution hyperspectral data present several impediments to conducting a spatial statistical
analysis of such data. Foremost is the requirement of popular spatial autoregressive models to compute eigenvalues for a row-standardized
geographic weights matrix that depicts the geographic configuration of an image's pixels. A second drawback arises from a
need to account for increased spatial heterogeneity. And a third concern stems from the usefulness of marrying geostatistical
and spatial autoregressive models in order to employ their combined power in a spatial analysis. Research reported in this
paper addresses all three of these topics, proposing successful ways to prevent them from hindering a spatial statistical
analysis. For illustrative purposes, the proposed techniques are employed in a spatial analysis of a high spatial resolution
hyperspectral image collected during research on riparian habitats in the Yellowstone ecosystem.
Received: 25 February 2001 / Accepted: 2 August 2001 相似文献
10.
H. Kutterer 《Journal of Geodesy》1999,73(7):350-361
A proper perturbation theory of a mathematical model and the quantities derived by means of least-squares adjustments is
indispensable if the results have to be interpreted in a wider context. The sensitivity of some characteristic results of
least-squares adjustments such as the estimated values of the parameters and their variance–covariance matrix due to imminent
uncertainties of the stochastic model is discussed in detail. Linearizations are used with rigorous error measures and interval
mathematics. Numerical examples conclude the investigations.
Received: 27 December 1997 / Accepted: 19 April 1999 相似文献
11.
在利用函数映射计算模型间对应关系时,提出了一种校准三维几何模型之间基矩阵的新方法,将模型间对应关系的构建转化为由模型特征函数构建的基矩阵之间的校准运算。首先计算三维模型的Laplace算子,获得模型的特征值和特征向量,并利用所得到的特征向量构建基矩阵;其次,提出了协方差的最小值校准算法,以计算模型基矩阵之间的校准矩阵 S ,并用矩阵 S 对两个模型的函数基进行校准;最后,计算校准模型所有点的高斯曲率来采样源模型尖端特征点,并在校准后的目标模型上遍历所有点,以寻求最优对应点来构建等距变换（或近似等距变换）的三维模型间的对应关系。通过计算采样点与最优对应点的测地错误,以衡量所提算法的匹配准确率。实验结果表明,与已有算法相比,本算法可以较为准确地构建两个或多个模型间的对应关系,同时也克服了模型自身对称性影响对应关系计算的问题。 相似文献
12.
Quality-control issues relating to instantaneous ambiguity resolution for real-time GPS kinematic positioning 总被引：23，自引：3，他引：23
S. Han 《Journal of Geodesy》1997,71(6):351-361
An integrated method for the instantaneous ambiguity resolution using dual-frequency precise pseudo-range and carrier-phase
observations is suggested in this paper. The algorithm combines the search procedures in the coordinate domain, the observation
domain and the estimated ambiguity domain (and therefore benefits from the integration of their most positive elements). A
three-step procedure is then proposed to enhance the reliability of the ambiguity resolution by: (1) improving the stochastic
model for the double-differenced functional model in real time; (2) refining the criteria which distinguish the integer ambiguity
set that generates the minimum quadratic form of residuals from that corresponding to the second minimum one; and (3) developing
a fault detection and adaptation procedure. Three test scenarios were considered, one static baseline (11.3 km) and two kinematic
experiments (baseline lengths from 5.2 to 13.7 km). These showed that the mean computation time for one epoch is less than
0.1 s, and that the success rate reaches 98.4% (compared to just 68.4% using standard ratio tests).
Received: 5 June 1996; Accepted: 16 January 1997 相似文献
13.
In satellite data analysis, one big advantage of analytical orbit integration, which cannot be overestimated, is missed in
the numerical integration approach: spectral analysis or the lumped coefficient concept may be used not only to design efficient
algorithms but overall for much better insight into the force-field determination problem. The lumped coefficient concept,
considered from a practical point of view, consists of the separation of the observation equation matrix A=BT into the product of two matrices. The matrix T is a very sparse matrix separating into small block-diagonal matrices connecting the harmonic coefficients with the lumped
coefficients. The lumped coefficients are nothing other than the amplitudes of trigonometric functions depending on three
angular orbital variables; therefore, the matrix N=B
T
B will become for a sufficient length of a data set a diagonal dominant matrix, in the case of an unlimited data string length
a strictly diagonal one. Using an analytical solution of high order, the non-linear observation equations for low–low SST range data can be transformed into a form to allow the application of the lumped concept.
They are presented here for a second-order solution together with an outline of how to proceed with data analysis in the spectral
domain in such a case. The dynamic model presented here provides not only a practical algorithm for the parameter determination
but also a simple method for an investigation of some fundamental questions, such as the determination of the range of the
subset of geopotential coefficients which can be properly determined by means of SST techniques or the definition of an optimal
orbital configuration for particular SST missions. Numerical results have already been obtained and will be published elsewhere.
Received: 15 January 1999 / Accepted: 30 November 1999 相似文献
14.
S. Ritter 《Journal of Geodesy》1998,72(2):101-106
The ellipsoidal Stokes problem is one of the basic boundary-value problems for the Laplace equation which arises in physical
geodesy. Up to now, geodecists have treated this and related problems with high-order series expansions of spherical and spheroidal
(ellipsoidal) harmonics. In view of increasing computational power and modern numerical techniques, boundary element methods
have become more and more popular in the last decade. This article demonstrates and investigates the nullfield method for
a class of Robin boundary-value problems. The ellipsoidal Stokes problem belongs to this class. An integral equation formulation
is achieved, and existence and uniqueness conditions are attained in view of the Fredholm alternative. Explicit expressions
for the eigenvalues and eigenfunctions for the boundary integral operator are provided.
Received: 22 October 1996 / Accepted: 4 August 1997 相似文献
15.
Evolution of the Earth's principal axes and moments of inertia: the canonical form of solution 总被引：4，自引：0，他引：4
Harmonic coefficients of the 2nd degree are separated into the invariant quantitative (the 2nd-degree variance) and the qualitative
(the standardized harmonic coefficients) characteristics of the behavior of the potential V
2(t). On this basis the evolution of the Earth's dynamical figure is described as a solution of the time-dependent eigenvalues–eigenvectors
problem in the canonical form. Such a canonical quadratic form is defined only by temporal variations of the harmonic coefficients
and always remains finite, even within an infinite time interval. An additional condition for the correction or the determination
of temporal variations of the 2nd degree is obtained. Temporal variations of the fully normalized sectorial harmonic coefficients
are estimated in addition to ˙Cˉ
20, ˙Cˉ
21, and ˙Sˉ
21 of the EGM96 gravity model. In addition, a non-linear hyperbolic model for Cˉ
2m
(t), Sˉ
2m
(t) is constructed. The trigonometric form of the hyperbolic model leads to the consideration of the potential V
2(ψ) instead of V
2(t) within the closed interval −π/2≤ψ≤+π/2. Thus, it is possible to evaluate the global trend of V
2(t), the Earth's principal axes and the differences of the moments of inertia within the whole infinite time interval.
Received: 25 September 1998 / Accepted: 28 June 2000 相似文献
16.
Calibrating the GOCE accelerations with star sensor data and a global gravity field model 总被引：1，自引：0，他引：1
A reliable and accurate gradiometer calibration is essential for the scientific return of the gravity field and steady-state
ocean circulation explorer (GOCE) mission. This paper describes a new method for external calibration of the GOCE gradiometer
accelerations. A global gravity field model in combination with star sensor quaternions is used to compute reference differential
accelerations, which may be used to estimate various combinations of gradiometer scale factors, internal gradiometer misalignments
and misalignments between star sensor and gradiometer. In many aspects, the new method is complementary to the GOCE in-flight
calibration. In contrast to the in-flight calibration, which requires a satellite-shaking phase, the new method uses data
from the nominal measurement phases. The results of a simulation study show that gradiometer scale factors can be estimated
on a weekly basis with accuracies better than 2 × 10−3 for the ultrasensitive and 10−2 for the less sensitive axes, which is compatible with the requirements of the gravity gradient error. Based on a 58-day data
set, scale factors are found that can reduce the errors of the in-flight-calibrated measurements. The elements of the complete
inverse calibration matrix, representing both the internal gradiometer misalignments and scale factors, can be estimated with
accuracies in general better than 10−3. 相似文献
17.
Let there be given a twodimensional symmetric rank two tensor of random type (examples:strain, stress) which is either directly observed or indirectly estimated from observations by an adjustment procedure. Under the assumption of normalityof tensor components we compute the joint probability density functionas well as the marginal probability density functionsof its eigenspectra (eigenvalues) and eigendirections (orientation parameters). Due to the nonlinearity of the relation between eigenspectra-eigendirections and the random tensor components, via the inverse nonlinear error propagationbiases and aliases of their first and centralized second moments (mean value, variance-covariance) are expressed in terms of Jacobianand Hessianmatrices. The joint probability density function and the first and second moments thus form the fundamental of hypothesis testing and qualify control of eigenspectra (eigenvalues, principal components) and eigendirections (orientation parameters, eigenvectors, principial direction) of a twodimensional, symmetric rank two random tensor. 相似文献
18.
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
19.
It is shown that also in a rank deficient Gauss-Markov model higher weights of the observations automatically improve the
precision of the estimated parameters as long as they are computed in thesame datum. However, the amount of improvement in terms of the trace of the dispersion matrix isminimum for the so-called “free datum” which corresponds to the pseudo-inverse normal equations matrix. This behaviour together with its consequences is discussed
by an example with special emphasis on geodetic networks for deformation analysis. 相似文献
20.
The spline interpolation technique is applied to estimate locally the radial component of a planetary gravity field from
residual acceleration data along a special direction, the direction of observation from the Earth. After the presentation
of the theoretical framework, the method is tested on synthetic and real data in the case of Venus. It is shown that this
spline technique can be used succesfully to build local models of radial gravity fields at the planet surface.
Received: 13 March 1997 / Accepted: 17 November 1998 相似文献