共查询到20条相似文献,搜索用时 46 毫秒
1.
A. A. Seemkooei 《Journal of Geodesy》2001,75(4):227-233
The proper and optimal design and subsequent assessment of geodetic networks is an integral part of most surveying engineering
projects. Optimization and design are carried out before the measurements are actually made. A geodetic network is designed
and optimized in terms of high reliability and the results are compared with those obtained by the robustness analysis technique.
The purpose of an optimal design is to solve for both the network configuration (first-order design) and observations accuracy
(second-order design) in order to meet the desired criteria. For this purpose, an analytical method is presented for performing
the first-order design, second-order design, and/or the combined design. In order to evaluate the geometrical strength of
a geodetic network, the results of robustness analysis are displayed in terms of robustness in rotation, robustness in shear,
and robustness in scale. Results showed that the robustness parameters were affected by redundancy numbers. The largest robustness
parameters were due to the observations with minimum redundancy numbers.
Received: 14 August 2000 / Accepted: 2 January 2001 相似文献
2.
Regularization of geopotential determination from satellite data by variance components 总被引:11,自引:18,他引:11
Different types of present or future satellite data have to be combined by applying appropriate weighting for the determination
of the gravity field of the Earth, for instance GPS observations for CHAMP with satellite to satellite tracking for the coming
mission GRACE as well as gradiometer measurements for GOCE. In addition, the estimate of the geopotential has to be smoothed
or regularized because of the inversion problem. It is proposed to solve these two tasks by Bayesian inference on variance
components. The estimates of the variance components are computed by a stochastic estimator of the traces of matrices connected
with the inverse of the matrix of normal equations, thus leading to a new method for determining variance components for large
linear systems. The posterior density function for the variance components, weighting factors and regularization parameters
are given in order to compute the confidence intervals for these quantities. Test computations with simulated gradiometer
observations for GOCE and satellite to satellite tracking for GRACE show the validity of the approach.
Received: 5 June 2001 / Accepted: 28 November 2001 相似文献
3.
A discrimination test procedure for ambiguity resolution on-the-fly 总被引:18,自引:2,他引:16
Ambiguity validation tests include the acceptance test and discrimination test, which are both important steps in the Global
Positioning System ambiguity resolution process. An ambiguity discrimination test procedure based on a test statistic which
is constructed by the difference (not the ratio as used in current procedures) between the minimum and second minimum quadratic
form of the residuals in ambiguity identification, and its standard deviation, is proposed. The distribution function of the
proposed test statistic is theoretically identified as a standard normal distribution when the known a priori variance factor
is used, or as a Student's t distribution when the estimated variance factor is used. With this procedure, the ambiguity discrimination test is based
on a more rigorous test statistic whose critical value can be calculated with any chosen level of significance. Test results
indicate that the proposed ambiguity discrimination test procedure is reliable for use in ambiguity resolution on-the-fly.
Received: 17 December 1997 / Accepted: 30 June 1998 相似文献
4.
P. J. G. Teunissen 《Journal of Geodesy》1997,71(9):541-551
In this contribution we analyse in a qualitative sense for the geometry-free model the dependency of the location, the size
and the shape of the ambiguity search space on different factors of the stochastic model. For this purpose a rather general
stochastic model is used. It includes time-correlation, cross-correlation, satellite elevation dependency and the use of an
a priori weighted ionospheric model, having the ionosphere-fixed model and the ionosphere-float model as special cases. It
is shown that the location is invariant for changes in the cofactor matrix of the phase observables. This also holds true
for the cofactor matrix of the code observables in the ionosphere-float case. As for time-correlation and satellite elevation
dependency, it is shown that they only affect the size of the search space, but not its shape and orientation. It is also
shown that the least-squares ambiguities, their variance matrix and its determinant, for, respectively, the ionosphere-fixed
model, the ionosphere-float model and the ionosphere-weighted model, are all related through the same scalar weighted mean,
the weight of which is governed by the variance ratio of the ionospheric delays and the code observables. A closed-form expression
is given for the area of the search space in which all contributing factors are easily recognized. From it one can infer by
how much the area gets blown up when the ionospheric spatial decorrelation increases. This multiplication factor is largest
when one switches from the ionosphere-fixed model to the ionosphere-float model, in which case it is approximately equal to
the ratio of the standard deviation of phase with that of code. The area gives an indication of the number of grid points
inside the search space.
Received: 11 November 1996 / Accepted: 21 March 1997 相似文献
5.
Khosro Moghtased-Azar Ramin Tehranchi Ali Reza Amiri-Simkooei 《Journal of Geodesy》2014,88(5):427-439
A typical problem of estimation principles of variance and covariance components is that they do not produce positive variances in general. This caveat is due, in particular, to a variety of reasons: (1) a badly chosen set of initial variance components, namely initial value problem (IVP), (2) low redundancy in functional model, (3) an improper stochastic model, and (4) data’s possibility of containing outliers. Accordingly, a lot of effort has been made in order to design non-negative estimates of variance components. However, the desires on non-negative and unbiased estimation can seldom be met simultaneously. Likewise, in order to search for a practical non-negative estimator, one has to give up the condition on unbiasedness, which implies that the estimator will be biased. On the other hand, unlike the variance components, the covariance components can be negative, so the methods for obtaining non-negative estimates of variance components are not applicable. This study presents an alternative method to non-negative estimation of variance components such that non-negativity of the variance components is automatically supported. The idea is based upon the use of the functions whose range is the set of all positive real numbers, namely positive-valued functions (PVFs), for unknown variance components in stochastic model instead of using variance components themselves. Using the PVF could eliminate the effect of IVP on the estimation process. This concept is reparameterized on the restricted maximum likelihood with no effect on the unbiasedness of the scheme. The numerical results show the successful estimation of non-negativity estimation of variance components (as positive values) as well as covariance components (as negative or positive values). 相似文献
6.
Generalized maximum-likelihood estimation of variance components with inverted gamma prior 总被引:2,自引:2,他引:0
J. Grodecki 《Journal of Geodesy》1999,73(7):367-374
A new method for the estimation of variance components is presented. The proposed method combines the concept of maximum-likelihood
estimation with the Bayesian approach and facilitates computationally efficient introduction of prior information into the
estimation process.
Received: 22 April 1998 / Accepted: 19 April 1999 相似文献
7.
As a conformal mapping of the sphere S 2
R
or of the ellipsoid of revolution E 2
A
,
B
the Mercator projection maps the equator equidistantly while the transverse Mercator projection maps the transverse metaequator,
the meridian of reference, with equidistance. Accordingly, the Mercator projection is very well suited to geographic regions
which extend east-west along the equator; in contrast, the transverse Mercator projection is appropriate for those regions
which have a south-north extension. Like the optimal transverse Mercator projection known as the Universal Transverse Mercator Projection (UTM), which maps the meridian of reference Λ0 with an optimal dilatation factor &ρcirc;=0.999 578 with respect to the World Geodetic Reference System WGS 84 and a strip [Λ0−Λ
W
,Λ0 + Λ
E
]×[Φ
S
,Φ
N
]= [−3.5∘,+3.5∘]×[−80∘,+84∘], we construct an optimal dilatation factor ρ for the optimal Mercator projection, summarized as the Universal Mercator Projection (UM), and an optimal dilatation factor ρ0 for the optimal polycylindric projection for various strip widths which maps parallel circles Φ0 equidistantly except for a dilatation factor ρ0, summarized as the Universal Polycylindric Projection (UPC). It turns out that the optimal dilatation factors are independent of the longitudinal extension of the strip and depend
only on the latitude Φ0 of the parallel circle of reference and the southern and northern extension, namely the latitudes Φ
S
and Φ
N
, of the strip. For instance, for a strip [Φ
S
,Φ
N
]= [−1.5∘,+1.5∘] along the equator Φ0=0, the optimal Mercator projection with respect to WGS 84 is characterized by an optimal dilatation factor &ρcirc;=0.999 887 (strip width 3∘). For other strip widths and different choices of the parallel circle of reference Φ0, precise optimal dilatation factors are given. Finally the UPC for the geographic region of Indonesia is presented as an
example.
Received: 17 December 1997 / Accepted: 15 August 1997 相似文献
8.
P. J. G. Teunissen 《Journal of Geodesy》1997,71(8):486-501
This contribution is the third of four parts. Based on the gain-number concept, canonical forms will be presented of the
ambiguity search spaces of the geometry-based model, the time-averaged model, and the geometry-free model. These forms reveal
the intrinsic geometry of the search spaces and allow one to study their size, shape, and orientation as function of data
precision, sampling rate, satellite redundancy, and change in receiver-satellite geometry. The canonical forms are also used
to address the problem of search halting. The phenomenon of search halting is explained and it is shown how decorrelating
ambiguity transformations can largely eliminate this computational burden.
Received: 16 July 1996 / Accepted: 14 November 1996 相似文献
9.
Two numerical techniques are used in recent regional high-frequency geoid computations in Canada: discrete numerical integration
and fast Fourier transform. These two techniques have been tested for their numerical accuracy using a synthetic gravity field.
The synthetic field was generated by artificially extending the EGM96 spherical harmonic coefficients to degree 2160, which
is commensurate with the regular 5′ geographical grid used in Canada. This field was used to generate self-consistent sets of synthetic gravity anomalies and
synthetic geoid heights with different degree variance spectra, which were used as control on the numerical geoid computation
techniques. Both the discrete integration and the fast Fourier transform were applied within a 6∘ spherical cap centered at each computation point. The effect of the gravity data outside the spherical cap was computed using
the spheroidal Molodenskij approach. Comparisons of these geoid solutions with the synthetic geoid heights over western Canada
indicate that the high-frequency geoid can be computed with an accuracy of approximately 1 cm using the modified Stokes technique,
with discrete numerical integration giving a slightly, though not significantly, better result than fast Fourier transform.
Received: 2 November 1999 / Accepted: 11 July 2000 相似文献
10.
Spectral analysis by least squares as developed by Vaníček is applied to a series of transit times measurements obtained with
a suspended gyrocompass (Wild) electronically equipped with three photocells and a printing chronograph. Instead of being
the Fourier transform of the autocovariance function as in the usual spectral analysis of time series (Wiener theory), the
spectral function used here is a function of an estimator of the variance factor obtained after a least squares fitting of
a sinusoid to the data. That function is normalized to values between zero and one. For step-by-step spectral analysis by
least squares each time a significant frequency appears in the spectrum it is removed by least squares fitting of the corresponding
sinusoid including a damping coefficient, the residuals being again examined by spectral analysis by least squares. We find
four significant frequencies: the well known principal period of about 7min in the spinning case; a very strong component with a period nearly exactly half the principal period and an amplitude of
about 70″, explained by taking into account the second-order term in the theory developed by Jeudy, and two remaining periods
with much smaller amplitudes (2″.9 and 0″.9). It is shown that the shortest period (0s.021), predicted by theory, exists in the measurements and cannot be neglected. The smallest component is considered to correspond
to the wobble which can easily be observed in the perturbed motion. 相似文献
11.
Simplified formulae for the BIQUE estimation of variance components in disjunctive observation groups 总被引:7,自引:1,他引:6
General rigorous and simplified formulae are reported for the best invariant quadratic unbiased estimates of the variance–covariance
components, which can be applied to all least-squares adjustments with the general linear stochastic model. Simplified procedures
are given for two cases frequently recurring in geodetic applications: uncorrelated groups of correlated or uncorrelated observations,
with more than one variance component in each group.
Received: 19 November 1998 / Accepted: 21 March 2000 相似文献
12.
Based on the Bayesian principle and the fact that GPS carrier-phase ambiguities are integers, the posterior distribution
of the ambiguities and the position parameters is derived. This is then used to derive the maximum posterior likelihood solution
of the ambiguities. The accuracy of the integer ambiguity solution and the position parameters is also studied according to
the posterior distribution. It is found that the accuracy of the integer solution depends not only on the variance of the
corresponding float ambiguity solution but also on its values.
Received: 27 July 1999 / Accepted: 22 November 2000 相似文献
13.
Astronomic azimuths are used in classical geodesy, through the Laplace equation, to control the orientation of geodetic networks.
The method most commonly used by the United States National Geodetic Survey for the determination of astronomic azimuth is
often referred to as the “direction method”, and is based on observations of Polaris at any hour angle.
We have analyzed repeat determinations, by analysis of variance (ANOVA) techniques, to derive realistic estimates of the expected
accuracy of typical astronomic azimuths to be used in the readjustment of the North American Datum.
We found that the dominant errors are systematic in nature, with a very important source being observer bias, or “personal
equation”. We were unable to decompose the remaining systematic error, which presumably consists primarily of instrument biases,
anomalous refraction, and setup errors.
We found, from an analysis of determinations that were first corrected for observer bias, an increase in the variance of repeat
azimuth determinations as a function of latitude that agrees reasonably well with theoretical expectations. 相似文献
14.
On the adjustment of combined GPS/levelling/geoid networks 总被引:12,自引:7,他引:5
A detailed treatment of adjustment problems in combined global positioning system (GPS)/levelling/geoid networks is given.
The two main types of `unknowns' in this kind of multi-data 1D networks are usually the gravimetric geoid accuracy and a 2D
spatial field that describes all the datum/systematic distortions among the available height data sets. An accurate knowledge
of the latter becomes especially important when we consider employing GPS techniques for levelling purposes with respect to
a local vertical datum. Two modelling alternatives for the correction field are presented, namely a pure deterministic parametric
model, and a hybrid deterministic and stochastic model. The concept of variance component estimation is also proposed as an
important statistical tool for assessing the actual gravimetric geoid noise level and/or testing a priori determined geoid
error models. Finally, conclusions are drawn and recommendations for further study are suggested.
Received: 9 September 1998 / Accepted: 8 June 1999 相似文献
15.
MINQUE for block diagonal bordered systems such as those encountered in VLBI data analysis 总被引:1,自引:1,他引:0
A sparse matrix method is developed for computing variance factors for block-diagonal, bordered systems of equations using
MINQUE (Minimum Norm Quadratic Unbiased Estimation). This method greatly reduces the computational effort required to apply
MINQUE, thus making it practical to compute variance factors for some very large systems of equations. The computer implementation
of the method is described and applied to the computation of variance factors for a combination of 1609 VLBI (Very Long Baseline
Interferometry) observing sessions. The purpose of this test was to compute a variance factor for each of the data sets and,
perhaps, to obtain more realistic variance estimates to replace those in common use for the analysis of VLBI data. It was
found that the method is satisfactory for use with such large problems, and the test served to verify that the variances in
current use in VLBI data adjustments are adequate.
Received: 26 November 1996 / Accepted: 12 December 1997 相似文献
16.
Considering a GPS satellite and two terrestrial stations, two types of equations are derived relating the heights of the
two stations to the measured data (frequency ratio or clock rate differences) and the coordinates and velocity components
of all three participating objects. The potential possibilities of using such relations for the determination of heights (in
terms of geopotential numbers or orthometric heights) are discussed.
Received: 6 December 2000 / Accepted: 9 July 2001 相似文献
17.
The Spatial Interaction Model proposed by Alonso as “Theory of Movements” offers an innovative specification of spatial origin-destination
flow models. Equations for flows between regions, total outflow from and total inflow to a region are linked by balancing
factors. This paper presents a consistent formulation of Spatial Interaction Models in the Wilson tradition and Alonso's Theory
of Movements. The paper is intended as an introduction to the model and a review of␣the state of the art. Besides it is argued
that simultaneous equation techniques are required to estimate the so-called systemic parameters.
Received: 21 May 2000 / Accepted: 18 January 2001 相似文献
18.
Computation of spherical harmonic coefficients and their error estimates using least-squares collocation 总被引:4,自引:0,他引:4
C. C. Tscherning 《Journal of Geodesy》2001,75(1):12-18
Equations expressing the covariances between spherical harmonic coefficients and linear functionals applied on the anomalous
gravity potential, T, are derived. The functionals are the evaluation functionals, and those associated with first- and second-order derivatives
of T. These equations form the basis for the prediction of spherical harmonic coefficients using least-squares collocation (LSC).
The equations were implemented in the GRAVSOFT program GEOCOL. Initially, tests using EGM96 were performed using global and
regional sets of geoid heights, gravity anomalies and second-order vertical gravity gradients at ground level and at altitude.
The global tests confirm that coefficients may be estimated consistently using LSC while the error estimates are much too
large for the lower-order coefficients. The validity of an error estimate calculated using LSC with an isotropic covariance
function is based on a hypothesis that the coefficients of a specific degree all belong to the same normal distribution. However,
the coefficients of lower degree do not fulfil this, and this seems to be the reason for the too-pessimistic error estimates.
In order to test this the coefficients of EGM96 were perturbed, so that the pertubations for a specific degree all belonged
to a normal distribution with the variance equal to the mean error variance of the coefficients. The pertubations were used
to generate residual geoid heights, gravity anomalies and second-order vertical gravity gradients. These data were then used
to calculate estimates of the perturbed coefficients as well as error estimates of the quantities, which now have a very good
agreement with the errors computed from the simulated observed minus calculated coefficients. Tests with regionally distributed
data showed that long-wavelength information is lost, but also that it seems to be recovered for specific coefficients depending
on where the data are located.
Received: 3 February 2000 / Accepted: 23 October 2000 相似文献
19.
Burkhard Schaffrin 《Journal of Geodesy》1987,61(3):276-280
The Bayesian estimates
b of the standard deviation σ in a linear model—as needed for the evaluation of reliability—is well known to be proportional
to the square root of the Bayesian estimate (s
2)
b
of the variance component σ2 by a proportionality factor
involving the ratio of Gamma functions. However, in analogy to the case of the respective unbiased estimates, the troublesome
exact computation ofa
b may be avoided by a simple approximation which turns out to be good enough for most applications even if the degree of freedom
ν is rather small.
Paper presented to the Int. Conf. on “Practical Bayesian Statistics”, Cambridge (U.K.), 8.–11. July 1986. 相似文献