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1.
With the advances in the field of GPS positioning and the global densification of permanent GPS tracking stations, it is now
possible to determine at the highest level of accuracy the transformation parameters connecting various international terrestrial
reference frame (ITRF) realizations. As a by-product of these refinements, not only the seven usual parameters of the similarity
transformations between frames are available, but also their rates, all given at some epoch t
k
. This paper introduces rigorous matrix equations to estimate variance–covariance matrices for transformed coordinates at
any epoch t based on a stochastic model that takes into consideration all a priori information of the parameters involved at epoch t
k
, and the coordinates and velocities at the reference frame initial epoch t
0. The results of this investigation suggest that in order to attain maximum accuracy, the agencies determining the 14-parameter
transformations between reference frames should also publish their full variance–covariance matrix.
Electronic Publication 相似文献
2.
J. Grodecki 《Journal of Geodesy》2001,75(2-3):157-163
A new estimator of variance–covariance components is presented. The proposed estimator is derived by applying the principle
of maximum-likelihood estimation to the posterior probability density function for the case when no prior information is available.
Received: 9 August 1999 / Accepted: 10 November 2000 相似文献
3.
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
4.
A constrained LAMBDA method for GPS attitude determination 总被引：4，自引：0，他引：4
An improved method to obtain fixed integer ambiguity in GPS attitude determination is presented. Known conditions are utilized
as constraints to acquire attitude information when the float solution and its variance–covariance matrix are not accurate
enough. The searching ellipsoidal region is first expanded to compensate for errors caused by the inaccurate float solution.
Then the constraints are used to shrink the region to a proper size, which maintains the true integer ambiguity. Experimental
results demonstrate that this scheme gives a fast search time and a higher success rate in determining the fixed integer ambiguity
than the unconstrained method. The accuracy of attitude angles is also improved.
相似文献
| Bo WangEmail: |
5.
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
6.
A detailed accuracy assessment of the geopotential model Jgm3 is made based on independent single- and dual-satellite sea-height
differences at crossovers from altimetry with Jgm3-based orbits. These differences, averaged over long time spans and in latitude
bands, are converted to spectra (latitude-lumped coefficients) by least-squares estimation. The observed error spectra so
obtained are then compared directly to error projections for them from the Jgm3 variance–covariance matrix. It is found from
these comparisons that Jgm3 is generally well calibrated with respect to the crossover altimetry of and between Geosat, TOPEX/Poseidon
(T/P), and Ers 1. Some significant discrepancies at a few lower orders (namely m=1 and 3) indicate a need for further improvement of Jgm3. A companion calibration (by order) of the geopotential model Jgm2
shows its variance–covariance matrix also to be generally well calibrated for the same single- and dual-satellite altimeter
data sets (but based on Jgm2 orbits), except that the error projections for Geosat are too pessimistic. The analysis of the
dual-satellite crossovers reveals possible relative coordinate system offsets (particularly for Geosat with respect to T/P)
which have been discussed previously. The long-term detailed seasonally averaged Geosat sea level with respect to T/P (covering
1985–1996) should be useful in gauging the relative change in sea level between different parts of the ocean over the single
4-year gap between these missions (1988–1992).
Received: 16 February 1998 / Accepted: 25 November 1998 相似文献
7.
Adaptive Kalman Filtering for INS/GPS 总被引：69，自引：0，他引：69
After reviewing the two main approaches of adaptive Kalman filtering, namely, innovation-based adaptive estimation (IAE)
and multiple-model-based adaptive estimation (MMAE), the detailed development of an innovation-based adaptive Kalman filter
for an integrated inertial navigation system/global positioning system (INS/GPS) is given. The developed adaptive Kalman filter
is based on the maximum likelihood criterion for the proper choice of the filter weight and hence the filter gain factors.
Results from two kinematic field tests in which the INS/GPS was compared to highly precise reference data are presented. Results
show that the adaptive Kalman filter outperforms the conventional Kalman filter by tuning either the system noise variance–covariance
(V–C) matrix `Q' or the update measurement noise V–C matrix `R' or both of them.
Received: 14 September 1998 / Accepted: 21 December 1998 相似文献
8.
The weighted Procrustes algorithm is presented as a very effective tool for solving the three-dimensional datum transformation
problem. In particular, the weighted Procrustes algorithm does not require any initial datum parameters for linearization
or any iteration procedure. As a closed-form algorithm it only requires the values of Cartesian coordinates in both systems
of reference. Where there is some prior information about the variance–covariance matrix of the two sets of Cartesian coordinates,
also called pseudo-observations, the weighted Procrustes algorithm is able to incorporate such a quality property of the input
data by means of a proper choice of weight matrix. Such a choice is based on a properly designed criterion matrix which is
discussed in detail. Thanks to the weighted Procrustes algorithm, the problem of incorporating the stochasticity measures
of both systems of coordinates involved in the seven parameter datum transformation problem [conformal group ℂ7(3)] which is free of linearization and any iterative procedure can be considered to be solved. Illustrative examples are
given.
Received: 7 January 2002 / Accepted: 9 September 2002
Correspondence to: E. W. Grafarend 相似文献
9.
Georges Balmino 《Journal of Geodesy》2009,83(10):989-995
We have applied efficient methods for computing variances and covariances of functions of a global gravity field model expanded
in spherical harmonics, using the full variance–covariance matrix of the coefficients. Examples are given with recent models
derived from GRACE (up to degree and order 150), and with simulated GOCE derived solutions (up to degree and order 200). 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.
12.
Least-squares variance component estimation 总被引：19，自引：15，他引：4
Least-squares variance component estimation (LS-VCE) is a simple, flexible and attractive method for the estimation of unknown
variance and covariance components. LS-VCE is simple because it is based on the well-known principle of LS; it is flexible
because it works with a user-defined weight matrix; and it is attractive because it allows one to directly apply the existing
body of knowledge of LS theory. In this contribution, we present the LS-VCE method for different scenarios and explore its
various properties. The method is described for three classes of weight matrices: a general weight matrix, a weight matrix
from the unit weight matrix class; and a weight matrix derived from the class of elliptically contoured distributions. We
also compare the LS-VCE method with some of the existing VCE methods. Some of them are shown to be special cases of LS-VCE.
We also show how the existing body of knowledge of LS theory can be used to one’s advantage for studying various aspects of
VCE, such as the precision and estimability of VCE, the use of a-priori variance component information, and the problem of
nonlinear VCE. Finally, we show how the mean and the variance of the fixed effect estimator of the linear model are affected
by the results of LS-VCE. Various examples are given to illustrate the theory. 相似文献
13.
Atmospheric turbulence theory applied to GPS carrier-phase data 总被引：3，自引：3，他引：0
Turbulent irregularities in the lower atmosphere cause physical correlations between Global Positioning System (GPS) carrier-phase
measurements. Based on turbulence theory, a variance–covariance model is developed in this paper that reflects these correlations.
The main result shows that the obtained fully-populated variance–covariance matrices depend not only on the satellite-station
geometry, but also on the prevailing atmospheric conditions, which are parameterised by, e.g., the von Karman spectrum of
refractivity fluctuations and the wind velocity vector. It is shown that the amount of the correlation between two GPS carrier-phase
observations is inversely related to the separation distance of the corresponding ray paths through the turbulent atmosphere.
Furthermore, the wind velocity and direction play a key role in the correlation. 相似文献
14.
Peiliang Xu 《Journal of Geodesy》1999,73(1):35-46
The biases and accuracy of the extended Kalman filter (EKF) and a second-order nonlinear filter (SONF) are discussed from
the point of view of a frequentist; these are often derived by applying the relevant conditional quantities to the linear
Kalman algorithm under the Bayesian framework. The EKF and the SONF are biased, although the SONF has been derived in the
hope of improving first-order filters. Unfortunately the biases of the SONF may be magnified further, because the second-order
terms of the relevant Bayesian conditional quantities have never been properly used to derive the SONF from the frequentist
point of view. The variance–covariance matrix of the SONF given in the literature is proven to be incorrect up to the second-order
approximation, and the correct one is derived. Finally, also from the point of view of a frequentist, an alternative, almost
unbiased SONF is proposed, if the randomness of partials is neglected.
Received: 12 July 1997 / Accepted: 5 October 1998 相似文献
15.
G. Even-Tzur 《Journal of Geodesy》2002,76(8):455-461
The performance of geodetic monitoring networks is heavily influenced by the configuration of the measured GPS vectors. As
an effective design of the GPS measurements will decrease GPS campaign costs and increase the accuracy and reliability of
the entire network, the identification of the preferred GPS vectors for measurement has been highlighted as a core problem
in the process of deformation monitoring. An algorithm based on a sensitivity analysis of the network, as dependent upon a
postulated velocity field, is suggested for the selection of the optimal GPS vectors. Relevant mathematical and statistical
concepts are presented as the basis for an improved method of vector configuration design. A sensitivity analysis of the geodetic
geodynamic network in the north of Israel is presented, where the method is examined against two deformation models, the Simple
Transform Fault and the Locked Fault. The proposed method is suggested as a means for the improvement of the design of monitoring
networks, a common practice worldwide.
Received: 30 July 2001 / Accepted: 3 June 2002
Acknowledgments. It is my pleasant duty to thank the Survey of Israel and Dr. E. Ostrovsky for providing the variance–covariance matrix of
the G1 network in northern Israel. I would like to thank the reviewers of this paper for their constructive and helpful remarks. 相似文献
16.
If the force field acting on an artificial Earth satellite is not known a priori with sufficient accuracy to represent its observations on their accuracy level, one may introduce so-called pseudo-stochastic parameters into an orbit determination process, e.g. instantaneous velocity changes at user-defined epochs or piecewise constant accelerations in user-defined adjacent time subintervals or piecewise linear and continuous accelerations in adjacent time subintervals. The procedures, based on standard least-squares, associated with such parameterizations are well established, but they become inefficient (slow) if the number of pseudo-stochastic parameters becomes large. We develop two efficient methods to solve the orbit determination problem in the presence of pseudo-stochastic parameters. The results of the methods are identical to those obtained with conventional least-squares algorithms. The first efficient algorithm also provides the full variance–covariance matrix; the second, even more efficient algorithm, only parts of it. 相似文献
17.
Stochastic significance of peaks in the least-squares spectrum 总被引：3，自引：1，他引：2
S. D. Pagiatakis 《Journal of Geodesy》1999,73(2):67-78
The least-squares spectral analysis method is reviewed, with emphasis on its remarkable property to accept time series with
an associated, fully populated covariance matrix. Two distinct cases for the input covariance matrix are examined: (a) it
is known absolutely (a-priori variance factor known); and (b) it is known up to a scale factor (a-priori variance factor unknown),
thus the estimated covariance matrix is used. For each case, the probability density function that underlines the least-squares
spectrum is derived and criteria for the statistical significance of the least-squares spectral peaks are formulated. It is
shown that for short series (up to about 150 values) with an estimated covariance matrix (case b), the spectral peaks must
be stronger to be statistically significant than in the case of a known covariance matrix (case a): the shorter the series
and the lower the significance level, the higher the difference becomes. For long series (more than about 150 values), case
(b) converges to case (a) and the least-squares spectrum follows the beta distribution. The results of this investigation are formulated in two new theorems.
Received: 27 May 1997/Accepted: 30 September 1998 相似文献
18.
The differencing technique is useful in global positioning system (GPS) positioning when two or more GPS receivers collect simultaneous observables from common satellites at each epoch, and all carrier-phase observables have the same normal distribution. An analytical probability distribution of the single-, double-, triple- and multi-difference GPS observables is obtained. This analytical model, called ISO2002, has a good matrix structure, in which I indicates the number of receivers, S indicates the number of observed satellites, and O indicates the number of epochs. The variance–covariance matrix can be expressed as the Kronecker product of several small matrices, so its inverse is equal to the Kronecker product of the inverses of these sub-matrices. Moreover, these small matrices are circulant or symmetric diagonal Toeplitz matrices, so their inverses have analytical solutions. The analytical model ISO2002 proposed to compute the inverse variance–covariance matrix is shown to be very effective. 相似文献
19.
A systematic investigation of optimal carrier-phase combinations for modernized triple-frequency GPS 总被引：12，自引：6，他引：6
The upcoming modernization of the GPS signals will allow for measurements on an additional third frequency L5 located at 1176.45 MHz.
To take advantage of carrier-phase measurements on this new signal, the strategies for integer ambiguity resolution, required
for centimeter-level accuracy, may need to be revised. The Least-squares Ambiguity Decorrelation Adjustment method remains
perhaps the most powerful tool for finding the best combinations based on a complete decorrelation of the variance–covariance
matrix related to the ambiguities. However, the computational load of that method plus the opportunity to comprehensively
study the interaction of multiple frequencies suggest a reconsideration of approaches using predefined combinations between
frequencies is not out of place. In this paper a systematic investigation is made of all possible triple-frequency geometry-free
carrier-phase combinations which retain the integer nature of the ambiguities. The concept of the lane-number is presented
to unambiguously describe the wavelength of a particular combination. The propagation of the observation noise and of the
ionospheric bias on these combinations is presented. These noise and ionospheric amplification factors are analysed with respect
to the resulting wavelength, in an effort to highlight optimal combinations characterized by a long wavelength, low noise
and limited ionospheric impact. 相似文献
20.
This paper presents the new linear estimation method of G. Matheron, based on the concept of minimum variance. The important
point is that it takes into account the regional trend, called “drift” in the present text. It is always of great interest, particularly in the case of interpolation of Bouguer anomalies.
The stress is also put on the structural use of the semi-variogram in the Earth Sciences. This new function is simply related
to the well-knowns covariance function.
An illustrative application in automatic contouring is given.
Paper presented at the CGI Meeting in Paris-September 1970. 相似文献