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1.
The least-squares ambiguity decorrelation adjustment: its performance on short GPS baselines and short observation spans 总被引:9,自引:2,他引:9
The least-squares ambiguity decorrelation adjustment is a method for fast GPS double-difference (DD) integer ambiguity estimation.
The performance of the method will be discussed, and although it is stressed that the method is generally applicable, attention
is restricted to short-baseline applications in the present contribution. With reference to the size and shape of the ambiguity
search space, the volume of the search space will be introduced as a measure for the number of candidate grid points, and
the signature of the spectrum of conditional variances will be used to identify the difficulty one has in computing the integer
DD ambiguities. It is shown that the search for the integer least-squares ambiguities performs poorly when it takes place
in the space of original DD ambiguities. This poor performance is explained by means of the discontinuity in the spectrum
of conditional variances. It is shown that through a decorrelation of the ambiguities, transformed ambiguities are obtained
which generally have a flat and lower spectrum, thereby enabling a fast and efficient search. It is also shown how the high
precision and low correlation of the transformed ambiguities can be used to scale the search space so as to avoid an abundance
of unnecessary candidate grid points. Numerical results are presented on the spectra of conditional variances and on the statistics
of both the original and transformed ambiguities. Apart from presenting numerical results which can typically be achieved,
the contribution also emphasizes and explains the impact on the method's performance of different measurement scenarios, such
as satellite redundancy, single vs dual-frequency data, the inclusion of code data and the length of the observation time
span.
Received: 31 October 1995 / Accepted: 21 March 1997 相似文献
2.
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
3.
The problem of phase ambiguity resolution in global positioning system (GPS) theory is considered. The Bayesian approach
is applied to this problem and, using Monte Carlo simulation to search over the integer candidates, a practical expression
for the Bayesian estimator is obtained. The analysis of the integer grid points inside the search ellipsoid and their evolution
with time, while measurements are accumulated, leads to the development of a Bayesian theory based on a mathematical mixture
model for the ambiguity.
Received: 29 March 2001 / Accepted: 3 September 2001 相似文献
4.
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
5.
整数模糊度参数的快速检索算法 总被引:1,自引:0,他引:1
GPS快速定位中,由于模糊度参数之间的强相关性,模糊度参数置信区间定义的检索区域比相应的置信椭球大得多。本文通过模糊度参数向量的正交变换,定义出包含模糊度参数置信椭球的最小正交多面体,借助在其中构造的均匀正交网格点,找出置信椭球中的所有整数模糊度参数向量。该方法显著地减少了整数模糊度参数的检索范围,提高了计算效率。 相似文献
6.
Apropos laser tracking to GPS satellites 总被引:3,自引:0,他引:3
. Laser tracking to GPS satellites (PRN5 and 6) provides an opportunity to compare GPS and laser systems directly and to combine
data of both in a single solution. A few examples of this are given in this study. The most important results of the analysis
are that (1) daily SLR station coordinate solutions could be generated with a few cm accuracy; (2) coordinates of nine stations
were determined in a 2.3-year-long arc solution; (3) the contribution of laser data on the `SLR-GPS' combined orbit, resulting
from the simultaneous processing of SLR and GPS data, is significant and (4) laser-only orbits have an accuracy of 10–20 cm,
1-day predictions of SLR orbits differ from IGS orbits by about 20–40 cm, 2-day predictions by 50–60 cm.
Received: 1 October 1996 / Accepted: 14 February 1997 相似文献
7.
Possible improvement of Earth orientation forecast using autocovariance prediction procedures 总被引:3,自引:2,他引:1
Autocovariance prediction has been applied to attempt to improve polar motion and UT1-UTC predictions. The predicted polar
motion is the sum of the least-squares extrapolation model based on the Chandler circle, annual and semiannual ellipses, and
a bias fit to the past 3 years of observations and the autocovariance prediction of these extrapolation residuals computed
after subtraction of this model from pole coordinate data. This prediction method has been applied also to the UT1-UTC data,
from which all known predictable effects were removed, but the prediction error has not been reduced with respect to the error
of the current prediction model. However, the results show the possibility of decreasing polar motion prediction errors by
about 50 for different prediction lengths from 50 to 200 days with respect to the errors of the current prediction model.
Because of irregular variations in polar motion and UT1-UTC, the accuracy of the autocovariance prediction does depend on
the epoch of the prediction. To explain irregular variations in x, y pole coordinate data, time-variable spectra of the equatorial components of the effective atmospheric angular momentum, determined
by the National Center for Environmental Prediction, were computed. These time-variable spectra maxima for oscillations with
periods of 100–140 days, which occurred in 1985, 1988, and 1990 could be responsible for excitation of the irregular short-period
variations in pole coordinate data. Additionally, time-variable coherence between geodetic and atmospheric excitation function
was computed, and the coherence maxima coincide also with the greatest irregular variations in polar motion extrapolation
residuals.
Received: 22 October 1996 / Accepted: 16 September 1997 相似文献
8.
P. J. G. Teunissen 《Journal of Geodesy》2001,75(7-8):399-407
Carrier phase ambiguity resolution is the key to fast and high-precision GNSS (Global Navigation Satellite System) kinematic
positioning. Critical in the application of ambiguity resolution is the quality of the computed integer ambiguities. Unsuccessful
ambiguity resolution, when passed unnoticed, will too often lead to unacceptable errors in the positioning results. Very high
success rates are therefore required for ambiguity resolution to be reliable. Biases which are unaccounted for will lower
the success rate and thus increase the chance of unsuccessful ambiguity resolution. The performance of integer ambiguity estimation
in the presence of such biases is studied. Particular attention is given to integer rounding, integer bootstrapping and integer
least squares. Lower and upper bounds, as well as an exact and easy-to-compute formula for the bias-affected success rate,
are presented. These results will enable the evaluation of the bias robustness of ambiguity resolution.
Received: 28 September 2000 / Accepted: 29 March 2001 相似文献
9.
The parameter distributions of the integer GPS model 总被引:6,自引:0,他引:6
P. J. G. Teunissen 《Journal of Geodesy》2002,76(1):41-48
A parameter estimation theory is incomplete if no rigorous measures are available for describing the uncertainty of the parameter
estimators. Since the classical theory of linear estimation does not apply to the integer GPS model, rigorous probabilistic
statements cannot be made with reference to the classical results. The fact that integer parameters are involved in the estimation
process forces a reappraisal of the propagation of uncertainty. It is with this purpose in mind that the joint and marginal
distributional properties of both the integer and non-integer parameters of the GPS model are determined. These joint distributions
can also be used to determine the distribution of functions of the parameters. As an important example, the distribution of
the vector of ambiguity residuals is determined.
Received: 30 January 2001 / Accepted: 31 July 2001 相似文献
10.
The success rate and precision of GPS ambiguities 总被引:8,自引:1,他引:7
P. J. G. Teunissen 《Journal of Geodesy》2000,74(3-4):321-326
An application of a theorem on the optimality of integer least-squares (LS) is described. This theorem states that the integer
LS estimator maximizes the ambiguity success rate within the class of admissible integer estimators. This theorem is used
to show how the probability of correct integer estimation depends on changes in the second moment of the ambiguity `float'
solution. The distribution of the `float' solution is considered to be a member of the broad family of elliptically contoured
distributions. Eigenvalue-based bounds for the ambiguity success rate are obtained.
Received: 11 January 1999 / Accepted: 2 November 1999 相似文献
11.
P. J. G. Teunissen 《Journal of Geodesy》2001,75(5-6):267-275
The purpose of carrier phase ambiguity resolution is to improve upon the quality of the estimated global navigation satellite
system baseline by means of the integer ambiguity constraints. However, in order to evaluate the quality of the ambiguity
resolved baseline rigorously, its probability distribution is required. This baseline distribution depends on the random characteristics
of the estimated integer ambiguities, which in turn depend on the chosen integer estimator. In this contribution is presented
an exact and closed-form expression for the baseline distribution in the case that use is made of integer bootstrapping. Also
presented are the bootstrapped probability mass function and easy-to-compute measures for the bootstrapped baseline's probability
of concentration.
Received: 28 September 2000 / Accepted: 11 January 2001 相似文献
12.
Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates 总被引:3,自引:2,他引:1
The success rate of carrier phase ambiguity resolution (AR) is the probability that the ambiguities are successfully fixed
to their correct integer values. In existing works, an exact success rate formula for integer bootstrapping estimator has
been used as a sharp lower bound for the integer least squares (ILS) success rate. Rigorous computation of success rate for
the more general ILS solutions has been considered difficult, because of complexity of the ILS ambiguity pull-in region and
computational load of the integration of the multivariate probability density function. Contributions of this work are twofold.
First, the pull-in region mathematically expressed as the vertices of a polyhedron is represented by a multi-dimensional grid,
at which the cumulative probability can be integrated with the multivariate normal cumulative density function (mvncdf) available
in Matlab. The bivariate case is studied where the pull-region is usually defined as a hexagon and the probability is easily
obtained using mvncdf at all the grid points within the convex polygon. Second, the paper compares the computed integer rounding
and integer bootstrapping success rates, lower and upper bounds of the ILS success rates to the actual ILS AR success rates
obtained from a 24 h GPS data set for a 21 km baseline. The results demonstrate that the upper bound probability of the ILS
AR probability given in the existing literatures agrees with the actual ILS success rate well, although the success rate computed
with integer bootstrapping method is a quite sharp approximation to the actual ILS success rate. The results also show that
variations or uncertainty of the unit–weight variance estimates from epoch to epoch will affect the computed success rates
from different methods significantly, thus deserving more attentions in order to obtain useful success probability predictions. 相似文献
13.
A formula for computing the gravity disturbance from the second radial derivative of the disturbing potential 总被引:6,自引:0,他引:6
J. Li 《Journal of Geodesy》2002,76(4):226-231
A formula for computing the gravity disturbance and gravity anomaly from the second radial derivative of the disturbing potential
is derived in detail using the basic differential equation with spherical approximation in physical geodesy and the modified
Poisson integral formula. The derived integral in the space domain, expressed by a spherical geometric quantity, is then converted
to a convolution form in the local planar rectangular coordinate system tangent to the geoid at the computing point, and the
corresponding spectral formulae of 1-D FFT and 2-D FFT are presented for numerical computation.
Received: 27 December 2000 / Accepted: 3 September 2001 相似文献
14.
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
15.
The global positioning system (GPS) model is distinctive in the way that the unknown parameters are not only real-valued,
the baseline coordinates, but also integers, the phase ambiguities. The GPS model therefore leads to a mixed integer–real-valued
estimation problem. Common solutions are the float solution, which ignores the ambiguities being integers, or the fixed solution,
where the ambiguities are estimated as integers and then are fixed. Confidence regions, so-called HPD (highest posterior density)
regions, for the GPS baselines are derived by Bayesian statistics. They take care of the integer character of the phase ambiguities
but still consider them as unknown parameters. Estimating these confidence regions leads to a numerical integration problem
which is solved by Monte Carlo methods. This is computationally expensive so that approximations of the confidence regions
are also developed. In an example it is shown that for a high confidence level the confidence region consists of more than
one region.
Received: 1 February 2001 / Accepted: 18 July 2001 相似文献
16.
Random simulation and GPS decorrelation 总被引:13,自引:1,他引:13
Peiliang Xu 《Journal of Geodesy》2001,75(7-8):408-423
(i) A random simulation approach is proposed, which is at the centre of a numerical comparison of the performances of different
GPS decorrelation methods. The most significant advantage of the approach is that it does not depend on nor favour any particular
satellite–receiver geometry and weighting system. (ii) An inverse integer Cholesky decorrelation method is proposed, which
will be shown to out-perform the integer Gaussian decorrelation and the Lenstra, Lenstra and Lovász (LLL) algorithm, and thus
indicates that the integer Gaussian decorrelation is not the best decorrelation technique and that further improvement is
possible. (iii) The performance study of the LLL algorithm is the first of its kind and the results have shown that the algorithm
can indeed be used for decorrelation, but that it performs worse than the integer Gaussian decorrelation and the inverse integer
Cholesky decorrelation. (iv) Simulations have also shown that no decorrelation techniques available to date can guarantee
a smaller condition number, especially in the case of high dimension, although reducing the condition number is the goal of
decorrelation.
Received: 26 April 2000 / Accepted: 5 March 2001 相似文献
17.
The total optimal search criterion in solving the mixed integer linear model with GNSS carrier phase observations 总被引:3,自引:2,他引:1
Existing algorithms for GPS ambiguity determination can be classified into three categories, i.e. ambiguity resolution in
the measurement domain, the coordinate domain and the ambiguity domain. There are many techniques available for searching
the ambiguity domain, such as FARA (Frei and Beutler in Manuscr Geod 15(4):325–356, 1990), LSAST (Hatch in Proceedings of KIS’90, Banff, Canada, pp 299–308, 1990), the modified Cholesky decomposition method (Euler and Landau in Proceedings of the sixth international geodetic symposium on satellite positioning,
Columbus, Ohio, pp 650–659, 1992), LAMBDA (Teunissen in Invited lecture, section IV theory and methodology, IAG general meeting, Beijing, China, 1993), FASF (Chen and Lachapelle in J Inst Navig 42(2):371–390, 1995) and modified LLL Algorithm (Grafarend in GPS Solut 4(2):31–44, 2000; Lou and Grafarend in Zeitschrift für Vermessungswesen 3:203–210, 2003). The widely applied LAMBDA method is based on the Least Squares Ambiguity Search (LSAS) criterion and employs an effective decorrelation technique in addition. G. Xu (J Glob Position Syst 1(2):121–131,
2002) proposed also a new general criterion together with its equivalent objective function for ambiguity searching that can be
carried out in the coordinate domain, the ambiguity domain or both. Xu’s objective function differs from the LSAS function,
leading to different numerical results. The cause of this difference is identified in this contribution and corrected. After
correction, the Xu’s approach and the one implied in LAMBDA are identical. We have developed a total optimal search criterion
for the mixed integer linear model resolving integer ambiguities in both coordinate and ambiguity domain, and derived the
orthogonal decomposition of the objective function and the related minimum expressions algebraically and geometrically. This
criterion is verified with real GPS phase data. The theoretical and numerical results show that (1) the LSAS objective function
can be derived from the total optimal search criterion with the constraint on the fixed integer ambiguity parameters, and
(2) Xu’s derivation of the equivalent objective function was incorrect, leading to an incorrect search procedure. The effects
of the total optimal criterion on GPS carrier phase data processing are discussed and its practical implementation is also
proposed. 相似文献
18.
Variance reduction of GNSS ambiguity in (inverse) paired Cholesky decorrelation transformation 总被引:1,自引:0,他引:1
It has been discovered that (a) the variance of all entries of the ambiguity vector transformed by a (inverse) paired Cholesky integer transformation is reduced relative to that of the corresponding entries of the original ambiguity vector; (b) the higher the dimension of the ambiguity vector, the more significantly the transformed variance will be decreased. The property of variance reduction is explained theoretically in detail. In order to better measure the property of variance reduction, an efficiency factor on variance reduction of ambiguities is defined. Since the (inverse) paired Cholesky integer transformation is generally performed many times for the GNSS high-dimensional ambiguity vector, the computation formula of the efficiency factor on the multi-time (inverse) paired Cholesky integer transformation is deduced. The computation results in the example show that (a) the (inverse) paired Cholesky integer transformation has a very good property of variance reduction, especially for the GNSS high-dimensional ambiguity vector; (b) this property of variance reduction can obviously improve the success rate of the transformed ambiguity vector. 相似文献
19.
The analysis of lunar laser ranging (LLR) data enables the determination of many parameters of the Earth–Moon system, such
as lunar gravity coefficients, reflector and station coordinates which contribute to the realisation of the International
Terrestrial Reference Frame 2000 (ITRF 2000), Earth orientation parameters [EOPs, which contribute to the global EOP solutions
at the International Earth Rotation Service (IERS)] or quantities which parameterise relativistic effects in the solar system.
The big advantage of LLR is the long time span of lunar observations (1970–2000). The accuracy of the normal points nowadays
is about 1 cm.
The capability of LLR to determine tidal parameters is investigated. In principle, it could be assumed that LLR would contribute
greatly to the investigation of tidal effects, because the Moon is the most important tide-generating body. In this respect
some special topics such as treatment of the permanent tide and the effect of atmospheric loading are addressed and results
for the tidal parameters h
2 and l
2 as well as values for the eight main tides are given.
Received: 14 August 2000 / Accepted: 15 October 2001 相似文献
20.
首先指出了基于传统的假设检验理论的三步法在评价模糊度整数解正确性时存在的理论缺陷,然后介绍了模糊度归整域的概念和可容许整数估计的定义,并在可容许整数估计原定义的基础上给出了更为严密的新定义。最后,基于这个可容许整数估计的新定义,讨论了模糊度成功率的概念及其计算公式。从理论上讲,只有模糊度的成功率才是评价模糊度整数解正确性的严密尺度。 相似文献