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1.
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
2.
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
3.
The probability distribution of the GPS baseline for a class of integer ambiguity estimators 总被引：12，自引：2，他引：10
P. J. G. Teunissen 《Journal of Geodesy》1999,73(5):275-284
In current global positioning system (GPS) ambiguity resolution practice there is not yet a rigorous procedure in place to
diagnose its expected performance and to evaluate the probabilistic properties of the computed baseline. The necessary theory
to bridge this gap is presented. Probabilistic statements about the `fixed' GPS baseline can be made once its probability
distribution is known. This distribution is derived for a class of integer ambiguity estimators. Members from this class are
the ambiguity estimators that follow from `integer rounding', `integer bootstrapping' and `integer least squares' respectively.
It is also shown how this distribution differs from the one which is usually used in practice. The approximations involved
are identified and ways of evaluating them are given. In this comparison the precise role of GPS ambiguity resolution is clarified.
Received: 3 August 1998 / Accepted: 4 March 1999 相似文献
4.
Penalized GNSS Ambiguity Resolution 总被引：1，自引：1，他引：1
P. J. G. Teunissen 《Journal of Geodesy》2004,78(4-5):235-244
Global Navigation Satellite System (GNSS) carrier phase ambiguity resolution is the process of resolving the carrier phase ambiguities as integers. It is the key to fast and high precision GNSS positioning and it applies to a great variety of GNSS models which are currently in use in navigation, surveying, geodesy and geophysics. A new principle of carrier phase ambiguity resolution is introduced. The idea is to give the user the possibility to assign penalties to the possible outcomes of the ambiguity resolution process: a high penalty for an incorrect integer outcome, a low penalty for a correct integer outcome and a medium penalty for the real valued float solution. As a result of the penalty assignment, each ambiguity resolution process has its own overall penalty. Using this penalty as the objective function which needs to be minimized, it is shown which ambiguity mapping has the smallest possible penalty. The theory presented is formulated using the class of integer aperture estimators as a framework. This class of estimators was introduced elsewhere as a larger class than the class of integer estimators. Integer aperture estimators, being of a hybrid nature, can have integer outcomes as well as non-integer outcomes. The minimal penalty ambiguity estimator is an example of an integer aperture estimator. The computational steps involved for determining the outcome of the minimal penalty estimator are given. The additional complexity in comparison with current practice is minor, since the optimal integer estimator still plays a major role in the solution of the minimal penalty ambiguity estimator. 相似文献
5.
Integer aperture bootstrapping: a new GNSS ambiguity estimator with controllable fail-rate 总被引：1，自引：0，他引：1
P.J.G. Teunissen 《Journal of Geodesy》2005,79(6-7):389-397
In this contribution, we introduce a new bootstrap-based method for Global Navigation Satellite System (GNSS) carrier-phase ambiguity resolution. Integer bootstrapping is known to be one of the simplest methods for integer ambiguity estimation with close-to-optimal performance. Its outcome is easy to compute due to the absence of an integer search, and its performance is close to optimal if the decorrelating Z-transformation of the LAMBDA method is used. Moreover, the bootstrapped estimator is presently the only integer estimator for which an exact and easy-to-compute expression of its fail-rate can be given. A possible disadvantage is, however, that the user has only a limited control over the fail-rate. Once the underlying mathematical model is given, the user has no freedom left in changing the value of the fail-rate. Here, we present an ambiguity estimator for which the user is given additional freedom. For this purpose, use is made of the class of integer aperture estimators as introduced in Teunissen (2003). This class is larger than the class of integer estimators. Integer aperture estimators are of a hybrid nature and can have integer outcomes as well as non-integer outcomes. The new estimator is referred to as integer aperture bootstrapping. This new estimator has all the advantages known from integer bootstrapping with the additional advantage that its fail-rate can be controlled by the user. This is made possible by giving the user the freedom over the aperture of the pull-in region. We also give an exact and easy-to-compute expression for its controllable fail-rate. 相似文献
6.
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
7.
一个新的GNSS模糊度估计类 总被引：2，自引：0，他引：2
P.J.G.Teunissen 《武汉大学学报(信息科学版)》2004,29(9):757-762
介绍了一类新的GNSS模糊度估计。因为该类遵循移去一恢复原理，称之为整数等变估计类。本文将说明整数等变估计类较整数估计类和线性无偏估计类的范围要大，同时给出一个相当有用的整数等变估计类的表达式。这个表达式揭示了整数等变估计类的结构，并显示该表达式如何在浮点解的基础上实现整数等变估计。最后还提出最优整数估计。 相似文献
8.
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
9.
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
10.
Influence of ambiguity precision on the success rate of GNSS integer ambiguity bootstrapping 总被引：1，自引：0，他引：1
P. J. G. Teunissen 《Journal of Geodesy》2007,81(5):351-358
In this contribution, we study the dependence of the bootstrapped success rate on the precision of the GNSS carrier phase
ambiguities. Integer bootstrapping is, because of its ease of computation, a popular method for resolving the integer ambiguities.
The method is however known to be suboptimal, because it only takes part of the information from the ambiguity variance matrix
into account. This raises the question in what way the bootstrapped success rate is sensitive to changes in precision of the
ambiguities. We consider two different cases. (1) The effect of improving the ambiguity precision, and (2) the effect of using
an approximate ambiguity variance matrix. As a by-product, we also prove that integer bootstrapping is optimal within the
restricted class of sequential integer estimators. 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.
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
13.
A new approach to GPS ambiguity decorrelation 总被引：13，自引：1，他引：12
Ambiguity decorrelation is a useful technique for rapid integer ambiguity fixing. It plays an important role in the least-squares
ambiguity decorrelation adjustment (Lambda) method. An approach to multi-dimension ambiguity decorrelation is proposed by
the introduction of a new concept: united ambiguity decorrelation. It is found that united ambiguity decorrelation can provide
a rapid and effective route to ambiguity decorrelation. An approach to united ambiguity decorrelation, the HL process, is
described in detail. The HL process performs very well in high-dimension ambiguity decorrelation tests.
Received: 9 March 1998 / Accepted: 1 June 1999 相似文献
14.
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
15.
Integer GNSS ambiguity resolution involves estimation and validation of the unknown integer carrier phase ambiguities. A problem
then is that the classical theory of linear estimation does not apply to the integer GPS model, and hence rigorous validation
is not possible when use is made of the classical results. As with the classical theory, a first step for being able to validate
the integer GPS model is to make use of the residuals and their probabilistic properties. The residuals quantify the inconsistency
between data and model, while their probabilistic properties can be used to measure the significance of the inconsistency.
Existing validation methods are often based on incorrect assumptions with respect to the probabilistic properties of the parameters
involved. In this contribution we will present and evaluate the joint probability density function (PDF) of the multivariate
integer GPS carrier phase ambiguity residuals. The residuals and their properties depend on the integer estimation principle
used. Since it is known that the integer least-squares estimator is the optimal choice from the class of admissible integer
estimators, we will only focus on the PDF of the ambiguity residuals for this estimator. Unfortunately the PDF cannot be evaluated
exactly. It will therefore be shown how to obtain a good approximation. The evaluation will be completed by some examples. 相似文献
16.
J. Mäkinen 《Journal of Geodesy》2002,76(6-7):317-322
A bound is established for the Euclidean norm of the difference between the best linear unbiased estimator and any linear
unbiased estimator in the general linear model. The bound involves the spectral norm of the difference between the dispersion
matrices of the two estimators, and the residual sum of squares, all evaluated at the assumed model, but is independent of
the provenance of the observation vector at hand. The bound, a straightforward consequence of first principles in Gauss–Markov
theory, generalizes previous results on the difference between the best linear unbiased estimator and the ordinary least-squares
estimator. In a numerical example from repeated precise levelling, the bound is used to analyse the sensitivity of estimates
of vertical motion to the choice of estimator.
Received: 9 September 1999 / Accepted: 15 March 2002 相似文献
17.
P. J. G. Teunissen 《Journal of Geodesy》2003,77(7-8):402-410
Carrier phase ambiguity resolution is the key to high-precision global navigation satellite system (GNSS) positioning and navigation. It applies to a great variety of current and future models of GPS, modernized GPS and Galileo. The so-called fixed baseline estimator is known to be superior to its float counterpart in the sense that its probability of being close to the unknown but true baseline is larger than that of the float baseline, provided that the ambiguity success rate is sufficiently close to its maximum value of one. Although this is a strong result, the necessary condition on the success rate does not make it hold for all measurement scenarios. It is discussed whether or not it is possible to take advantage of the integer nature of the ambiguities so as to come up with a baseline estimator that is always superior to both its float and its fixed counterparts. It is shown that this is indeed possible, be it that the result comes at the price of having to use a weaker performance criterion. The main result of this work is a Gauss–Markov-like theorem which introduces a new minimum variance unbiased estimator that is always superior to the well-known best linear unbiased (BLU) estimator of the Gauss–Markov theorem. This result is made possible by introducing a new class of estimators. This class of integer equivariant estimators obeys the integer remove–restore principle and is shown to be larger than the class of integer estimators as well as larger than the class of linear unbiased estimators. The minimum variance unbiased estimator within this larger class is referred to as the best integer equivariant (BIE) estimator. The theory presented applies to any model of observation equations having both integer and real-valued parameters, as well as for any probability density function the data might have.
AcknowledgementsThis contribution was finalized during the authors stay, as a Tan Chin Tuan Professor, at the Nanyang Technological Universitys GPS Centre (GPSC) in Singapore. The hospitality of the GPSCs director Prof Law Choi Look and his colleagues is greatly appreciated. 相似文献
18.
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
19.
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
20.
Modeling and quality control for reliable precise point positioning integer ambiguity resolution with GNSS modernization 总被引：3，自引：2，他引：1
Recent research has demonstrated that the undifferenced integer ambiguities can be recovered using products from a network solution. The standard dual-frequency PPP integer ambiguity resolution consists of two aspects: Hatch-Melbourne-Wübbena wide-lane (WL) and ionosphere-free narrow-lane (NL) integer ambiguity resolution. A major issue affecting the performance of dual-frequency PPP applications is the time it takes to fix these two types of integer ambiguities, especially if the WL integer ambiguity resolution suffers from the noisy pseudorange measurements and strong multipath effects. With modernized Global Navigation Satellite Systems, triple-frequency measurements will be available to global users and an extra WL (EWL) model with very long wavelength can be formulated. Then, the easily resolved EWL integer ambiguities can be used to construct linear combinations to accelerate the PPP WL integer ambiguity resolution. Therefore, we propose a new reliable procedure for the modeling and quality control of triple-frequency PPP WL and NL integer ambiguity resolution. First, we analyze a WL integer ambiguity resolution model based on triple-frequency measurements. Then, an optimal pseudorange linear combination which is ionosphere-free and has minimum measurement noise is developed and used as constraint in the WL and the NL integer ambiguity resolution. Based on simulations, we have investigated the inefficiency of dual-frequency WL integer ambiguity resolution and the performance of EWL integer ambiguity resolution. Using almanacs of GPS, Galileo and BeiDou, the performances of the proposed triple-frequency WL and NL models have been evaluated in terms of success rate. Comparing with dual-frequency PPP, numerical results indicate that the proposed triple-frequency models can outperform the dual-frequency PPP WL and NL integer ambiguity resolution. With 1 s sampling rate, generally, only several minutes of data are required for reliable triple-frequency PPP WL and NL integer ambiguity resolution. Under benign observation situations and good geometries, the integer ambiguity can be reliably resolved even within 10 s. 相似文献