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The least-squares ambiguity decorrelation adjustment: a method for fast GPS integer ambiguity estimation 总被引:71,自引:26,他引:71
P. J. G. Teunissen 《Journal of Geodesy》1995,70(1-2):65-82
The GPS double difference carrier phase measurements are ambiguous by an unknown integer number of cycles. High precision relative GPS positioning based on short observational timespan data, is possible, when reliable estimates of the integer double difference ambiguities can be determined in an efficient manner. In this contribution a new method is introduced that enables very fast integer least-squares estimation of the ambiguities. The method makes use of an ambiguity transformation that allows one to reformulate the original ambiguity estimation problem as a new problem that is much easier to solve. The transformation aims at decorrelating the least-squares ambiguities and is based on an integer approximation of the conditional least-squares transformation. This least-squares ambiguity decorrelation approach, flattens the typical discontinuity in the GPS-spectrum of ambiguity conditional variances and returns new ambiguities that show a dramatic improvement in correlation and precision. As a result, the search for the transformed integer least-squares ambiguities can be performed in a highly efficient manner. 相似文献
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In order to achieve a precise positioning solution from GPS, the carrier-phase measurements with correctly resolved integer ambiguities must be used. Based on the integration of GPS with pseudolites and Inertial Navigation Systems (INS), this paper proposes an effective procedure for single-frequency carrier-phase integer ambiguity resolution. With the inclusion of pseudolites and INS measurements, the proposed procedure can speed up the ambiguity resolution process and increase the reliability of the resolved ambiguities. In addition, a recently developed ambiguity validation test, and a stochastic modelling scheme (based on-line covariance matrix estimation) are adapted to enhance the quality of ambiguity resolution. The results of simulation studies and field experiments indicate that the proposed procedure indeed improves the performance of single-frequency ambiguity resolution in terms of both reliability and time-to-fix-ambiguity. 相似文献
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Particle filter-based estimation of inter-system phase bias for real-time integer ambiguity resolution 总被引:2,自引:2,他引:0
Although double-differenced (DD) observations between satellites from different systems can be used in multi-GNSS relative positioning, the inter-system DD ambiguities cannot be fixed to integer because of the existence of the inter-system bias (ISB). Obviously, they can also be fixed as integer along with intra-system DD ambiguities if the associated ISBs are well known. It is critical to fix such inter-system DD ambiguities especially when only a few satellites of each system are observed. In most of the existing approaches, the ISB is derived from the fractional part of the inter-system ambiguities after the intra-system DD ambiguities are successfully fixed. In this case, it usually needs observations over long times depending on the number of observed satellites from each system. We present a new method by means of particle filter to estimate ISBs in real time without any a priori information based on the fact that the accuracy of a given ISB value can be qualified by the related fixing RATIO. In this particle filter-based method, the ISB parameter is represented by a set of samples, i.e., particles, and the weight of each sample is determined by the designed likelihood function related to the corresponding RATIO, so that the true bias value can be estimated successfully. Experimental validations with the IGS multi-GNSS experiment data show that this method can be carried out epoch by epoch to provide precise ISB in real time. Although there are only one, two, or at most three Galileo satellites observed, the successfully fixing rate increases from 75.5% for GPS only to 81.2%. In the experiment with five GPS satellites and one Galileo satellites, the first successfully fixing time is reduced to half of that without fixing the inter-system DD ambiguities. 相似文献
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Fast integer least-squares estimation for GNSS high-dimensional ambiguity resolution using lattice theory 总被引:4,自引:0,他引:4
GNSS ambiguity resolution is the key issue in the high-precision relative geodetic positioning and navigation applications.
It is a problem of integer programming plus integer quality evaluation. Different integer search estimation methods have been
proposed for the integer solution of ambiguity resolution. Slow rate of convergence is the main obstacle to the existing methods
where tens of ambiguities are involved. Herein, integer search estimation for the GNSS ambiguity resolution based on the lattice
theory is proposed. It is mathematically shown that the closest lattice point problem is the same as the integer least-squares
(ILS) estimation problem and that the lattice reduction speeds up searching process. We have implemented three integer search
strategies: Agrell, Eriksson, Vardy, Zeger (AEVZ), modification of Schnorr–Euchner enumeration (M-SE) and modification of
Viterbo-Boutros enumeration (M-VB). The methods have been numerically implemented in several simulated examples under different
scenarios and over 100 independent runs. The decorrelation process (or unimodular transformations) has been first used to
transform the original ILS problem to a new one in all simulations. We have then applied different search algorithms to the
transformed ILS problem. The numerical simulations have shown that AEVZ, M-SE, and M-VB are about 320, 120 and 50 times faster
than LAMBDA, respectively, for a search space of dimension 40. This number could change to about 350, 160 and 60 for dimension
45. The AEVZ is shown to be faster than MLAMBDA by a factor of 5. Similar conclusions could be made using the application
of the proposed algorithms to the real GPS data. 相似文献
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Efficiency of carrier-phase integer ambiguity resolution for precise GPS positioning in noisy environments 总被引:1,自引:0,他引:1
Precise GPS positioning relies on tracking the carrier-phase. The fractional part of carrier-phase can be measured directly
using a standard phase-locked loop, but the integer part is ambiguous and the ambiguity must be resolved based on sequential
carrier-phase measurements to ensure the required positioning precision. In the presence of large phase-measurement noise,
as can be expected in a jamming environment for example, the amount of data required to resolve the integer ambiguity can
be large, which requires a long time for any generic integer parameter estimation algorithm to converge. A key question of
interest in significant applications of GPS where fast and accurate positioning is desired is then how the convergence time
depends on the noise amplitude. Here we address this question by investigating integer least-sqaures estimation algorithms.
Our theoretical derivation and numerical experiments indicate that the convergence time increases linearly with the noise
variance, suggesting a less stringent requirement for the convergence time than intuitively expected, even in a jamming environment
where the phase noise amplitude is large. This finding can be useful for practical design of GPS-based systems in a jamming
environment, for which the ambiguity resolution time for precise positioning may be critical. 相似文献
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Success probability of integer GPS ambiguity rounding and bootstrapping 总被引:19,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
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A Grid Point Search Algorithm (GRIPSA) for fast integer ambiguity resolution is presented. In the proposed algorithm, after
the orthogonal transformation of the original ambiguity parameters, the confidence ellipsoid of the new parameters is represented
by a rectangular polyhedron with its edges parallel to the corresponding axes. A cubic grid covering the whole polyhedron
is then identified and transformed back to the original coordinate system. The integer values of the corresponding transformed
grid points are obtained by rounding off the transformed values to their nearest integer values. These values are then tested
as to whether they are located inside the polyhedron. Since the identification of the grid points in the transformed coordinate
system greatly reduces the search region of the integer ambiguities, marked improvements are obtained in the computational
effort.
Received: 13 October 1997 / Accepted: 9 June 1998 相似文献
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A comparison of three PPP integer ambiguity resolution methods 总被引:7,自引:5,他引:2
Precise point positioning (PPP) integer ambiguity resolution with a single receiver can be achieved using advanced satellite augmentation corrections. Several PPP integer ambiguity resolution methods have been developed, which include the decoupled clock model, the single-difference between-satellites model, and the integer phase clock model. Although similar positioning performances have been demonstrated, very few efforts have been made to explore the relationship between those methods. Our aim is to compare the three PPP integer ambiguity resolution methods for their equivalence. First, several assumptions made in previous publications are clarified. A comprehensive comparison is then conducted using three criteria: the integer property recovery, the system redundancy, and the necessary corrections through which the equivalence of these three PPP integer ambiguity resolution methods in the user solution is obtained. 相似文献
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Yang Liu Maorong Ge Chuang Shi Yidong Lou Jens Wickert Harald Schuh 《Journal of Geodesy》2016,90(8):715-726
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Christian Tiberius Thomas Pany Bernd Eissfeller Peter Joosten Sandra Verhagen 《GPS Solutions》2002,6(1-2):96-99
In this short contribution it is demonstrated how integer carrier phase cycle ambiguity resolution will perform in near future,
when the US GPS gets modernized and the European Galileo becomes operational. The capability of ambiguity resolution is analyzed
in the context of precise differential positioning over short, medium and long distances. Starting from dual-frequency operation
with GPS at present, particularly augmenting the number of satellites turns out to have beneficial consequences on the capability
of correctly resolving the ambiguities. With a 'double' constellation, on short baselines, the confidence of the integer ambiguity
solution increases to a level of 0.99999999 or beyond.
Electronic Publication 相似文献
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Yanyan Liu Yidong Lou Shirong Ye Rui Zhang Weiwei Song Xing Zhang Qingquan Li 《GPS Solutions》2017,21(4):1647-1659
Although integer ambiguity resolution (IAR) can improve positioning accuracy considerably and shorten the convergence time of precise point positioning (PPP), it requires an initialization time of over 30 min. With the full operation of GLONASS globally and BDS in the Asia–Pacific region, it is necessary to assess the PPP–IAR performance by simultaneous fixing of GPS, GLONASS, and BDS ambiguities. This study proposed a GPS + GLONASS + BDS combined PPP–IAR strategy and processed PPP–IAR kinematically and statically using one week of data collected at 20 static stations. The undifferenced wide- and narrow-lane fractional cycle biases for GPS, GLONASS, and BDS were estimated using a regional network, and undifferenced PPP ambiguity resolution was performed to assess the contribution of multi-GNSSs. Generally, over 99% of a posteriori residuals of wide-lane ambiguities were within ±0.25 cycles for both GPS and BDS, while the value was 91.5% for GLONASS. Over 96% of narrow-lane residuals were within ±0.15 cycles for GPS, GLONASS, and BDS. For kinematic PPP with a 10-min observation time, only 16.2% of all cases could be fixed with GPS alone. However, adding GLONASS improved the percentage considerably to 75.9%, and it reached 90.0% when using GPS + GLONASS + BDS. Not all epochs could be fixed with a correct set of ambiguities; therefore, we defined the ratio of the number of epochs with correctly fixed ambiguities to the number of all fixed epochs as the correct fixing rate (CFR). Because partial ambiguity fixing was used, when more than five ambiguities were fixed correctly, we considered the epoch correctly fixed. For the small ratio criteria of 2.0, the CFR improved considerably from 51.7% for GPS alone, to 98.3% when using GPS + GLONASS + BDS combined solutions. 相似文献
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In satellite navigation, the key to high precision is to make use of the carrier-phase measurements. The periodicity of the carrier-phase, however, leads to integer ambiguities. Often, resolving the full set of ambiguities cannot be accomplished for a given reliability constraint. In that case, it can be useful to resolve a subset of ambiguities. The selection of the subset should be based not only on the stochastic system model but also on the actual measurements from the tracking loops. This paper presents a solution to the problem of joint subset selection and ambiguity resolution. The proposed method can be interpreted as a generalized version of the class of integer aperture estimators. Two specific realizations of this new class of estimators are presented, based on different acceptance tests. Their computation requires only a single tree search, and can be efficiently implemented, e.g., in the framework of the well-known LAMBDA method. Numerical simulations with double difference measurements based on Galileo E1 signals are used to evaluate the performance of the introduced estimation schemes under a given reliability constraint. The results show a clear gain of partial fixing in terms of the probability of correct ambiguity resolution, leading to improved baseline estimates. 相似文献
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GPS定位中确定整周模糊度是关键问题,而在进行短时段的短基线向量的解算时,由于观测值较少以及卫星星座几何形状变化不大等因素,会出现整周模糊度不能固定为整数的现象。本文综述了当前求解整周模糊度的主要方法,并对GPS精密快速定位中整周模糊度定位问题提出了一定看法,可供GPS研究及定位工作者参考。 相似文献
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Rapid GPS ambiguity resolution for short and long baselines 总被引:3,自引:0,他引:3
A method of quick initial carrier cycle ambiguity resolution is described. The method applies to high-quality dual-band global
positioning system observations. Code measurements on both frequencies must be available. The rapidity of the method is achieved
through smoothing pseudoranges by phase observables and forming linear combinations between the phase observables. Two cases
are investigated. Case 1: ionospheric bias is neglected (short distances); and case 2: the bias is taken into account (longer
distances, more than, say, 10 km). The method was tested on six baselines, from 1 to 31 km long. In most cases, single-epoch
ambiguity resolution was achieved.
Received: 6 October 1999 / Accepted: 4 March 2002 相似文献