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1.
GNSS algebraic structures 总被引：4，自引：3，他引：1
The first objective of this paper is to show that some basic concepts used in global navigation satellite systems (GNSS) are
similar to those introduced in Fourier synthesis for handling some phase calibration problems. In experimental astronomy,
the latter are at the heart of what is called ‘phase closure imaging.’ In both cases, the analysis of the related structures
appeals to the algebraic graph theory and the algebraic number theory. For example, the estimable functions of carrier-phase
ambiguities, which were introduced in GNSS to correct some rank defects of the undifferenced equations, prove to be ‘closure-phase
ambiguities:’ the so-called ‘closure-delay’ (CD) ambiguities. The notion of closure delay thus generalizes that of double
difference (DD). The other estimable functional variables involved in the phase and code undifferenced equations are the receiver
and satellite pseudo-clock biases. A related application, which corresponds to the second objective of this paper, concerns
the definition of the clock information to be broadcasted to the network users for their precise point positioning (PPP).
It is shown that this positioning can be achieved by simply having access to the satellite pseudo-clock biases. For simplicity,
the study is restricted to relatively small networks. Concerning the phase for example, these biases then include five components:
a frequency-dependent satellite-clock error, a tropospheric satellite delay, an ionospheric satellite delay, an initial satellite
phase, and an integer satellite ambiguity. The form of the PPP equations to be solved by the network user is then similar
to that of the traditional PPP equations. As soon as the CD ambiguities are fixed and validated, an operation which can be
performed in real time via appropriate decorrelation techniques, estimates of these float biases can be immediately obtained.
No other ambiguity is to be fixed. The satellite pseudo-clock biases can thus be obtained in real time. This is not the case
for the satellite-clock biases. The third objective of this paper is to make the link between the CD approach and the GNSS
methods based on the notion of double difference. In particular, it is shown that the information provided by a maximum set
of independent DDs may not reach that of a complete set of CDs. The corresponding defect is analyzed. One of the main results
of the corresponding analysis concerns the DD–CD relationship. In particular, it is shown that the DD ambiguities, once they
have been fixed and validated, can be used as input data in the ‘undifferenced CD equations.’ The corresponding algebraic
operations are described. The satellite pseudo-clock biases can therefore be also obtained via particular methods in which
the notion of double differencing is involved. 相似文献
2.
CGCS2000精化及其全球拓展需要采用最新的模型,处理长期积累的大型GNSS观测网数据,大型GNSS网联合、快速和协同解算是空间基准精化、维持与服务的重要技术方向.在大数据技术背景下,以并行计算、云计算为代表的高性能计算技术逐渐成为大规模数据处理的首选方法.针对海量、多源、异构GNSS数据在解算处理与平差分析等方面面... 相似文献
3.
Integer least-squares theory for the GNSS compass 总被引：7，自引：2，他引：5
P. J. G. Teunissen 《Journal of Geodesy》2010,84(7):433-447
Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to high-precision positioning
and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model,
together with efficient integer search strategies. It extends current unconstrained ILS theory to the nonlinearly constrained
case, an extension that is particularly suited for precise attitude determination. As opposed to current practice, our method
does proper justice to the a priori given information. The nonlinear baseline constraint is fully integrated into the ambiguity
objective function, thereby receiving a proper weighting in its minimization and providing guidance for the integer search.
Different search strategies are developed to compute exact and approximate solutions of the nonlinear constrained ILS problem.
Their applicability depends on the strength of the GNSS model and on the length of the baseline. Two of the presented search
strategies, a global and a local one, are based on the use of an ellipsoidal search space. This has the advantage that standard
methods can be applied. The global ellipsoidal search strategy is applicable to GNSS models of sufficient strength, while
the local ellipsoidal search strategy is applicable to models for which the baseline lengths are not too small. We also develop
search strategies for the most challenging case, namely when the curvature of the non-ellipsoidal ambiguity search space needs
to be taken into account. Two such strategies are presented, an approximate one and a rigorous, somewhat more complex, one.
The approximate one is applicable when the fixed baseline variance matrix is close to diagonal. Both methods make use of a
search and shrink strategy. The rigorous solution is efficiently obtained by means of a search and shrink strategy that uses
non-quadratic, but easy-to-evaluate, bounding functions of the ambiguity objective function. The theory presented is generally
valid and it is not restricted to any particular GNSS or combination of GNSSs. Its general applicability also applies to the
measurement scenarios (e.g. single-epoch vs. multi-epoch, or single-frequency vs. multi-frequency). In particular it is applicable
to the most challenging case of unaided, single frequency, single epoch GNSS attitude determination. The success rate performance
of the different methods is also illustrated. 相似文献
4.
全球导航卫星系统（GNSS）参考网多用于估计卫星轨道/钟差、监测地表形变和速度场、确定精密地球自转参数等方面。相关数据处理模式包括：双差基线解（DD）和非差精密单点定位（PPP）等。本文首先从GNSS基本观测方程出发,通过选取两组基准参数,导出了上述两模式下的列满秩观测方程,然后分析了它们的不足,例如：相位偏差在DD模式中吸收了钟差,丧失了时不变特性;模糊度在PPP模式中吸收了相位偏差,失去了整数性。基于上述分析,本文提出了一种新的参考网数据处理方案,以充分融合DD和PPP模式的优势。它的关键策略是精选基准参数,以达到消秩亏的目的,具体优点体现在：相位偏差独立可估,若合理约束为时不变参数,可充分减少参数个数,提高网解精度;待估模糊度具备整周特性,经由模糊度固定,可改善网解可靠性。 相似文献
5.
Regional height systems do not refer to a common equipotential surface, such as the geoid. They are usually referred to the mean sea level at a reference tide gauge. As mean sea level varies (by ±1 to 2 m) from place to place and from continent to continent each tide gauge has an unknown bias with respect to a common reference surface, whose determination is what the height datum problem is concerned with. This paper deals with this problem, in connection to the availability of satellite gravity missions data. Since biased heights enter into the computation of terrestrial gravity anomalies, which in turn are used for geoid determination, the biases enter as secondary or indirect effect also in such a geoid model. In contrast to terrestrial gravity anomalies, gravity and geoid models derived from satellite gravity missions, and in particular GRACE and GOCE, do not suffer from those inconsistencies. Those models can be regarded as unbiased. After a review of the mathematical formulation of the problem, the paper examines two alternative approaches to its solution. The first one compares the gravity potential coefficients in the range of degrees from 100 to 200 of an unbiased gravity field from GOCE with those of the combined model EGM2008, that in this range is affected by the height biases. This first proposal yields a solution too inaccurate to be useful. The second approach compares height anomalies derived from GNSS ellipsoidal heights and biased normal heights, with anomalies derived from an anomalous potential which combines a satellite-only model up to degree 200 and a high-resolution global model above 200. The point is to show that in this last combination the indirect effects of the height biases are negligible. To this aim, an error budget analysis is performed. The biases of the high frequency part are proved to be irrelevant, so that an accuracy of 5 cm per individual GNSS station is found. This seems to be a promising practical method to solve the problem. 相似文献
6.
As one of the major contributors to the realisation of the International Terrestrial Reference System (ITRS), the Global Navigation Satellite Systems (GNSS) are prone to suffer from irregularities and discontinuities in time series. While often associated with hardware/software changes and the influence of the local environment, these discrepancies constitute a major threat for ITRS realisations. Co-located GNSS at fundamental sites, with two or more available instruments, provide the opportunity to mitigate their influence while improving the accuracy of estimated positions by examining data breaks, local biases, deformations, time-dependent variations and the comparison of GNSS baselines with existing local tie measurements. With the use of co-located GNSS data from a subset sites of the International GNSS Service network, this paper discusses a global multi-year analysis with the aim of delivering homogeneous time series of coordinates to analyse system-specific error sources in the local baselines. Results based on the comparison of different GNSS-based solutions with the local survey ties show discrepancies of up to 10 mm despite GNSS coordinate repeatabilities at the sub-mm level. The discrepancies are especially large for the solutions using the ionosphere-free linear combination and estimating tropospheric zenith delays, thus corresponding to the processing strategy used for global solutions. Snow on the antennas causes further problems and seasonal variations of the station coordinates. These demonstrate the need for a permanent high-quality monitoring of the effects present in the short GNSS baselines at fundamental sites. 相似文献
7.
Compared with the traditional GPS L1 C/A BPSK-R(1) signal, wideband global navigation satellite system (GNSS) signals suffer more severe distortion due to ionospheric dispersion. Ionospheric dispersion inevitably introduces additional errors in pseudorange and carrier phase observations that cannot be readily eliminated by traditional methods. Researchers have reported power losses, waveform ripples, correlation peak asymmetries, and carrier phase shifts caused by ionospheric dispersion. We analyze the code tracking bias induced by ionospheric dispersion and propose an efficient all-pass filter to compensate the corresponding nonlinear group delay over the signal bandwidth. The filter is constructed in a cascaded biquad form based on the estimated total electron content (TEC). The effects of TEC accuracy, filter order, and fraction parameter on the filter fitting error are explored. Taking the AltBOC(15,10) signal as an example, we compare the time domain signal waveforms, correlation peaks, code tracking biases, and carrier phase biases with and without this all-pass filter and demonstrate that the proposed delay-equalization all-pass filter is a potential solution to ionospheric dispersion compensation and mitigation of observation biases for wideband GNSS signals. 相似文献
8.
Xiaopeng Gong Shengfeng Gu Yidong Lou Fu Zheng Maorong Ge Jingnan Liu 《Journal of Geodesy》2018,92(7):797-809
Global navigation satellite systems (GNSS) are acting as an indispensable tool for geodetic research and global monitoring of the Earth, and they have been rapidly developed over the past few years with abundant GNSS networks, modern constellations, and significant improvement in mathematic models of data processing. However, due to the increasing number of satellites and stations, the computational efficiency becomes a key issue and it could hamper the further development of GNSS applications. In this contribution, this problem is overcome from the aspects of both dense linear algebra algorithms and GNSS processing strategy. First, in order to fully explore the power of modern microprocessors, the square root information filter solution based on the blocked QR factorization employing as many matrix–matrix operations as possible is introduced. In addition, the algorithm complexity of GNSS data processing is further decreased by centralizing the carrier-phase observations and ambiguity parameters, as well as performing the real-time ambiguity resolution and elimination. Based on the QR factorization of the simulated matrix, we can conclude that compared to unblocked QR factorization, the blocked QR factorization can greatly improve processing efficiency with a magnitude of nearly two orders on a personal computer with four 3.30 GHz cores. Then, with 82 globally distributed stations, the processing efficiency is further validated in multi-GNSS (GPS/BDS/Galileo) satellite clock estimation. The results suggest that it will take about 31.38 s per epoch for the unblocked method. While, without any loss of accuracy, it only takes 0.50 and 0.31 s for our new algorithm per epoch for float and fixed clock solutions, respectively. 相似文献
9.
We provide a comprehensive overview of pseudorange biases and their dependency on receiver front-end bandwidth and correlator design. Differences in the chip shape distortions among GNSS satellites are the cause of individual pseudorange biases. The different biases must be corrected for in a number of applications, such as positioning with mixed signals or PPP with ambiguity resolution. Current state-of-the-art is to split the pseudorange bias into a receiver- and a satellite-dependent part. As soon as different receivers with different front-end bandwidths or correlator designs are involved, the satellite biases differ between the receivers and this separation is no longer practicable. A test with a special receiver firmware, which allows tracking a satellite with a range of different correlator spacings, has been conducted with live signals as well as a signal simulator. In addition, the variability of satellite biases is assessed through zero-baseline tests with different GNSS receivers using live satellite signals. The receivers are operated with different settings for multipath mitigation, and the changes in the satellite-dependent biases depending on the receivers’ configuration are observed. 相似文献
10.
Daniela Thaller Rolf Dach Manuela Seitz Gerhard Beutler Maria Mareyen Bernd Richter 《Journal of Geodesy》2011,85(5):257-272
Satellite Laser Ranging (SLR) observations to Global Navigation Satellite System (GNSS) satellites may be used for several
purposes. On one hand, the range measurement may be used as an independent validation for satellite orbits derived solely
from GNSS microwave observations. On the other hand, both observation types may be analyzed together to generate a combined
orbit. The latter procedure implies that one common set of orbit parameters is estimated from GNSS and SLR data. We performed
such a combined processing of GNSS and SLR using the data of the year 2008. During this period, two GPS and four GLONASS satellites
could be used as satellite co-locations. We focus on the general procedure for this type of combined processing and the impact
on the terrestrial reference frame (including scale and geocenter), the GNSS satellite antenna offsets (SAO) and the SLR range
biases. We show that the combination using only satellite co-locations as connection between GNSS and SLR is possible and
allows the estimation of SLR station coordinates at the level of 1–2 cm. The SLR observations to GNSS satellites provide the
scale allowing the estimation of GNSS SAO without relying on the scale of any a priori terrestrial reference frame. We show
that the necessity to estimate SLR range biases does not prohibit the estimation of GNSS SAO. A good distribution of SLR observations
allows a common estimation of the two parameter types. The estimated corrections for the GNSS SAO are 119 mm and −13 mm on
average for the GPS and GLONASS satellites, respectively. The resulting SLR range biases suggest that it might be sufficient
to estimate one parameter per station representing a range bias common to all GNSS satellites. The estimated biases are in
the range of a few centimeters up to 5 cm. Scale differences of 0.9 ppb are seen between GNSS and SLR. 相似文献
11.
GNSS（global navigation satellite systems）系统时使用原子钟作为时间基准,相比使用晶振的GNSS接收机,其稳定度高出几个量级。GNSS系统间钟差相比接收机钟差具有更高的稳定度,如果可以充分利用此先验信息将有助于优化多GNSS系统的定位结果。分析如何充分利用系统间钟差更稳定这一先验信息,并测试引入这一先验信息对多系统单点定位结果的影响,推导了基于两种不同钟差估计方法的定位解算模型,给出了最小二乘和扩展卡尔曼滤波两种参数估计算法。通过比较不同模型和估计算法在静态和动态定位的实验结果,最小二乘法无法利用系统间钟差更稳定的特点改善定位精度;静态实验结果表明,扩展卡尔曼滤波自身有一定的降噪效果,若引入系统间钟差更稳定的先验信息,将更有利于减小噪声;动态实验结果表明,引入系统间钟差更稳定的先验信息可减弱扩展卡尔曼滤波的发散现象。 相似文献
12.
The problem of datum definition as applied to local-area geodetic networks is investigated using data collected from global navigation satellite systems (GNSS). It is shown that the process of double differencing makes the model more sensitive to computational errors that reduce the ability of the satellites alone to control the translation component of the datum definition, and as a result additional regularization is required. Traditionally, datum definition has been accomplished by constraining one station to set coordinates. Alternative regularization strategies are analysed in terms of their effects on positioning and ambiguity resolution. In doing so, processing strategies are developed which can improve the quality of global positioning system (GPS)-based position solutions in geodetic network applications of limited spatial extent, such as high-precision engineering and deformation monitoring networks. 相似文献
13.
Integer ambiguity resolution in precise point positioning: method comparison 总被引：24，自引：10，他引：14
Integer ambiguity resolution at a single receiver can be implemented by applying improved satellite products where the fractional-cycle
biases (FCBs) have been separated from the integer ambiguities in a network solution. One method to achieve these products
is to estimate the FCBs by averaging the fractional parts of the float ambiguity estimates, and the other is to estimate the
integer-recovery clocks by fixing the undifferenced ambiguities to integers in advance. In this paper, we theoretically prove
the equivalence of the ambiguity-fixed position estimates derived from these two methods by assuming that the FCBs are hardware-dependent
and only they are assimilated into the clocks and ambiguities. To verify this equivalence, we implement both methods in the
Position and Navigation Data Analyst software to process 1 year of GPS data from a global network of about 350 stations. The
mean biases between all daily position estimates derived from these two methods are only 0.2, 0.1 and 0.0 mm, whereas the
standard deviations of all position differences are only 1.3, 0.8 and 2.0 mm for the East, North and Up components, respectively.
Moreover, the differences of the position repeatabilities are below 0.2 mm on average for all three components. The RMS of
the position estimates minus those from the International GNSS Service weekly solutions for the former method differs by below
0.1 mm on average for each component from that for the latter method. Therefore, considering the recognized millimeter-level
precision of current GPS-derived daily positions, these statistics empirically demonstrate the theoretical equivalence of
the ambiguity-fixed position estimates derived from these two methods. In practice, we note that the former method is compatible
with current official clock-generation methods, whereas the latter method is not, but can potentially lead to slightly better
positioning quality. 相似文献
14.
Haim B. Papo 《Journal of Geodesy》1985,59(4):378-390
The contribution of geodetic measurements to the establishment of a control network can be partitioned into global and local
(individual) components. The global component epitomized in a number of geometrically meaningful parameters can be estimated
together with the individual point coordinates. The additional rank defect created by the extension of the parameter list
is corrected by free net adjustment constraints which are extended beyond those needed for a solution of the network datum
problem. Two applications of extended free net adjustment are outlined and illustrated by elementary numerical examples. A
non-Cartesian (skew) reference system discussed in the Appendix provides an exotic interpretation of the estimated global
and individual parameters.
Prepared during a grant period (September 1984 through February 1985) while serving as a Visiting Senior Scientist in Geodesy,
National Research Council, National Academy of Sciences, Washington, D.C. 相似文献
15.
Testing of a new single-frequency GNSS carrier phase attitude determination method: land,ship and aircraft experiments 总被引：4，自引：1，他引：3
Global navigation satellite system (GNSS) ambiguity resolution is the process of resolving the unknown cycle ambiguities of
the carrier phase data as integers. The sole purpose of ambiguity resolution is to use the integer ambiguity constraints as
a means of improving significantly on the precision of the remaining GNSS model parameters. In this contribution, we consider
the problem of ambiguity resolution for GNSS attitude determination. We analyse the performance of a new ambiguity resolution
method for GNSS attitude determination. As it will be shown, this method provides a numerically efficient, highly reliable
and robust solution of the nonlinearly constrained integer least-squares GNSS compass estimators. The analyses have been done
by means of a unique set of extensive experimental tests, using simulated as well as actual GNSS data and using receivers
of different manufacturers and type as well as different platforms. The executed field tests cover two static land experiments,
one in the Netherlands and one in Australia, and two dynamic experiments, a low-dynamics vessel experiment and high-dynamics
aircraft experiment. In our analyses, we focus on stand-alone, unaided, single-frequency, single-epoch attitude determination,
as this is the most challenging case of GNSS compass processing. 相似文献
16.
基于同伦法的非线性最小二乘平差统一模型 总被引：2，自引：1，他引：2
基于非线性同伦思想，提出了非线性同伦最小二乘平差统一模型，该方法既可适用于满秩网非线性最小二乘平差，也可适用于秩亏网非线性最小二乘平差。算例表明，对于精度较差的初始值，算法仍能精确地收敛到原方程的参数估值。 相似文献
17.
Due to the limited frequency stability and poor accuracy of typical quartz oscillators built-in GNSS receivers, an additional receiver clock error has to be estimated in addition to the coordinates. This leads to several drawbacks especially in kinematic applications: At least four satellites in view are needed for navigation, high correlations between the clock estimates and the up-coordinates. This situation can be improved distinctly when connecting atomic clocks to GNSS receivers and modeling their behavior in a physically meaningful way (receiver clock modeling). Recent developments in miniaturizing atomic clocks result in so-called chip-scale atomic clocks and open up the possibility of using stable atomic clocks in GNSS navigation. We present two different methods of receiver clock modeling, namely in an extended Kalman filter and a sequential least-squares adjustment for code-based GNSS navigation using three different miniaturized atomic clocks. Using the data of several kinematic test drives, the benefits of clock modeling for GPS navigation solutions are assessed: decrease in the noise of the up-coordinates by up to 69 % to 20 cm level, decrease in minimal detectable biases by 16 %, and elimination of spikes and subsequently decrease in large position errors (35 %). Hence, a more robust position is obtained. Additionally, artificial partial satellite outages are generated to demonstrate position solutions with only three satellites in view. 相似文献
18.
秩亏水准网按附加条件法平差的法方程系数阵和参数先验权阵具有对称特性,利用此特性和水准网附加矩阵的特殊形式,以及文献［２］中给出的线性方程组未知数及其函数、系数阵逆阵计算的一维公式,可导出秩亏水准网按附加条件法平差的一维平差计算公式,使秩亏水准网平差计算和程序设计简单易行。 相似文献
19.
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
20.
Mean sea surface heights and residual radial orbit errors are estimated simultaneously in a single global crossover adjustment
of multiple cycles of satellite altimetry data. The rank defect inherent in the estimation problem is explicitly identified
and treated in various ways to give solutions that minimise (in norm) either orbit errors or mean sea surface heights. The
rank defect gives rise to geographically correlated orbit error, consisting of those components of the orbit error or those
components of the map of sea surface heights which fall within the nullspace of the estimation problem and which cannot be
distinguished as orbit error or ocean signal. We show that, in the case of Topex/Poseidon data, the geographically correlated error consists largely of long-wavelength and long-period sea surface fluctuations, which
in the past has often been assigned as orbit error.
Received 11 September 1995; Accepted 2 September 1996 相似文献