GPS多差相位观测量数学相关性的分析表示

给出了GPS载波相位测量中Ⅰ个测站同步观测S颗相同卫星0个观测历元所在弧段内单差、双差、三差乃至更高次差分相位观测量之间数学相关性的分析表示.它克服了多条基线同时求解时无法精确顾及多差相位观测量之间相关性的缺陷,使得单、多基线矢量解算无需用大型矩阵求逆就能得到相关权阵,只需列出误差方程,组成法矩阵后求解有限个待估参数,从而极大地提高了求解速度,具有重要的实用价值.     

Surveying co-located space-geodetic instruments for ITRF computation

A new and comprehensive method is presented that can be used for estimating eccentricity vectors between global positioning system (GPS) antennas, doppler orbitography and radiopositioning integrated by satellites (DORIS) antennas, azimuth-elevation (AZ-EL) very long baseline interferometry (VLBI) telescopes, and satellite laser ranging (SLR) and lunar laser ranging (LLR) telescopes. The problem of reference point (RP) definition for these space-geodetic instruments is addressed and computed using terrestrial triangulation and electronic distance measurement (EDM) trilateration. The practical ground operations, the surveying approach and the terrestrial data processing are briefly illustrated, and the post-processing procedure is discussed. It is a geometrically based analytical approach that allows computation of RPs along with a rigorous statistical treatment of measurements. The tight connection between the geometrical model and the surveying procedure is emphasized. The computation of the eccentricity vector and the associated variance–covariance matrix between an AZ-EL VLBI telescope (with or without intersecting axes) and a GPS choke ring antenna is concentrated upon, since these are fundamental for computing the International Terrestrial Reference Frame (ITRF). An extension to RP computation and eccentricity vectors involving DORIS, SLR and LLR techniques is also presented. Numerical examples of the quality that can be reached using the authors approach are given. Working data sets were acquired in the years 2001 and 2002 at the radioastronomical observatory of Medicina (Italy), and have been used to estimate two VLBI-GPS eccentricity vectors and the corresponding SINEX files.     

Rigorous transformation of variance–covariance matrices of GPS-derived coordinates and velocities

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     

Preliminary evaluation of the Russian GLONASS system as a potential geodetic tool

By the beginning of 1996 the Russian Global Navigation Satellite System (GLONASS) constellation was completely deployed, although several satellites have already been decommissioned since then. With 17 satellites in operation (status as of 21 December 1997, although two of them are unusable and one is a non-operative spare), GLONASS is now an alternative and a complement to GPS. We present an evaluation of the current status of the GLONASS system, paying particular attention to its possible geodetic applications. Data from several receivers were used for this evaluation, including data from GPS receivers in order to allow for a comparison between GLONASS and GPS. We tested the quality of the geodetic observables, the consistency of the broadcast orbits, the single-point positioning results, and we also looked at multipath errors and cycle slips in our GLONASS data. In general the GLONASS performance has been found to be very satisfactory, even better than GPS in aspects such as single-receiver positioning or in the quality of the second-frequency pseudo-ranges due to the degradation of the GPS measurement quality under selective availability and anti-spoofing. Received: 26 November 1996 / Accepted: 16 January 1998     

Precision, Cross Correlation, and Time Correlation of GPS Phase and Code Observations

In high-precision Global Positioning System (GPS) relative positioning applications, the stochastic properties of the GPS observables play a crucial role. The misspecification of the a priori covariance matrix can lead ton non-optimal results and false decisions. In this article, the noise characteristics of seven commonly used GPS receivers are examined. The main areas of our study are the precision of the observations, the time correlation of the observations, and the correlation between the different observation types. In order to examine these characteristics, an experiment was carried out, which will be briefly discussed. As results, the autocorrelation functions, standard deviation, and correlation numbers will be given for the undifferenced observations of the seven receivers. The standard deviation of the phase observation is usually at the submillimeter level, and that of the code observations is some centimeters to decimeters. It will be also shown that none of the receivers are free from correlation between observation types and time correlation, especially the code observations, which suffer from time correlation. The results presented can help to refine stochastic models currently in use. ? 2000 John Wiley & Sons, Inc.     

Characteristics of GPS positioning error with non-uniform pseudorange error

We study the characteristics of the random GPS positioning errors when the pseudorange errors differ for each satellite. A concise, explicit, analytical formula is derived for the covariance of the positioning error by using singular value decomposition. It is composed of a uniform error covariance together with additional contributions from those satellites with larger pseudorange errors. The eigenvectors of the uniform error covariance define the principal directions of the 4-dimensional error ellipsoid, and the eigenvalues are the squares of the semi-axes. The additional part from individual satellites has only one eigenvector and one eigenvalue. This makes the error ellipsoid enlarge mainly along a direction related to both the overall satellite geometry and the position of the specific satellites. The theory is validated by simulating the GPS constellation and pseudorange measurements. The random positioning error is examined while any one or more pseudorange errors are increased. Horizontal positioning error distributions are presented to demonstrate the variations of the orientation and size of the error ellipses with the pseudorange error of a specific satellite. The results show that the analytical formula describes the positioning error accurately.     

On weighted total least-squares adjustment for linear regression

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.     

Atmospheric turbulence theory applied to GPS carrier-phase data

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.     

Evaluation of the accuracy of the EIGEN-1S and -2 CHAMP-derived gravity field models by satellite crossover altimetry

Since the advent of CHAMP, the first in a series of low-altitude satellites being almost continuously and precisely tracked by GPS, a new generation of long-wavelength gravitational geopotential models can be derived. The accuracy evaluation of these models depends to a large extent on the comparison with external data of comparable quality. Here, two CHAMP-derived models, EIGEN-1S and EIGEN-2, are tested with independent long-term-averaged single satellite crossover (SSC) sea heights from three altimetric satellites (ERS-1, ERS-2 and Geosat). The analyses show that long-term averages of crossover residuals still are powerful data to test CHAMP gravity field models. The new models are tested in the spatial domain with the aid of ERS-1/-2 and Geosat SSCs, and in the spectral domain with latitude-lumped coefficient (LLC) corrections derived from the SSCs. The LLC corrections allow a representation of the satellite-orbit-specific error spectra per order of the models spherical harmonic coefficients. These observed LLC corrections are compared to the LLC projections from the models variance–covariance matrix. The excessively large LLC errors at order 2 found in the case of EIGEN-2 with the ERS data are discussed. The degree-dependent scaling factors for the variance-covariance matrices of EIGEN-1S and –2, applied to obtain more realistic error estimates of the solved-for coefficients, are compatible with the results found here.     

A closed-form formula for GPS GDOP computation

Geometric dilution of precision (GDOP) is often used for selecting good satellites to meet the desired positioning precision. An efficient closed-form formula for GDOP has been developed when exactly four satellites are used. It has been proved that increasing the number of satellites for positioning will always reduce the GDOP. Since most GPS receivers today can receive signals from more than four satellites, it is desirable to compute GDOP efficiently for the general case. Previous studies have partially solved this problem with artificial neural network (ANN). Though ANN is a powerful function approximation technique, it needs costly training and the trained model may not be applicable to data deviating too much from the training data. Using Newton’s identities from the theory of symmetric polynomials, this paper presents a simple closed-form formula for computing GDOP with the inputs used in previous studies. These inputs include traces of the measurement matrix and its second and third powers, and the determinant of the matrix.     

单频GPS快速定位中病态问题的解法研究

研究只利用少数历元GPS载波相位观测值进行快速定位时的新解法.在分析病态法矩阵结构特性的基础上,基于TIKHONOV正则化原理,提出一种选择正则化矩阵R的新方法,减弱法方程的病态性.与其他方法相比,新方法得到与模糊度准确值更接近的浮动解及其相应的均方误差矩阵.结合LAMBDA方法,用均方误差矩阵代替协方差阵确定模糊度的搜索范围,可准确快速地确定模糊度,最后得到基线向量的解.结合算例,将新解法与最小二乘估计、岭估计和截断奇异值法分别结合LAMBDA方法解算模糊度的结果进行比较分析,展示新解法的效果.     

Optimizing the Number of Double-Differenced Observations for GPS Networks in Support of Deformation Monitoring Applications

Deformation monitoring using GPS is usually carried out by installing and operating a local network of GPS receivers mounted on the deforming body, e. g., the flanks of a volcano. For continuous monitoring applications a near-real-time, epoch-by-epoch solution obtained from multi-baseline processing is desired in order to take into account between-baseline correlations and to detect movements over as short a period of time as possible. In the case of the volcano monitoring application, the sides of the volcano will block out part of the sky, hence the receivers are not likely to track a lot of satellites that are visible from all receiver stations at the same time. If the usual base-station/base-satellite approach is used in the baseline processing, only the common satellites are considered, resulting in the number of possible double-differenced observables being comparatively low; hence a ot of valuable information may be lost. The proposed method, based on the work by Saalfeld (1999), considers satellites that are visible from a small number of network stations only. Thus the number of independent double-differenced observables can be maximized in order to obtain a better solution. A numerical example is given that verifies the improved solutions that can be obtained using this data processing approach. ? 2001 John Wiley & Sons, Inc.     

Adaptive Kalman Filtering for INS/GPS

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     

Code and carrier phase based short baseline GPS positioning: computational aspects

A recursive least squares algorithm is presented for short baseline GPS positioning using both carrier phase and code measurements. We take advantage of the structure of the problem to make the algorithm computationally efficient and use orthogonal transformations to ensure that the algorithm is numerically reliable. Details are given for computing position estimates and error covariance matrices with possible satellite rising and setting. Real data test results suggest our algorithm is effective.This research was supported by NSERC of Canada Grant RGPIN217191–99, FCAR of Quebec Grant 2001-NC-66487, and NSERCGEOIDE Network Project ENV#14 for Xiao-Wen Chang, and by NSERC of Canada Grant RGPIN9236–01 for Christopher C. Paige.An erratum to this article can be found at     

Code and carrier phase based short baseline GPS positioning: computational aspects

A recursive least squares algorithm is presented for short baseline GPS positioning using both carrier phase and code measurements. We take advantage of the structure of the problem to make the algorithm computationally efficient and use orthogonal transformations to ensure that the algorithm is numerically reliable. Details are given for computing position estimates and error covariance matrices with possible satellite rising and setting. Real data test results suggest our algorithm is effective.This research was supported by NSERC of Canada Grant RGPIN217191–99, FCAR of Quebec Grant 2001-NC-66487, and NSERCGEOIDE Network Project ENV#14 for Xiao-Wen Chang, and by NSERC of Canada Grant RGPIN9236–01 for Christopher C. Paige.The online version of the original article can be found at     

Heading and Pitch Determination Using GPS/GLONASS

This article describes a single difference approach to estimate heading and pitch with a twin global positoning system (GPS)/GLONASS (GG) receiver system. Augmentation of GPS with GLONASS is not straightforward, however, because the latter system employs the frequency division multiple access technique to distinguish the signals form different satellites, rather than the code division multiple access technique used by GPS. The fact that each GLONASS signal has its own slightly different frequency makes the double difference (DD) of carrier phase observables no longer possible without modification. To get around this problem, the use of the between-receiver single difference (SD) of the carrier phase observables is proposed. In this case, however, receiver clock and other errors do not cancel out. The possibility of using a common external oscillator for the two receivers is explored. Remaining time and other biases are estimated using a low-pass averaging filter. The single difference integer ambiguities can then be resolved and the heading and pitch can be determined with a relatively good level of accuracy. Static and kinematic tests conducted with a pair of GPS/GLONASS receivers are used to validate the approach. Under reduced visibility, the combined GPS/GLONASS approach is shown to yield superior availability. ? 2000 John Wiley & Sons, Inc.     

北斗区域卫星导航系统定位性能的纬度效应

与全球定位系统（global positioning system,GPS）不同,北斗区域卫星导航系统（BeiDou navigation satellite system,BDS）采用了5颗地球静止轨道卫星、5颗倾斜地球同步轨道卫星和4颗中圆轨道卫星的混合星座,星座分布不均匀。特殊星座决定了不同纬度地区用户的可见卫星数量和观测几何结构存在明显差异,用户的导航定位性能存在明显的纬度效应。分别从理论模型和实际观测两个方面对不同纬度地区用户的可见卫星数目、观测几何结构和导航定位性能进行较全面分析,使用了多家厂商的接收机,在不同纬度地区进行了GPS、BDS以及两系统融合定位试验。结果表明,BDS定位性能存在明显的纬度效应,即定位精度随纬度升高而降低;GPS导航定位性能没有明显的纬度效应;BDS/GPS数据融合可以减弱纬度效应,提高导航定位服务的精度和可靠性。