Demonstration of sub-meter GPS orbit determination and 1.5 parts in 108 three-dimensional baseline accuracy

Differential tracking of theGPS satellites in high-earth orbit provides a powerful relative positioning capability, even when a relatively small continental U.S. fiducial tracking network is used with less than one-third of the fullGPS constellation. To demonstrate this capability, we have determined baselines of up to2000 km in North America by estimating high-accuracyGPS orbits and ground receiver positions simultaneously. The2000 km baselines agree with very long baseline interferometry(VLBI) solutions at the level of1.5 parts in10 ⁸ and showrms daily repeatability of0.3–2 parts in10 ⁸. The orbits determined for the most thoroughly trackedGPS satellites are accurate to better than1 m. GPS orbit accuracy was assessed from orbit predictions, comparisons with independent data sets, and the accuracy of the continental baselines determined along with the orbits. The bestGPS orbit strategies included data arcs of at least one week, process noise models for tropospheric fluctuations, estimation ofGPS solar pressure coefficients, and combined processing ofGPS carrier phase and pseudorange data. For data arcs of two weeks, constrained process noise models forGPS dynamic parameters significantly improved the solutions.     

华测GPS连续参考站系统(CORS)定位精度检测方法

CORS系统的定位精度和可靠性直接关系到系统的可用性和工程建设的安全性,因此必须对系统各个指标进行检测.本文介绍了用华测X60双频接收机作参考站接收机的CORS,对其常用的定位精度的四种检测方法:静态已知点检测方法、实时动态观测值与后处理结果比较的检测方法、固定基线长度相对检测方法和动态规则几何轨迹检测方法,进行了介绍.     

Stability of the determination of earth rotation parameters (ERP) from VLBI

The observations of theIRIS network are used to study the stability of the determination ofERP fromVLBI. It is concluded that the uncertainties in the initial values ofERP, the errors of other parameters and analyst noise are at the same level as the formal errors in the determination ofERP. The geometric effect on the determination ofERP is important and gives rise to systematic errors. The geometric effect on polar motion is greate than onUT1, and much greater for the continental network. The stability of the determination ofERP fromVLBI can be improved either by creating new stations at reasonable locations in a network or by creating new networks. At last a comparison is provided between the determinations ofERP from theIRIS andTEMPO networks.     

Singular value decomposition and cluster analysis as regression diagnostics tools for geodetic applications

It is well known that high-leverage observations significantly affect the estimation of parameters. In geodetic literature, mainly redundancy numbers are used for the detection of single high-leverage observations or of single redundant observations. In this paper a further objective method for the detection of groups of important and less important (and thus redundant) observations is developed. In addition, the parameters which are predominantly affected by these groups of observations are identified. This method thus complements other diagnostics tools, such as, e.g., multiple row diagnostics methods as described in statistical literature (see, e.g., Belsley et al. in Regression diagnostics: identifying influential data and sources of collinearity. Wiley, New York, 1980). The method proposed in this paper is based on geometric aspects of adjustment theory and uses the singular value decomposition of the design matrix of an adjustment problem together with cluster analysis methods for regression diagnostics. It can be applied to any geodetic adjustment problem and can be used for the detection of (groups of) observations that significantly affect the estimated parameters or that are of negligible impact. One of the advantages of the proposed method is the improvement of the reliability of observation plans and thus the reduction of the impact of individual observations (and outliers) on the estimated parameters. This is of particular importance for the very long baseline interferometry technique which serves as an application example of the regression diagnostics tool.     

Stochastic estimation of tropospheric path delays in global positioning system geodetic measurements

Water vapor radiometric (WVR) and surface meteorological (SM) measurements taken during three Global Positioning System (GPS) geodetic experiments are used to calculate process noise levels for random walk and first-order Gauss-Markov temporal models of tropospheric path delays. Entire wet and combined wet and dry zenith delays at each network site then are estimated simultaneously with the geodetic parameters without prior calibration. The path delays and corresponding baseline estimates are compared to those obtained with calibrated data and stochastic residual delays. In this manner, the marginal utility of a priori tropospheric calibration is assessed given the ability to estimate the path delays directly using only theGPS data. Estimation of total zenith path delays with appropriate random walk or Gauss-Markov models yields baseline repeatabilities of a few parts in 10⁸. This level of geodetic precision, and accuracy as suggested by analyses on collocated baselines estimated independently by very long baseline interferometry, is comparable to or better than that obtained after path delay calibration usingWVR and/orSM measurements. Results suggest thatGPS data alone have sufficient strength to resolve centimeter-level zenith path delay fluctuations over periods of a few minutes.     

Laser station coordinates and baselines from long-ARC and short-ARC analyses of starlette

Laser ranging to Starlette from April 1983 to April 1984 has been used to determine a coordinate set, UASC.ST1, of laser reference points for 18 tracking stations. The coordinates were derived by application of the least-squares data reduction procedure in a simultaneous solution along with geodynamic parameters for 49 near consecutive 5–6 day arcs. Comparisons with the University of Texas station coordinates,LSC 8112 andLSC 8402, and theRGO, Herstmonceux, coordinates,RGOSC.LG2, reveal consistency to near 30 cm in each coordinate. Furthermore, the translation vectors of the comparisons are not significantly different from zero indicating consistency in the implied origins of the systems. The period of analysis included seven occasions in which STARLETTE was tracked near simultaneously by three or four laser stations in North America. Using the short arcs as reference frameworks, station coordinates were determined by application of two contrasting methods, namely, a multi-arc simultaneous analysis and a weighted mean of the individual pass solutions. The former compared more favourably with baselines from the long-arc solution with anRMS error of near 16 cm. Comparison against theLSC 8402 coordinates confirmed that baselines accurate to within 15 cm can be achieved by satellite laser ranging to Starlette.     

GPS连续参考站系统（CORS）定位精度检测方法

CORS系统的定位精度和可靠性直接关系到系统的可用性和工程建设的安全性,因此必须对系统各个指标进行检测。本文介绍了对CORS常用的定位精度的检测方法：静态已知点检测方法、实时动态观测值与后处理结果比较的检测方法、动态规则几何轨迹检测方法和固定基线长度相对检测方法。     

A demonstration of 1–2 parts in 107 accuracy using GPS

By interferometric analysis ofGPS phase observations made at Owens Valley, Mojave, and Mammoth Lakes, California, we determined the coordinate components of the71–245–313 km triangle of baselines connecting these sites. A separate determination was made on each of four days, April 1–4, 1985. The satellite ephemerides used in these determinations had been derived from observations on other baselines. Therms scatters of the four daily determinations of baseline vector components about their respective means ranged from a minimum of6 mm for the north component of the71-km baseline to a maximum of34 mm for the vertical component of the245-km baseline. To test accuracy, we compared the mean of ourGPS determinations of the245-km baseline between Owens Valley and Mojave with independent determinations by others using very-long-baseline interferometry(VLBI) and satellite laser ranging(SLR). TheGPS-VLBI difference was within 2 parts in10 ⁷ for every vector component. TheGPS-SLR difference was within6 parts in10 ⁸ in the horizontal coordinates, but83 mm in height.     

Approximate representation of thep-norm distribution

［1］Liu D J,Shi W Z,Tong X H,et al.Precision analysis and quality cont rol of GIS spatial data.Shanghai:Shanghai Publishing House of Scientific Documen ts,1999 ［2］Chen X R,Fang Z B,Li G Y,et al.Non_parameter statistics.S hanghai:Shanghai Publishing House of Science and Technology,1989 ［3］Li Q H,Tao B Z.Application of probability statistical theory in survey ing.Beijing:Beijing Publishing House of Surveying and Mapping,1982 ［4］Sun H Y.p_norm distribution theory and its application in surveyin g data processing:[Ph.D Thesis].Wuhan:Wuhan Technical University of Surveying and Mapping,1995     

SE‐KGE: A location‐aware Knowledge Graph Embedding model for Geographic Question Answering and Spatial Semantic Lifting

Learning knowledge graph (KG) embeddings is an emerging technique for a variety of downstream tasks such as summarization, link prediction, information retrieval, and question answering. However, most existing KG embedding models neglect space and, therefore, do not perform well when applied to (geo)spatial data and tasks. Most models that do consider space primarily rely on some notions of distance. These models suffer from higher computational complexity during training while still losing information beyond the relative distance between entities. In this work, we propose a location‐aware KG embedding model called SE‐KGE. It directly encodes spatial information such as point coordinates or bounding boxes of geographic entities into the KG embedding space. The resulting model is capable of handling different types of spatial reasoning. We also construct a geographic knowledge graph as well as a set of geographic query–answer pairs called DBGeo to evaluate the performance of SE‐KGE in comparison to multiple baselines. Evaluation results show that SE‐KGE outperforms these baselines on the DBGeo data set for the geographic logic query answering task. This demonstrates the effectiveness of our spatially‐explicit model and the importance of considering the scale of different geographic entities. Finally, we introduce a novel downstream task called spatial semantic lifting which links an arbitrary location in the study area to entities in the KG via some relations. Evaluation on DBGeo shows that our model outperforms the baseline by a substantial margin.     

Triple-frequency carrier ambiguity resolution for Beidou navigation satellite system

The Chinese Beidou system, also known as Compass, has entered its trial operational stage and can already provide services for triple-frequency users. Using triple-frequency signals is expected to be of great benefit for ambiguity resolution. Based on error characteristic analysis of the Beidou frequencies, we introduce the procedure of selecting the best combinations of triple-frequency signals. The geometry-based model and geometry-free model of triple-frequency signals are presented. Three triple-frequency carrier ambiguity resolution (TCAR) methods are described, which include the cascading rounding method, the stepwise AR method and the modified stepwise AR method. In order to evaluate the performance of these methods, observations from baselines of various lengths were collected using Beidou triple-frequency receivers and were processed epoch-by-epoch using the three methods. The same observation data were also processed in a dual-frequency mode for comparison. The results show that, compared to the dual-frequency based solution, the single epoch ambiguity resolution success rate with triple frequency improved nearly 30 % for the short baselines (<20 km) and 100 % for the mid-length baselines (20–50 km) using the proposed modified stepwise AR method.     

GPS监测网数据质量分析

为保证GPS监测网络满足监测精度要求，本文提出了GPS外业数据采集，基线解算应采取的措施及数据处理方法，并对两期观测数据及处理结果进行质量分析，以保证变形分析的可靠性。     

Regional geopotential model improvement for the Iranian geoid determination

Spherical harmonic expansions of the geopotential are frequently used for modelling the earth’s gravity field. Degree and order of recently available models go up to 360, corresponding to a resolution of about50 km. Thus, the high degree potential coefficients can be verified nowadays even by locally distributed sets of terrestrial gravity anomalies. These verifications are important when combining the short wavelength model impact, e.g. for regional geoid determinations by means of collocation solutions. A method based on integral formulae is presented, enabling the improvement of geopotential models with respect to non-global distributed gravity anomalies. To illustrate the foregoing, geoid computations are carried out for the area of Iran, introducing theGPM2 geopotential model in combination with available regional gravity data. The accuracy of the geoid determination is estimated from a comparison with Doppler and levelling data to ±1.4m.     

Monitoring selective availability dither frequencies and their effect on GPS data

Summary The signals transmitted by Block II satellites of the Global Positioning System (GPS) can be degraded to limit the highest accuracy of the system (10 m or better point positioning) to authorized users. This mode of degraded operation is called Selective Availability (S/A). S/A involves the degradation in the quality of broadcast orbits and satellite clock dithering. We monitored the dithered satellite oscillator and investigated the effect of this clock dithering on high accuracy relative positioning. The effect was studied over short 3-meter and zero-baselines with two GPS receivers. The equivalent S/A effects for baselines ranging from 0 to >10,000 km can be examined with short test baselines if the receiver clocks are deliberately mis-synchronized by a known and varying amount. Our results show that the maximum effect of satellite clock dithering on GPS double difference phase residuals grows as a function of the clock synchronization error according to: S/A _effect =0.04 cm/msec, and it increases as a function of baseline length like: S/A _effect =0.014 cm/100 km. These are equations for maximum observed values of post-fit residuals due to S/A. The effect on GPS baselines is likely to be smaller than the 0.14 mm for a baseline separation of 100 km. We therefore conclude, for our limited data set, and for the level of S/A during our tests, that S/A clock dithering has negligible effect on all terrestrial GPS baselines if double difference processing techniques are employed and if the GPS receivers remain synchronized to better than 10 msec. S/A may constitute a problem, however, if accurate point processing is required, or if GPS receivers are not synchronized. We suggest and test two different methods to monitor satellite frequency offsets due to S/A. S/A modulates GPS carrier frequencies in the range of-2 Hz to +2 Hz over time periods of several minutes. The methods used in this paper to measure the satellite clock dither could be applied by the civilian GPS community to continuously monitor S/A clock dithering. The monitored frequencies may aid high accuracy point positioning applications in a postprocessing mode (Malys and Ortiz 1989), and differential GPS with poorly synchronized receivers (Feigl et al. 1991).     

External atmospheric corrections in geodetic very-long-baseline interferometry

Three methods to correct for the atmospheric propagation delay in very-long-baseline interferometry (VLBI) measurements were investigated. In the analysis, the NASA R&D experiments from January 1993 to June 1995 were used. The methods were compared in correcting for the excess propagation delay due to water vapour, the “wet” delay, at one of the sites, the Onsala Space Observatory on the west coast of Sweden. The three methods were: (1) estimating the wet delay using the VLBI data themselves; (2) inferring the wet delay from water vapour radiometer (WVR) data, and (3) using independent estimates based on data from the global positioning system (GPS). Optimum elevation cutoff angles were 22^∘ and 26^∘ when using WVR and GPS data, respectively. The results were found to be similar in terms of reproducibility of the estimated baseline lengths. The shortest baselines tend to benefit from external measurements, whereas the lack of improvement in the longer baselines may be partly due to the large amount of data thrown away when removing observations at low elevation angles. Over a 2 week period of intensive measurements, the two methods using external data showed an overall improvement, for all baseline lengths, compared to the first method. This indicates that there are long-term systematic errors in the wet delay data estimated using WVR and GPS data. Received: 27 October 1998 / Accepted: 20 May 1999     

Probability distribution of eigenspectra and eigendirections of a twodimensional,symmetric rank two random tensor

Let there be given a twodimensional symmetric rank two tensor of random type (examples:strain, stress) which is either directly observed or indirectly estimated from observations by an adjustment procedure. Under the assumption of normalityof tensor components we compute the joint probability density functionas well as the marginal probability density functionsof its eigenspectra (eigenvalues) and eigendirections (orientation parameters). Due to the nonlinearity of the relation between eigenspectra-eigendirections and the random tensor components, via the inverse nonlinear error propagationbiases and aliases of their first and centralized second moments (mean value, variance-covariance) are expressed in terms of Jacobianand Hessianmatrices. The joint probability density function and the first and second moments thus form the fundamental of hypothesis testing and qualify control of eigenspectra (eigenvalues, principal components) and eigendirections (orientation parameters, eigenvectors, principial direction) of a twodimensional, symmetric rank two random tensor.     

空间碎片轨道协方差传播及其动态校正

轨道误差传播研究在空间碰撞风险分析、任务规划等空间态势感知领域具有重要作用。轨道误差常用误差协方差矩阵表达,其传播方式主要有线性传播模型与非线性传播模型两种。线性传播模型通过状态转移矩阵外推初始协方差矩阵,计算快速,但因将高度非线性化的轨道动力学问题线性化描述,导致传播精度随时间快速降低。非线性传播模型精度高但计算慢,难以进行大规模碎片群的轨道误差传播。在轨道误差传播特性分析的基础上,提出了一种获得较为真实的空间碎片轨道预报误差的方法,分3步进行:初始协方差矩阵的构建、初始轨道协方差线性传播以及基于实测数据对轨道预报协方差的动态校正。经大量案例统计分析,结果表明,校正后的轨道预报协方差,相较于线性传播结果,精度提高了60%以上,可服务于空间碰撞风险分析等高精度空间任务。     

Performance analysis of triple-frequency ambiguity resolution with BeiDou observations

We investigate triple-frequency ambiguity resolution performance using real BeiDou data. We test four ambiguity resolution (AR) methods which are applicable to triple-frequency observations. These are least squares ambiguity decorrelation adjustment (LAMBDA), GF-TCAR (geometry-free three-carrier ambiguity resolution), GB-TCAR (geometry-based three-carrier ambiguity resolution) and GIF-TCAR (three-carrier ambiguity resolution based on the geometry-free and ionospheric-free combination). A comparison between LAMBDA, GF-TCAR and GB-TCAR was conducted over three short baselines and two medium baselines. The results indicated that LAMBDA is optimal in both short baseline and medium baseline cases. However, the performances of GB-TCAR and LAMBDA differ slightly for short baselines. Compared with GF-TCAR, which uses the geometry-free model, the GB-TCAR using the geometry-based model improves the AR performance significantly. Compared with dual-frequency observations, the LAMBDA AR results show a significant improvement when using triple-frequency observations over short baselines. The performance of GIF-TCAR is evaluated using multi-epoch observations. The results indicated that multi-path errors on carrier phases will have a significant influence on GIF-TCAR AR results, which leads to different GIF-TCAR AR performance for different type of satellites. For GEO (Geostationary Orbit) satellites, the ambiguities can barely be correctly fixed because the multi-path errors on carrier phases are very systematic. For IGSO (Inclined Geosynchronous Orbit) and MEO (Medium Earth Orbit) satellites, when the elevation cutoff angle is set as 30°, several tens to several hundreds of epochs are needed for correctly fixing the narrow lane ambiguities. The comparison of positioning performance between dual-frequency observations and triple-frequency observations was also conducted. The results indicated that a minor improvement can be achieved by using triple-frequency observations compared with using dual-frequency observations.     

An investigation into the correlations among GNSS observations and their impact on height and zenith wet delay estimation for medium and long baselines

Most stochastic modelling techniques neglect the correlations among the raw un-differenced observations when forming the variance–covariance matrix of the Global Navigation Satellite System (GNSS) observations. Some methods were developed to model these correlations. One such method is the Minimum Norm Quadratic Unbiased Estimator (MINQUE). Studies have shown that MINQUE improves ambiguity resolution, and ultimately, the positioning solution in short baselines. However, its effect in cases of processing with longer baselines and on the estimation of zenith wet delay (ZWD) is somewhat unknown. In this paper, a comparison between the impact of neglecting the correlations among the observations using an elevation-angle-dependent model (EADM) and modelling the correlations using MINQUE on height determination and ZWD for medium and long baselines is carried out. The initial testing was carried out across two Australian GNSS stations with a medium-length baseline throughout a three-week campaign. The results showed that using MINQUE did not resolve the coordinate, height and wet delay components as accurately as the EADM. The results were further verified with two long-baseline campaigns whereby EADM was also able to provide better wet delay estimates. The coordinate results were, however, mixed. Overall, the study concluded that the inclusion of the correlations among the observations, in general, do not improve the resolution of the coordinate and wet delay estimates.