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.     

Accuracy analysis for the NAD 83 geodetic reference system

The North American Datum of 1983 (NAD 83) provides horizontal coordinates for more than 250,000 geodetic stations. These coordinates were derived by a least squares adjustment of existing terrestrial and space-based geodetic data. For pairs of first order stations with interstation distances between 10km and 100km, therms discrepancy between distances derived fromNAD 83 coordinates and distances derived from independentGPS data may be suitably approximated by the empirical rulee=0.008 K^0.7 where e denotes therms discrepancy in meters and K denotes interstation distance in kilometers. For the same station pairs, therms discrepancy in azimuth may be approximated by the empirical rule e=0.020 K^0.5. Similar formulas characterize therms discrepancies for pairs involving second and third order stations. Distance and orientation accuracies, moreover, are well within adopted standards. While these expressions indicate that the magnitudes of relative positional accuracies depend on station order, absolute positional accuracies are similar in magnitude for first, second, and third order stations. Adjustment residuals reveal a few local problems with theNAD 83 coordinates and with the weights assigned to certain classes of observations.     

A unified scheme for processing GPS dual-band phase observations

A unified computational scheme is presented for sequential least-squares processing ofGPS dual-band carrier-beat-phase observations in network-mode positioning with orbit relaxation, and in orbit determination applications. This scheme is applicable to any spatial and temporal distribution of stations and satellites during a particularGPS experiment. Full covariance matrices can be specified for carrier-beat-phases and for weighted constraints on the ionosphere in order to improve phase ambiguity resolution. Physically meaningful choices for these covariance matrices are developed.     

Global positioning system carrier phase: Description and use

After removing the modulation from the Global Positioning System (GPS) signal (L ₁ orL ₂) a pure carrier signal remains. Suppose this carrier is continuously and precisely tracked by aGPS receiver. Furthermore, suppose the phase of the carrier is periodically measured and recorded (nearly simultaneously at two or more locations) with respect to receiver oscillators having the same nominal frequency as theGPS carrier. This paper first considers alternative modeling and processing approaches to these observational data for static operations. Then an approach to dynamic relative positioning using triple differences is presented. This approach should lend itself to performing centimeter accuracy relative surveys in seconds rather than hours. An approach to fixing cycle slips, automatically, is included.     

Time-Relative Positioning with a Single Civil GPS Receiver

Time-relative positioning is a recent method for processing GPS phase observations. The operational method undertaken in this paper consists of the following steps: first, recording phase observations at a station of known coordinates; second, moving the GPS receiver to an unknown station (which can be located up to a few hundred meters away, dependint on what type of transportation – e. g., walking, motorcycle – is available) while continuously observing carrier phases; and, third, recording phase observations at a second station of unknown coordinates with a single GPS receiver. To obtain the position of the unknown station relative to the first (known) station, the processing method uses combined observations taken at two different epochs and two different stations with the same receiver. For this reason, the errors that vary between two epochs must be taken into account in an appropriate way, especially errors in satellite clock corrections and ephemerides, and errors related to tropospheric and ionospheric delays. Ionospheric modeling using IONEX files (the ionospheric maps calculated by the International GPS Service) was also tested to correct L1 phase observations. This method has been used to calculate short vectors with an accuracy of a few centimeters (for a processing interval of 30 s) using a single civil GPS receiver. ? 2001 John Wiley & Sons, Inc.     

Generating basis sets of double differences

When a collection of double differences is used to compute global-positioning-system satellite orbits from a permanent network of receiving stations, linear dependence among the double-differenced observations reduces the number of double differences that contribute new information to the computations. A maximal linearly independent subset of a large collection of double differences contains all the information content of the full set. If r is the number of receivers and s is the number of satellites, the original collection of double differences may have size O(r ² s ²), whereas the linearly independent subset has size no greater than O(rs). Only such a smaller independent subset needs to participate in the more expensive double-precision matrix computations to correctly correlate all double differences, detect cycle slips, resolve ambiguities, and compute satellite orbits and station positions and relative velocities. Dependence among double differences is characterized using vector space methods together with geometric characterizations of Boolean matrices. These characterizations lend themselves to fast, robust algorithms for computing maximal linearly independent sets (bases) of double differences. An algorithm is given for constructing a generating independent set of double differences from the Boolean array of receiving-station/satellite connections. Characterizations of generator equivalence allow alternative generating sets to be identified and selected. An updating algorithm to handle local changes in the satellite–receiver connection matrix is also described. Received: 27 August 1996 / Accepted: 28 January 1999     

Establishment of a 3-dimensional geodetic network using the MACROMETER IItm dual-band surveyor

Summary During July of 1985, Aero Service conducted aGPS research project over a900 square km area in the Sacramento Valley of California. The project was partially funded by the California Department of Water Resources and was coordinated with the Sacramento office of U.S.G.S. The survey was designed to evaluate the accuracy, efficiency, and reliability ofMACROMETER II technology, as an alternative to conventional leveling techniques, for the monitoring of land subsidence. Thirty independent baseline vectors were determined between21 pre-existing benchmark locations. The majority of baseline vectors measured approximately10 km in length and were observed in a highly productive mode of three,1-hour observations per day. Six baseline vectors ranging from34 to56 km in length were observed as single day, 3.5 hour observations. In all cases the integer values ofL ₁ andL ₂ double-differenced phase biases were determined. The relative positions of stations in the network were determined to within1 part per million(1 ppm) in both horizontal coordinates, and about1.6 ppm in the vertical. Operational aspects of the project are described. Project results are examined with emphasis on the added benefits of dual-frequency measurements; the repeatability of interferometric determinations of individual baseline vectors; and the three-dimensional vector closure of the networks as a whole.     

W0: an estimate in the Finnish Height Datum N60, epoch 1993.4, from twenty-five GPS points of the Baltic Sea Level Project

Based upon a data set of 25 points of the Baltic Sea Level Project, second campaign 1993.4, which are close to mareographic stations, described by (1) GPS derived Cartesian coordinates in the World Geodetic Reference System 1984 and (2) orthometric heights in the Finnish Height Datum N60, epoch 1993.4, we have computed the primary geodetic parameter W ₀(1993.4) for the epoch 1993.4 according to the following model. The Cartesian coordinates of the GPS stations have been converted into spheroidal coordinates. The gravity potential as the additive decomposition of the gravitational potential and the centrifugal potential has been computed for any GPS station in spheroidal coordinates, namely for a global spheroidal model of the gravitational potential field. For a global set of spheroidal harmonic coefficients a transformation of spherical harmonic coefficients into spheroidal harmonic coefficients has been implemented and applied to the global spherical model OSU 91A up to degree/order 360/360. The gravity potential with respect to a global spheroidal model of degree/order 360/360 has been finally transformed by means of the orthometric heights of the GPS stations with respect to the Finnish Height Datum N60, epoch 1993.4, in terms of the spheroidal “free-air” potential reduction in order to produce the spheroidal W ₀(1993.4) value. As a mean of those 25 W ₀(1993.4) data as well as a root mean square error estimation we computed W ₀(1993.4)=(6 263 685.58 ± 0.36) kgal × m. Finally a comparison of different W ₀ data with respect to a spherical harmonic global model and spheroidal harmonic global model of Somigliana-Pizetti type (level ellipsoid as a reference, degree/order 2/0) according to The Geodesist's Handbook 1992 has been made. Received: 7 November 1996 / Accepted: 27 March 1997     

A reference station-based GNSS computing mode to support unified precise point positioning and real-time kinematic services

Currently, the GNSS computing modes are of two classes: network-based data processing and user receiver-based processing. A GNSS reference receiver station essentially contributes raw measurement data in either the RINEX file format or as real-time data streams in the RTCM format. Very little computation is carried out by the reference station. The existing network-based processing modes, regardless of whether they are executed in real-time or post-processed modes, are centralised or sequential. This paper describes a distributed GNSS computing framework that incorporates three GNSS modes: reference station-based, user receiver-based and network-based data processing. Raw data streams from each GNSS reference receiver station are processed in a distributed manner, i.e., either at the station itself or at a hosting data server/processor, to generate station-based solutions, or reference receiver-specific parameters. These may include precise receiver clock, zenith tropospheric delay, differential code biases, ambiguity parameters, ionospheric delays, as well as line-of-sight information such as azimuth and elevation angles. Covariance information for estimated parameters may also be optionally provided. In such a mode the nearby precise point positioning (PPP) or real-time kinematic (RTK) users can directly use the corrections from all or some of the stations for real-time precise positioning via a data server. At the user receiver, PPP and RTK techniques are unified under the same observation models, and the distinction is how the user receiver software deals with corrections from the reference station solutions and the ambiguity estimation in the observation equations. Numerical tests demonstrate good convergence behaviour for differential code bias and ambiguity estimates derived individually with single reference stations. With station-based solutions from three reference stations within distances of 22–103 km the user receiver positioning results, with various schemes, show an accuracy improvement of the proposed station-augmented PPP and ambiguity-fixed PPP solutions with respect to the standard float PPP solutions without station augmentation and ambiguity resolutions. Overall, the proposed reference station-based GNSS computing mode can support PPP and RTK positioning services as a simpler alternative to the existing network-based RTK or regionally augmented PPP systems.     

Improvement of the GPS time comparisons by simultaneous relative positioning of the receiver antennas

The Global Positioning System,GPS, is widely used for time comparisons between distant laboratories. Over distances of the order of 1000km or less, the system has the capability of 1 to 2ns accuracy. However this requires a relative positioning with errors lower than 30cm. We show that this positioning can be derived from theGPS time comparisons themselves. An example for European laboratories is given.     

The terrestrial and lunar reference frame in lunar laser ranging

The initial value problem and the stability of solution in the determination of the coordinates of three observing stations and four retro-reflectors by lunar laser ranging are discussed. Practical iterative computations show that the station coordinates can be converged to about 1 cm, but there will be a slight discrepancy of the longitudinal components computed by various analysis centers or in different years. There are several factors, one of which is the shift of the right ascension of the Moon, caused by the orientation deviation of the adopted lunar ephemeris, which can make the longitudinal components of all observing stations rotate together along the longitudinal direction with same angle. Additionally, the frame of selenocentric coordinates is stable, but a variation or adjustment of lunar third-degree gravitational coefficients will cause a simultaneous shift along the reflectors' longitudes or rotation around the Y axis. Received: 21 August 1996 / Accepted: 17 November 1998     

Local geoid determination and comparison with GPS results

Ellipsoidal heights have been determined for a test network in Lower Saxony withGPS. TheGPS results, with a relative precision of a few centimeters, have been used to compute quasigeoid heights by substracting leveling heights. This data set is compared to mainly gravimetrically determined quasigeoid heights using least squares collocation techniques. The discrepancies between the two data sets amount to about ±2cm, the maximum interstation distance is about50 km. This agreement shows, thatGPS can be used in combination with gravity information to obtain normal heights withcm-precision.     

Network design strategies applicable to GPS surveys using three or four receivers

Strategies applicable to the design ofGPS surveys involving deployment of either three or four compatible receivers are presented. During aGPS observing session, the receivers operate simultaneously, producing three-dimensional cartesian coordinate differences for the lines interconnecting the receivers. Different strategies provide the network designer with several options for planning the survey. The designer may opt for a survey in which each mark is occupied three times, that is, during three separate observing sessions, or he may elect a more economical survey in which each mark is occupied only twice. The designer may also choose between two fundamentally different network geometries (a loop geometry or an areal geometry) to design a survey compatible with the spatial distribution of network marks. The strategies can be extended to other geometries. The strategies produce efficient networks in that no two marks are jointly occupied for more than one observing session. This feature produces the maximum number of distinct, directly observed lines for the given number of receivers and observing sessions. The strategies also favor observations over those lines connecting marks near one another. This feature helps survey logistics by reducing travel time between observing sessions.     

A review on the inter-frequency biases of GLONASS carrier-phase data

GLONASS ambiguity resolution (AR) between inhomogeneous stations requires correction of inter-frequency phase biases (IFPBs) (a “station” here is an integral ensemble of a receiver, an antenna, firmware, etc.). It has been elucidated that IFPBs as a linear function of channel numbers are not physical in nature, but actually originate in differential code-phase biases (DCPBs). Although IFPBs have been prevalently recognized, an unanswered question is whether IFPBs and DCPBs are equivalent in enabling GLONASS AR. Besides, general strategies for the DCPB estimation across a large network of heterogeneous stations are still under investigation within the GNSS community, such as whether one DCPB per receiver type (rather than individual stations) suffices, as tentatively suggested by the IGS (International GNSS Service), and what accuracy we are able to and ought to achieve for DCPB products. In this study, we review the concept of DCPBs and point out that IFPBs are only approximate derivations from DCPBs, and are potentially problematic if carrier-phase hardware biases differ by up to several millimeters across frequency channels. We further stress the station and observable specific properties of DCPBs which cannot be thoughtlessly ignored as conducted conventionally. With 212 days of data from 200 European stations, we estimated DCPBs per stations by resolving ionosphere-free ambiguities of \(\sim \)5.3 cm wavelengths, and compared them to the presumed truth benchmarks computed directly with L1 and L2 data on ultra-short baselines. On average, the accuracy of our DCPB products is around 0.7 ns in RMS. According to this uncertainty estimates, we could unambiguously confirm that DCPBs can typically differ substantially by up to 30 ns among receivers of identical types and over 10 ns across different observables. In contrast, a DCPB error of more than 6 ns will decrease the fixing rate of ionosphere-free ambiguities by over 20 %, due to their smallest frequency spacing and highest sensitivity to DCPB errors. Therefore, we suggest that (1) the rigorous DCPB model should be implemented instead of the classic, but inaccurate IFPB model; (2) DCPBs of sub-ns accuracy can be achieved over a large network by efficiently resolving ionosphere-free ambiguities; (3) DCPBs should be estimated and applied on account of their station and observable specific properties, especially for ambiguities of short wavelengths.     

Definition of a reconfigurable and modular multi-standard navigation receiver

The growth of innovative positioning-related services and applications within the wireless mass-market, and the green light for the development and modernization of Global Navigation Satellite Systems (GNSS) catalyze the research activity in the navigation field both at the system and user levels. In addition, different government institutions are working toward the definition of navigation plans and regulations which will require accurate locations of mobile users in case of emergency (US E-911 law and the European E-112 directive). From the technical standpoint, within every navigation/positioning system which will be available in the near future, the user terminal will play a central role. In fact, if navigation signals from different sources are available, the unique possibility to obtain the best navigation performance from the user perspective will be the employment of enhanced smart receivers able to fuse different data. With this aim, the Software Defined Radio (SDR) technology can be successfully employed for the design of innovative navigation receivers. The main goal of this paper is to present the overall SDR receiver architecture, focusing attention on reconfigurability and flexibility issues which are guaranteed by the use of reprogrammable high-speed hardware (FPGA–Field Programmable Gate Array and DSP–Digital Signal Processor). The direct benefit of such an implementation is the possibility to obtain a deep integration at the raw signal level between GPS and the future Galileo; the interoperability issue among different systems is then solved at the receiver level. Electronic Publication     

合肥市卫星定位连续运行基准站网融合改造的实践探讨

为了更好地服务于自然资源和规划,建立合肥市统一的卫星定位连续运行参考站(CORS)．针对当前合肥市三套卫星定位CORS独立运行、基准框架和服务标准不统一的问题,从基准站深度融合建设、系统软硬件升级、现有软硬件的兼容性、组网设计和CORS基准框架坐标联测与扩展服务的实践展开探讨. 综合运用了多种共享融合技术,通过外业实测验证方法的正确性和可行性,对城市CORS融合改造具有很好的借鉴意义.      

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.     

Determination of the earth rotation parameters from optical astrometry observations, 1962.0–1982.0

The optical astrometric data of the years 1962–1982 have been reduced once again at the Bureau International de l’Heure (BIH) in order to redetermine the Earth Rotation Parameters (ERP). This new reduction is based on serie largely revised by the stations since their use in the operational work of theBIH, and on some series which were not available previously. A total of 113 stations is considered, totaling nearly 500,000 measurements of time or latitude. TheERP are determined at five-day intervals. A new approach is developed: the catalog and local errors are analysed and corrected as group unknowns, which values are adjusted together with the main unknowns. The results obtained in the new reduction are compared to other series obtained by astrometry and space geodesy.     

Digital Signal Processors in GPS Receivers

Unlike the conventional hardware approaches to GPS base band signal processing, a software GPS receiver is extremely flexible as it comes with all the associated advantages of a software solution. With a software solution, the improvements of silicon technology can be easily translated into better performance at smaller form factors and lower power consumption, without a redesign and/or change to the ASIC. A general purpose Digital Signal Processor (DSP) can be used effectively for GPS signal processing. The memory and speed resources available determine the algorithms and applications that can be effectively implemented in the receiver. The performance of software GPS receivers will soon be difficult to be surpassed by the hardware counterparts, as high-performance processors become available at low cost. ? 2000 John Wiley & Sons, Inc.     

Defining the basic entities in a geodetic data base

The term “entity” covers, when used in the field of electronic data processing, the meaning of words like “thing”, “being”, “event”, or “concept”. Each entity is characterized by a set of properties. An information element is a triple consisting of an entity, a property and the value of a property. Geodetic information is sets of information elements with entities being related to geodesy. This information may be stored in the form ofdata and is called ageodetic data base provided (1) it contains or may contain all data necessary for the operations of a particular geodetic organization, (2) the data is stored in a form suited for many different applications and (3) that unnecessary duplications of data have been avoided. The first step to be taken when establishing a geodetic data base is described, namely the definition of the basic entities of the data base (such as trigonometric stations, astronomical stations, gravity stations, geodetic reference-system parameters, etc...). Presented at the “International Symposium on Optimization of Design and Computation of Control Networks”, Sopron, Hungary, July 1977.