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.     

An improvement to ionospheric delay correction for single-frequency GPS users – the APR-I scheme

 For the commonly used GPS wide-area augmentation systems (WAAS) with a grid ionospheric model, the efficient modelling of ionospheric delays in real time, for single-frequency GPS users, is still a crucial issue which needs further research. This is particularly necessary when differential ionospheric delay corrections cannot be broadcast, when users cannot receive them, or when there are ionospheric anomalies. Ionospheric delays have a severe effect on navigation performance of single-frequency receivers. A new scheme is proposed which can efficiently address the above problems. The robust recurrence technique is based on the efficient combination of single-frequency GPS observations by users and the high-precision differential ionospheric delay corrections from WAAS. Its effectiveness is verified with examples. Received: 24 December 1999 / Accepted 21 February 2001     

GPS-assisted GLONASS orbit determination

 Using 1 week of data from a network of GPS/GLONASS dual-tracking receivers, 15-cm accurate GLONASS orbit determination is demonstrated with an approach that combines GPS and GLONASS data. GPS data are used to define the reference frame, synchronize receiver clocks and determine troposphere delay for the GLONASS tracking network. GLONASS tracking data are then processed separately, with the GPS-defined parameters held fixed, to determine the GLONASS orbit. The quality of the GLONASS orbit determination is currently limited by the size and distribution of the tracking network, and by the unavailability of a sufficiently refined solar pressure model. Temporal variations in the differential clock bias of the dual-tracking receivers are found to have secondary impact on the orbit determination accuracy. Received: 5 January 2000 / Accepted: 15 February 2001     

GPS vector configuration design for monitoring deformation networks

 The performance of geodetic monitoring networks is heavily influenced by the configuration of the measured GPS vectors. As an effective design of the GPS measurements will decrease GPS campaign costs and increase the accuracy and reliability of the entire network, the identification of the preferred GPS vectors for measurement has been highlighted as a core problem in the process of deformation monitoring. An algorithm based on a sensitivity analysis of the network, as dependent upon a postulated velocity field, is suggested for the selection of the optimal GPS vectors. Relevant mathematical and statistical concepts are presented as the basis for an improved method of vector configuration design. A sensitivity analysis of the geodetic geodynamic network in the north of Israel is presented, where the method is examined against two deformation models, the Simple Transform Fault and the Locked Fault. The proposed method is suggested as a means for the improvement of the design of monitoring networks, a common practice worldwide. Received: 30 July 2001 / Accepted: 3 June 2002 Acknowledgments. It is my pleasant duty to thank the Survey of Israel and Dr. E. Ostrovsky for providing the variance–covariance matrix of the G1 network in northern Israel. I would like to thank the reviewers of this paper for their constructive and helpful remarks.     

An Artificial Intelligent design for GPS Surveying Networks

Metaheuristic techniques, which are based on ideas of Artificial Intelligence, are among the best methods for solving computationally the GPS surveying network problem. In this paper, the ant colony optimization metaheuristic, which is inspired by the behavior of real ant colonies, is developed to efficiently provide a general framework for optimizing GPS surveying networks. In this framework, a set of ants co-operate together using an indirect communication procedure to find good GPS observation schedules. A GPS surveying network can be defined as a set of stations, co-ordinated by a series of sessions formed by placing receivers on the stations. The problem is to search for the best order in which to observe these sessions to give the best schedule at minimum cost. Computational results obtained by applying the proposed technique on several networks, with known and unknown optimal schedules, prove the effectiveness of the proposed metaheuristic technique to solve the GPS surveying network problem.     

The northern European geoid: a case study on long-wavelength geoid errors

 The long-wavelength geoid errors on large-scale geoid solutions, and the use of modified kernels to mitigate these effects, are studied. The geoid around the Nordic area, from Greenland to the Ural mountains, is considered. The effect of including additional gravity data around the Nordic/Baltic land area, originating from both marine, satellite and ground-based measurements, is studied. It is found that additional data appear to increase the noise level in computations, indicating the presence of systematic errors. Therefore, the Wong–Gore modification to the Stokes kernel is applied. This method of removing lower-order terms in the Stokes kernel appears to improve the geoid. The best fit to the global positioning system (GPS) leveling points is obtained with a degree of modification of approximately 30. In addition to the study of modification errors, the results of different methods of combining satellite altimetry gravity and other gravimetry are presented. They all gave comparable results, at the 6-cm level, when evaluated for the Nordic GPS networks. One dimensional (1-D) and 2-D fast Fourier transform (FFT) methods are also compared. It is shown that even though methods differ by up to 6 cm, the fit to the GPS is essentially the same. A surprising conclusion is that the addition of more data does not always produce a better geoid, illustrating the danger of systematic errors in data. Received: 4 July 2001 / Accepted: 21 February 2002     

Combined processing of the IGS and the IGEX network

 Since the beginning of the International Global Navigation Satellite System (GLONASS) Experiment, IGEX, in October 1998, the Center for Orbit Determination in Europe (CODE) has acted as an analysis center providing precise GLONASS orbits on a regular basis. In CODE's IGEX routine analysis the Global Positioning System (GPS) orbits and Earth rotation parameters are introduced as known quantities into the GLONASS processing. A new approach is studied, where data from the IGEX network are combined with GPS observations from the International GPS Service (IGS) network and all parameters (GPS and GLONASS orbits, Earth rotation parameters, and site coordinates) are estimated in one processing step. The influence of different solar radiation pressure parameterizations on the GLONASS orbits is studied using different parameter subsets of the extended CODE orbit model. Parameterization with three constant terms in the three orthogonal directions, D, Y, and X (D = direction satellite–Sun, Y = direction of the satellite's solar panel axis), and two periodic terms in the X-direction, proves to be adequate for GLONASS satellites. As a result of the processing it is found that the solar radiation pressure effect for the GLONASS satellites is significantly different in the Y-direction from that for the GPS satellites, and an extensive analysis is carried out to investigate the effect in detail. SLR observations from the ILRS network are used as an independent check on the quality of the GLONASS orbital solutions. Both processing aspects, combining the two networks and changing the orbit parameterization, significantly improve the quality of the determined GLONASS orbits compared to the orbits stemming from CODE's IGEX routine processing. Received: 10 May 2000 / Accepted: 9 October 2000     

GPS precision as a function of session duration and reference frame using multi-point software

As an aid to survey design, we used data acquired from three European continuous GPS networks to test the precision of position estimates from static observations as a function of the length of the observing session and the number and distribution of reference stations. Our criterion was the weighted RMS of estimates over 31 days with respect to coordinates determined from 24-h sessions over a 2-year period. With a single reference station, a precision of 3 mm horizontal and 10 mm vertical could be achieved reliably only for session lengths of 3 h or longer and baselines less than 200 km. If four or more reference stations are used, these levels of precision were usually achieved with sessions as short as 2 h. With sessions 6 h or longer and four or more reference stations, the precision is typically 1–2 mm in horizontal and about 3–5 mm in vertical. Increasing the number of reference stations further provides only marginal improvement. Although there is some variation in precision in 4-station networks with the choice of reference stations, the dependence on distance and geometric distribution is weak.     

Local geoid determination combining gravity disturbances and GPS/levelling: a case study in the Lake Nasser area, Aswan, Egypt

 The use of GPS for height control in an area with existing levelling data requires the determination of a local geoid and the bias between the local levelling datum and the one implicitly defined when computing the local geoid. If only scarse gravity data are available, the heights of new data may be collected rapidly by determining the ellipsoidal height by GPS and not using orthometric heights. Hence the geoid determination has to be based on gravity disturbances contingently combined with gravity anomalies. Furthermore, existing GPS/levelling data may also be used in the geoid determination if a suitable general gravity field modelling method (such as least-squares collocation, LSC) is applied. A comparison has been made in the Aswan Dam area between geoids determined using fast Fourier transform (FFT) with gravity disturbances exclusively and LSC using only the gravity disturbances and the disturbances combined with GPS/levelling data. The EGM96 spherical harmonic model was in all cases used in a remove–restore mode. A total of 198 gravity disturbances spaced approximately 3 km apart were used, as well as 35 GPS/levelling points in the vicinity and on the Aswan Dam. No data on the Nasser Lake were available. This gave difficulties when using FFT, which requires the use of gridded data. When using exclusively the gravity disturbances, the agreement between the GPS/levelling data were 0.71 ± 0.17 m for FFT and 0.63 ± 0.15 for LSC. When combining gravity disturbances and GPS/levelling, the LSC error estimate was ±0.10 m. In the latter case two bias parameters had to be introduced to account for a possible levelling datum difference between the levelling on the dam and that on the adjacent roads. Received: 14 August 2000 / Accepted: 28 February 2001     

How to handle topography in practical geoid determination: three examples

 Three different methods of handling topography in geoid determination were investigated. The first two methods employ the residual terrain model (RTM) remove–restore technique, yielding the quasigeoid, whereas the third method uses the classical Helmert condensation method, yielding the geoid. All three methods were used with the geopotential model Earth Gravity Model (1996) (EGM96) as a reference, and the results were compared to precise global positioning system (GPS) levelling networks in Scandinavia. An investigation of the Helmert method, focusing on the different types of indirect effects and their effects on the geoid, was also carried out. The three different methods used produce almost identical results at the 5-cm level, when compared to the GPS levelling networks. However, small systematic differences existed. Received: 18 March 1999 / Accepted: 21 March 2000     

Confidence regions for GPS baselines by Bayesian statistics

 The global positioning system (GPS) model is distinctive in the way that the unknown parameters are not only real-valued, the baseline coordinates, but also integers, the phase ambiguities. The GPS model therefore leads to a mixed integer–real-valued estimation problem. Common solutions are the float solution, which ignores the ambiguities being integers, or the fixed solution, where the ambiguities are estimated as integers and then are fixed. Confidence regions, so-called HPD (highest posterior density) regions, for the GPS baselines are derived by Bayesian statistics. They take care of the integer character of the phase ambiguities but still consider them as unknown parameters. Estimating these confidence regions leads to a numerical integration problem which is solved by Monte Carlo methods. This is computationally expensive so that approximations of the confidence regions are also developed. In an example it is shown that for a high confidence level the confidence region consists of more than one region. Received: 1 February 2001 / Accepted: 18 July 2001     

Multi-level arc combination with stochastic parameters

 The method of square root information filtering and smoothing (SRIF/S) is reviewed and has been implemented in the combined square root information filter and smoother (CSRIFS) program. CSRIFS is a part of the GEOSAT space geodesy software developed at Forsvarets forskningsinstitutt (FFI, The Norwegian Defence Research Establishment). The state vectors and complete variance–covariance matrices from the analyses of a number of independent arcs of space geodesy data can be combined using CSRIFS. Four parameter levels are available and any parameter can, at each level, be represented as either a constant or a stochastic parameter (white noise, colored noise, or random walk). The batch length (i.e. the time interval between the addition of noise to the SRIF array) can be made time and parameter dependent. CSRIFS was applied in the combination of 623 very long baseline interferometry (VLBI) observing sessions. The purpose of this test was to validate the computer implementation of the SRIF/S method and to give an example of how this method can be used in the analysis of a large number of space geodetic observations. The results show that the implementation is very satisfactory. Received: 28 May 1999 / Accepted: 15 June 2000     

Precise estimation of residual tropospheric delays using a regional GPS network for real-time kinematic applications

 A new method called Trop_NetAdjust is described to predict in real time the residual tropospheric delays on the GPS carrier phase observables using the redundant measurements from a network of GPS reference stations. This method can not only enhance the effectiveness and reliability of real-time kinematic users within the network, but also provide a valid approach to tropospheric parameter variation forecasting. Trop_NetAdjust is theoretically based upon LS prediction criteria and enables the prediction of residual tropospheric delays remaining after a standard model has been applied to the raw GPS measurements. Two cases are analyzed, namely a first case when the delay is required for an existing satellite at a new point within the network and a second case when the delay is required for a new satellite. Field tests were conducted using data collected in a network of 11 reference stations covering a 400×600 km region in southern Norway. The results were analyzed in the measurement domain (ionospheric-free double-difference residuals) and showed improvements of 20 to 65% RMS errors using Trop_NetAdjust. The estimates of the Trop_NetAdjust prediction accuracy were also obtained using the covariance analysis method. The agreement was consistently better than 30% when compared with data from a real network. Received: 28 February 2000 / Accepted: 9 January 2001     

Comparison of baseline results for the TI-4100 and Trimble 4000SDT geodetic GPS receivers

Summary Many GPS networks which were initially surveyed with Texas Instruments TI-4100 receivers have now been resurveyed with mixtures of TI-4100 and Trimble 4000 receivers or exclusively with Trimble receivers. In order to make confident tectonic interpretation of displacements observed between such surveys, it is necessary to understand any biases which may be introduced by using different receiver types or by mixing receivers within a network. Therefore, one of the primary objectives of the Ecuador 1990 GPS campaign (February 1990) was to provide a direct long baseline comparison between the TI-4100 and Trimble 4000SDT GPS receivers. p ]During this campaign, TI and Trimble receivers were co-located at each end of a 1323 kilometer baseline (Jerusalen to Baltra). Solutions for this baseline show no variation with receiver type. Zero-length baseline solutions showed no evidence for any intrinsic bias caused by mixing the two receiver types. Short baseline solutions indicate a bias of -34±10 mm in the baseline vertical component; the sign of the bias indicates that either the assumed phase center location for the TI is too low or the assumed location for the Trimble is too high. The bias is explainable if the phase centers of the Trimble SDT and SST antennas are similarly located. p ]Solutions for baselines measured with codeless receivers (such as the Trimble) should be as precise as those for baselines measured with P-code receivers (such as the TI) as long as it is possible to resolve ambiguities. Resolution of the widelane ambiguity is the limiting factor in ambiguity resolution with any codeless receiver, and in the February 1990 campaigns it was not successful fore baselines longer than 100 km. Without explicit modeling of the ionospheric effect on the widelane, ambiguity resolution with codeless receivers will not be successful for baselines longer than about 100 km, depending on the local ionospheric conditions.     

Analysis of the first year of Earth rotation parameters with a sub-daily resolution gained at the CODE processing center of the IGS

 The solutions of the CODE Analysis Center submitted to the IGS, the International Global Position System (GPS) Service for Geodynamics, are based on three days of observation of about 80–100 stations of the IGS network. The Earth rotation parameters (ERPs) are assumed to vary linearly over the three days with respect to an a priori model. Continuity at the day boundaries as well as the continuity of the first derivatives are enforced by constraints. Since early April 1995 CODE has calculated a new ERP series with an increased time resolution of 2 hours. Again continuity is enforced at the 2-hours-interval boundaries. The analysis method is described, particularly how to deal with retrograde diurnal terms in the ERP series which may not be estimated with satellite geodetic methods. The results obtained from the first year of data covered by the time series (time interval from 4 April 1995 to 30 June 1996) are also discussed. The series is relatively homogeneous in the sense of the used orbit model and the a priori model for the ERPs. The largest source of excitation at daily and sub-daily periods is likely to be the effect of the ocean tides. There is good agreement between the present results and Topex/Poseidon ocean tide models, as well as with models based on Very Long Baseline Interferometry (VLBI) and Satellite Laser Ranging (SLR) data. Non-oceanic periodic variations are also observed in the series. Their origin is most probably a consequence of the GPS solution strategy; other possible sources are the atmospheric tides. Received: 13 July 1999 / Accepted: 21 March 2000     

Stochastic assessment of GPS carrier phase measurements for precise static relative positioning

 Global positioning system (GPS) carrier phase measurements are used in all precise static relative positioning applications. The GPS carrier phase measurements are generally processed using the least-squares method, for which both functional and stochastic models need to be carefully defined. Whilst the functional model for precise GPS positioning is well documented in the literature, realistic stochastic modelling for the GPS carrier phase measurements is still both a controversial topic and a difficult task to accomplish in practice. The common practice of assuming that the raw GPS measurements are statistically independent in space and time, and have the same accuracy, is certainly not realistic. Any mis-specification in the stochastic model will inevitably lead to unreliable positioning results. A stochastic assessment procedure has been developed to take into account the heteroscedastic, space- and time-correlated error structure of the GPS measurements. Test results indicate that the reliability of the estimated positioning results is improved by applying the developed stochastic assessment procedure. In addition, the quality of ambiguity resolution can be more realistically evaluated. Received: 13 February 2001 / Accepted: 3 September 2001     

Time and Frequency Transfer Using GPS Codes and Carrier Phases: Onsite Experiments

Recent studies have shown the capabilities of Global Positioning System (GPS) carrier phases for frequency transfer based on the observations from geodetic GPS receivers driven by stable atomic clocks. This kind of receiver configuration is the kind primarily used within the framework of the International GPS Service (IGS). The International GPS Service/Bureau International des Poids et Mesures (IGS/BIPM) pilot project aims at taking advantage of these GPS receivers to enlarge the network of Time Laboratories contributing to the realization of the International Atomic Time (TAI). In this article, we outline the theory necessary to describe the abilities and limitations of time and frequency transfer using the GPS code and carrier phase observations. We report on several onsite tests and evaluate the present setup of our 12-channel IGS receiver (BRUS), which uses a hydrogen maser as an external frequency reference, to contribute to the IGS/BIPM pilot project. In the initial experimental setup, the receivers had a common external frequency reference; in the second setup, separate external frequency references were used. Independent external clock monitoring provided the necessary information to validate the results. Using two receivers with a common frequency reference and connected to the same antenna, a zero baseline, we were able to use the carrier phase data to derive a frequency stability of 6 × 10⁻¹⁶ for averaging times of one day. The main limitation in the technique originates from small ambient temperature variations of a few degrees Celsius. While these temperature variations have no effect on the functioning of the GPS receiver within the IGS network, they reduce the capacities of the frequency transfer results based on the carrier phase data. We demonstrate that the synchronization offset at the initial measurement epoch can be estimated from a combined use of the code and carrier phase observations. In our test, the discontinuity between two consecutive days was about 140 ps. ? 1999 John Wiley & Sons, Inc.     

高精度GPS网数据处理中的系统误差分析

分析了高精度GPS网系统误差产生的原因和分类，推导了消除和估计GPS网系统误差的整体平差函数模型。     

Modeling and estimation of C1–P1 bias in GPS receivers

 Modern dual-frequency global positioning system (GPS) receivers are capable of providing direct measurements of both L1 C/A (C1) and P code (P1) without the use of the Y-codes under Anti-Spoofing. A discrepancy or bias between the C1 and P1 measurements from these receivers has however been of concern to operators and users of GPS reference networks. For the purpose of modeling and estimation, the nature and characteristics of the discrepancy must be investigated. The research results presented indicate that the discrepancy between the C1 and P1 measurements contains two different types of components: one is of constant type while another is time variant. A method has been developed for their modeling and estimation. The residual C1–P1 time series after a satellite-dependent bias removal agree at a few-centimeter level, indicating the effectiveness of the proposed model. This allows the C1–P1 discrepancy, both constant and non-constant components, to be removed from GPS reference network solutions. Numerical results are provided to support the analysis. Received: 12 October 1999 / Accepted: 11 May 2000     

GPS network monitors the Western Alps' deformation over a five-year period: 1993–1998

  The Western Alps are among the best studied collisional belts with both detailed structural mapping and also crustal geophysical investigations such as the ECORS and EGT seismic profile. By contrast, the present-day kinematics of the belt is still largely unknown due to small relative motions and the insufficient accuracy of the triangulation data. As a consequence, several tectonic problems still remain to be solved, such as the amount of N–S convergence in the Occidental Alps, the repartition of the deformation between the Alpine tectonic units, and the relation between deformation and rotation across the Alpine arc. In order to address these problems, the GPS ALPES group, made up of French, Swiss and Italian research organizations, has achieved the first large-scale GPS surveys of the Western Alps. More than 60 sites were surveyed in 1993 and 1998 with a minimum observation of 3 days at each site. GPS data processing has been done by three independent teams using different software. The different solutions have horizontal repeatabilities (N–E) of 4–7 mm in 1993 and 2–3 mm in 1998 and compare at the 3–5-mm level in position and 2-mm/yr level in velocity. A comparison of 1993 and 1998 coordinates shows that residual velocities of the GPS marks are generally smaller than 2 mm/yr, precluding a detailed tectonic interpretation of the differential motions. However, these data seem to suggest that the N–S compression of the Western Alps is quite mild (less than 2 mm/yr) compared to the global convergence between the African and Eurasian plate (6 mm/yr). This implies that the shortening must be accomodated elsewhere by the deformation of the Maghrebids and/or by rotations of Mediterranean microplates. Also, E–W velocity components analysis supports the idea that E–W extension exists, as already suggested by recent structural and seismotectonic data interpretation. Received: 27 November 2000 / Accepted: 17 September 2001