New improved orbit solutions for the ERS-1 and ERS-2 satellites

Improved orbit solutions of the European Remote Sensing Satellites ERS-1 and ERS-2 have been computed in the ITRF2005 terrestrial reference frame using the recent models based mainly on IERS Conventions 2003. These solutions cover the periods 3 August 1991 to 8 July 1996 for ERS-1, and 3 May 1995 to 4 July 2003 for ERS-2. For each satellite, the final orbit solution is based on a combination of three separate orbit solutions independently computed at the Delft Institute of Earth Observation and Space Systems (DEOS) of the Delft University of Technology (The Netherlands), the Navigation Support Office of the European Space Operations Centre (ESOC, Germany) and the Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences (Germany) using three different software packages for precise orbit determination, but using the same models in the same terrestrial reference frame within the European Space Agency (ESA) project ‘Reprocessing of Altimeter Products for ERS (REAPER)’. Validation using radar altimeter data indicates that the new combined orbits of ERS-1 and ERS-2 computed by us are significantly more accurate, approaching the 2–3 cm level in radial direction, than previously available orbit solutions.     

SPOT-2 and TOPEX/Poseidon precise orbit determination from DORIS doppler tracking

The French earth observation satellite SPOT-2 has served as a testbed for precise orbit determination from DORIS doppler tracking in anticipation of the TOPEX/Poseidon mission. Using the most up-to-data gravity field model, JGM-2, a radial orbit accuracy of about 2–9 cm was achieved, with an rms of fit of the tracking data of about 0.64 mm/s. Furthermore, it was found that the coordinates of the ground stations can be determined with an accuracy of the order of 2–5 cm after removal of common rotations, and translations.

Using a slightly different model for atmospheric drag, but the same gravity model, precise orbits of TOPEX/Poseidon from DORIS tracking data were determined with a radial orbit accuracy of the order of 4–5 cm, which is far within the 13 cm mission requirement. This conclusion is based on the analysis of 1-day overlap of successive 11-day orbits, and the comparisons with orbits computed from satellite laser tracking (SLR) and from the combination of SLR and DORIS tracking. Results indicate a consistency between the different orbits of 1–4 cm, 4–20 cm, and 6–13 cm in the radial, cross-track, and along-track directions, respectively. The residual rms is about 4–5 cm for SLR data and 0.56 mm/s for DORIS tracking. These numbers are roughly twice as large as the system noise levels, reflecting the fact that there are still some modeling errors left.     

Impact of ITRS 2014 realizations on altimeter satellite precise orbit determination

This paper evaluates orbit accuracy and systematic error for altimeter satellite precise orbit determination on TOPEX, Jason-1, Jason-2 and Jason-3 by comparing the use of four SLR/DORIS station complements from the International Terrestrial Reference System (ITRS) 2014 realizations with those based on ITRF2008. The new Terrestrial Reference Frame 2014 (TRF2014) station complements include ITRS realizations from the Institut National de l’Information Géographique et Forestière (IGN) ITRF2014, the Jet Propulsion Laboratory (JPL) JTRF2014, the Deutsche Geodätisches Forschungsinstitut (DGFI) DTRF2014, and the DORIS extension to ITRF2014 for Precise Orbit Determination, DPOD2014. The largest source of error stems from ITRF2008 station position extrapolation past the 2009 solution end time. The TRF2014 SLR/DORIS complement impact on the ITRF2008 orbit is only 1–2 mm RMS radial difference between 1992–2009, and increases after 2009, up to 5 mm RMS radial difference in 2016. Residual analysis shows that station position extrapolation error past the solution span becomes evident even after two years, and will contribute to about 3–4 mm radial orbit error after seven years. Crossover data show the DTRF2014 orbits are the most accurate for the TOPEX and Jason-2 test periods, and the JTRF2014 orbits for the Jason-1 period. However for the 2016 Jason-3 test period only the DPOD2014-based orbits show a strong and statistically significant margin of improvement. The positive results with DTRF2014 suggest the new approach to correct station positions or normal equations for non-tidal loading before combination is beneficial. We did not find any compelling POD advantage in using non-linear over linear station velocity models in our SLR & DORIS orbit tests on the Jason satellites. The JTRF2014 proof-of-concept ITRS realization demonstrates the need for improved SLR+DORIS orbit centering when compared to the Ries (2013) CM annual model. Orbit centering error is seen as an annual radial signal of 0.4 mm amplitude with the CM model. The unmodeled CM signals show roughly a 1.8 mm peak-to-peak annual variation in the orbit radial component. We find the TRF network stability pertinent to POD can be defined only by examination of the orbit-specific tracking network time series. Drift stability between the ITRF2008 and the other TRF2014-based orbits is very high, the relative mean radial drift error over water is no larger than 0.04 mm/year over 1993–2015. Analyses also show TRF induced orbit error meets current altimeter rate accuracy goals for global and regional sea level estimation.     

TOPEX/Poseidon precise orbit determination using GPS double difference phase observables

Data from the experimental onboard GPS receiver were used to accurately compute the orbit of TOPEX/Poseidon. This represents a unique opportunity to intercompare with two other classical tracking techniques (SLR and DORIS). A review of the methodology used is given together with current results.     

DPOD2014: A new DORIS extension of ITRF2014 for precise orbit determination

To support precise orbit determination of the altimetry missions, the International DORIS Service (IDS) regularly estimates the DPOD (DORIS terrestrial reference frame for Precise Orbit Determination) solution which includes mean positions and velocities of all the DORIS stations. This solution is aligned to the current realization of the International Terrestrial Reference Frame (ITRF) and so, can be seen as a DORIS extension of the ITRF. In 2016, moving to the IDS Combination Center, the DPOD construction scheme changed. The new DPOD solution is produced from a DORIS cumulative position and velocity solution. We present the new methodology used to compute DPOD2014 and its validation procedure. In order to present geophysical applications and interpretations of these results, we show two examples: (1) the Gorkha earthquake (M7.8 – April 2015) generates a 3-D mis-positioning of nearly 55?mm of the EVEB DORIS station at the Everest base camp 90?km from the epicenter. (2) Applying the results the DPOD2014 realization, we show that the most recent vertical velocity of Thule, Greenland is similar to that observed between 2006 and 2010, indicating further ongoing ice mass loss in the Thule region of northwest Greenland.     

Geosynchronous satellites expanding a future GNSS satellite constellation: A precise orbit determination study

The integration of geosynchronous orbit (GSO) satellites in Global Navigation Satellite Systems (GNSS) is mostly discussed to enable a regional enhancement for tracking. But how do GSO satellites affect the orbit determination of the rest of the constellation? How accurately can these orbits be determined in a future GNSS tracking scenario with optical links? In this simulation study we analyze the benefit of GSO satellites as an expansion of a MEO (Medium Earth Orbit) satellite constellation – we selected the Galileo satellite constellation – for MEO Precise Orbit Determination (POD). We address not only the impact on POD of MEO satellites but also the possibility to precisely determine the GSO satellites – geostationary orbits (GEO) and inclined geosynchronous orbits (IGSO) – in such an expanded MEO constellation. In addition to GNSS microwave observations, we analyze the influence of different optical links between the participating entities: Optical two-way Inter-Satellite Links (OISL) and ground-space oriented Optical Two-Way Links (OTWL). These optical measurements together with the GNSS microwave observations give a remarkable benefit for the POD capability. In the case of GNSS and OTWL, we simulate the measurements with regard to a network of 16 ground stations. We pay great attention to the simulation of systematic effects of all measurement techniques. We discuss the influence on the systematic errors as well as the formal orbit uncertainties. A MEO constellation expanded with GSO satellites as well as the use of optical links together with GNSS observations not only improves the MEO satellite orbits but also the GSOs to a great extent.     

Precision orbit determination performance for CryoSat-2

In this paper we discuss our efforts to perform precision orbit determination (POD) of CryoSat-2 which depends on Doppler and satellite laser ranging tracking data. A dynamic orbit model is set-up and the residuals between the model and the tracking data is evaluated. The average r.m.s. of the 10?s averaged Doppler tracking pass residuals is approximately 0.39?mm/s; and the average of the laser tracking pass residuals becomes 1.42?cm. There are a number of other tests to verify the quality of the orbit solution, we compare our computed orbits against three independent external trajectories provided by the CNES. The CNES products are part of the CryoSat-2 products distributed by ESA. The radial differences of our solution relative to the CNES precision orbits shows an average r.m.s. of 1.25?cm between Jun-2010 and Apr-2017. The SIRAL altimeter crossover difference statistics demonstrate that the quality of our orbit solution is comparable to that of the POE solution computed by the CNES. In this paper we will discuss three important changes in our POD activities that have brought the orbit performance to this level. The improvements concern the way we implement temporal gravity accelerations observed by GRACE; the implementation of ITRF2014 coordinates and velocities for the DORIS beacons and the SLR tracking sites. We also discuss an adjustment of the SLR retroreflector position within the satellite reference frame. An unexpected result is that we find a systematic difference between the median of the 10 s Doppler tracking residuals which displays a statistically significant pattern in the South Atlantic Anomaly (SSA) area where the median of the velocity residuals varies in the range of ?0.15 to +0.15?mm/s.     

Enhancing the kinematic precise orbit determination of low earth orbiters using GPS receiver clock modelling

Clock error estimation has been the focus of a great deal of research because of the extensive usage of clocks in GPS positioning applications. The receiver clock error in the spacecraft orbit determination is commonly estimated on an epoch-by-epoch basis, along with the spacecraft’s position. However, due to the high correlation between the spacecraft orbit altitude and the receiver clock parameters, estimates of the radial component are degraded in the kinematic approach. Using clocks with high stability, the predictable behaviour of the receiver oscillator can be exploited to improve the positioning accuracy, especially for the radial component. This paper introduces two GPS receiver clock models to describe the deterministic and stochastic property of the receiver clock, both of which can improve the accuracy of kinematic orbit determination for spacecraft in low earth orbit. In particular, the clock parameters are estimated as time offset and frequency offset in the two-state model. The frequency drift is also estimated as an unknown parameter in the three-state model. Additionally, residual non-deterministic random errors such as frequency white noise, frequency random walk noise and frequency random run noise are modelled. Test results indicate that the positioning accuracy could be improved significantly using one day of GRACE flight data. In particular, the error of the radial component was reduced by over 40.0% in the real-time scenario.     

Gravity field model adjustment from ERS-1 and TOPEX altimetry and SLR tracking using an analytical orbit perturbation theory

The JGM-2 gravity field model has been adjusted using 70 days of ERS-1 and 19 10-day repeat cycles of TOPEX/Poseidon SLR and single satellite altimeter crossover differences. In addition, dual satellite altimeter crossover differences between ERS-1 and TOPEX for the selected 70-day period of ERS-1 and TOPEX repeat cycle 18 have been used in the JGM-2 model adjustment. In the computation of the normal equations, use was made of the analytical Lagrange linear perturbation theory. The single satellite altimeter crossover difference rms was brought down from 15.2 to 14.1 cm for ERS-1 and from 10.6 to 10.5 cm for TOPEX. The dual satellite altimeter crossover difference rms was reduced from 17.7 to 16.9 cm. Furthermore, the weighted rms of fit of SLR measurements was brought down from 16.0 to 14.4 cm for ERS-1, and from 5.4 to 5.0 cm for TOPEX/Poseidon.     

Early analysis of precise orbit and clock offset determination for the satellites of the global BeiDou-3 system

Eight new-generation BeiDou satellites (BeiDou-3) have been launched into Medium Earth Orbit (MEO), allowing for global coverage since March 2018, and they are equipped with new hydrogen atomic clocks and updated rubidium clocks. Firstly, we analyzed the signals for the carrier-to-noise-density ratio (C/N0) and pseudorange multipath (MP) by using international GNSS (Global Navigation Satellite System) Monitoring and Assessment System (iGMAS) station data, and found that B1C has a lower C/N0, and B2a has the same level of C/N0 as the B1I and B3I signals. For pseudorange multipath, compared with the BeiDou-2 satellites, the obvious systematic variation of MP scatters related to the elevation angle is greatly improved for the BeiDou-3 and BeiDou-3e satellites signals. For the signals of the BeiDou-3 satellites, the order of the Root Mean Square (RMS) values of multipath and noise is B3I?<?B1I?<?B2a?<?B1C. Then, the comparison of the precise orbit determination and clock offset determination for the BeiDou-2, BeiDou-3, and BeiDou-3 experimental (BeiDou-3e) satellites was done by using 10 stations from iGMAS. The 3D precision of the 24?h orbit overlap is 24.55, 25.61, and 23.35?cm for the BeiDou-3, BeiDou-3e, and BeiDou-2 satellites, respectively. BeiDou-3 satellite has a comparable precision to that of the BeiDou-2 satellite. For the precision of clock offset estimation, the Standard Deviation (STD) of the BeiDou-3 MEO satellite is 0.350?ns, which is an improvement of 0.042?ns over that of the BeiDou-2 MEO satellite. The stabilities of the BeiDou-3 and BeiDou-3e onboard clocks are better than those of BeiDou-2 by factors of 2.84 and 1.61 at an averaging time of 1000 and 10,000?s, respectively.     

Some comparisons of orbit determination and parameter estimation based on LAGEOS 1 and LAGEOS 2 data

The modelling accuracy of the LAGEOS 1 orbit was continously improved since its launch in 1976. In spite of these experiences the modelling accuracy of LAGEOS 2 is still about 20 per cent worse. Considering e. g. only the influence of different gravity field models it has been shown that the orbital fits for arc lengths of one month is generally about 25 mm for LAGEOS 1 and more than 30 mm for LAGEOS 2. This is mainly due to the fact that LAGEOS 2 has not yet been used for the determination of most gravity field models. The influences of different model parameters on the estimation of station coordinates, Earth rotation parameters, the geogravitational coefficient, the radiation pressure coefficient, and the empirical acceleration has been studied. The differences and peculiarities of both satellites are discussed. Although the analysis of LAGEOS 2 data still does not reach the high level of LAGEOS 1 combination solutions using both satellites allow new insights, higher accuracies, and a higher time resolution for the parameters and phenomena investigated.     

Angles-only relative orbit determination in low earth orbit

The paper provides an overview of the angles-only relative orbit determination activities conducted to support the Autonomous Vision Approach Navigation and Target Identification (AVANTI) experiment. This in-orbit endeavor was carried out by the German Space Operations Center (DLR/GSOC) in autumn 2016 to demonstrate the capability to perform spaceborne autonomous close-proximity operations using solely line-of-sight measurements. The images collected onboard have been reprocessed by an independent on-ground facility for precise relative orbit determination, which served as ultimate instance to monitor the formation safety and to characterize the onboard navigation and control performances. During two months, several rendezvous have been executed, generating a valuable collection of images taken at distances ranging from 50?km to only 50?m. Despite challenging experimental conditions characterized by a poor visibility and strong orbit perturbations, angles-only relative positioning products could be continuously derived throughout the whole experiment timeline, promising accuracy at the meter level during the close approaches. The results presented in the paper are complemented with former angles-only experience gained with the PRISMA satellites to better highlight the specificities induced by different orbits and satellite designs.     

Chang’E-1 precision orbit determination and lunar gravity field solution

In this paper we present results assessing the role of Very Long Baseline Interferometry (VLBI) tracking data through precision orbit determination (POD) during the check-out phase for Chang’E-1, and the lunar gravity field solution CEGM-01 based on the orbital tracking data acquired during the nominal phase of the mission. The POD of Chang’E-1 is performed using S-band two-way Range and Range Rate (R&RR) data, together with VLBI delay and delay rate observations. The role of the VLBI data in the POD of Chang’E-1 is analyzed, and the resulting orbital accuracies are estimated for different solution strategies. The final orbital accuracies proved that the VLBI tracking data can improve the Chang’E-1 POD significantly. Consequently, CEGM-01 based on six-month tracking data during Chang’E-1 nominal mission phase is presented, and the accuracy of the model is assessed by means of the gravity field power spectrum, admittance and coherence between gravity and topography, lunar surface gravity anomaly and POD for both Chang’E-1 and Lunar Prospector (LP). Our analysis indicates that CEGM-01 has significant improvements over a prior model (i.e. GLGM-2), and shows the potential of Chang’E-1 tracking data in high resolution lunar gravity field model solution by combining with SELENE and LP tracking data.     

DORIS-based point mascons for the long term stability of precise orbit solutions

In recent years non-tidal Time Varying Gravity (TVG) has emerged as the most important contributor in the error budget of Precision Orbit Determination (POD) solutions for altimeter satellites’ orbits. The Gravity Recovery And Climate Experiment (GRACE) mission has provided POD analysts with static and time-varying gravity models that are very accurate over the 2002–2012 time interval, but whose linear rates cannot be safely extrapolated before and after the GRACE lifespan. One such model based on a combination of data from GRACE and Lageos from 2002–2010, is used in the dynamic POD solutions developed for the Geophysical Data Records (GDRs) of the Jason series of altimeter missions and the equivalent products from lower altitude missions such as Envisat, Cryosat-2, and HY-2A. In order to accommodate long-term time-variable gravity variations not included in the background geopotential model, we assess the feasibility of using DORIS data to observe local mass variations using point mascons. In particular, we show that the point-mascon approach can stabilize the geographically correlated orbit errors which are of fundamental interest for the analysis of regional Mean Sea Level trends based on altimeter data, and can therefore provide an interim solution in the event of GRACE data loss. The time series of point-mass solutions for Greenland and Antarctica show good agreement with independent series derived from GRACE data, indicating a mass loss at rate of 210 Gt/year and 110 Gt/year respectively.     

CHAMP and GRACE accelerometer calibration by GPS-based orbit determination

Current and planned Earth observation missions are equipped with highly sensitive accelerometers. Before using the data, the instrument has to be calibrated by determining scale and bias parameters for each axis. Here, the accelerometer measurements are used in a GPS-based reduced-dynamic orbit determination approach, replacing the non-gravitational force models, and nominally daily calibration parameters are estimated. Additional empirical accelerations are estimated to account for deficiencies in the applied force models. This method is applied to 5 years of CHAMP and GRACE data, resulting in an orbit precision at the level of a few centimeters. In along-track direction the calibration parameters can be estimated freely, scale factors of 0.96 ± 0.014 and 0.95 ± 0.015 are obtained for GRACE A and B, and 0.85 ± 0.024 for CHAMP. A constant scale factor results in the smoothest bias series, with clear trends and occasional jumps. In radial and cross-track direction tight constraints to a priori biases have to be applied. Furthermore, the determined orbits are analyzed with respect to reference trajectories, and SLR, phase and KBR residuals are presented.     

Evaluation of JGM 2 geopotential errors from Geosat, TOPEX/Poseidon and ERS-1 crossover altimetry

World-ocean distribution of the crossover altimetry data from Geosat, TOPEX/Poseidon (T/P) and the ERS 1 missions have provided strong independent evidence that NASA's/CSR's JGM 2 geopotential model (70 × 70 in spherical harmonics) yields accurate radial ephemerides for these satellites. In testing the sea height crossover differences found from altimetry and JGM 2 orbits for these satellites, we have used the sea height differences themselves (of ascending minus descending passes averaged at each location over many exact repeat cycles) and the Lumped Latitude Coefficients (LLC) derived from them. For Geosat we find the geopotential-induced LLC errors (exclusive of non-gravitational and initial state discrepancies) mostly below 6 cm, for TOPEX the corresponding errors are usually below 2 cm, and for ERS 1 (35-day cycle) they are generally below 5 cm. In addition, we have found that these observations agree well overall with predictions of accuracy derived from the JGM 2 variance-covariance matrix; the corresponding projected LLC errors for Geosat, T/P, and ERS 1 are usually between 1 and 4 cm, 1 – 2 cm, and 1 – 4 cm, respectively (they depend on the filtering of long-periodic perturbations and on the order of the LLC). This agreement is especially impressive for ERS 1 since no data of any kind from this mission was used in forming JGM 2.

The observed crossover differences for Geosat, T/P and ERS 1 are 8, 3, and 11 cm (rms), respectively. These observations also agree well with prediction of accuracy derived from the JGM 2 variance-covariance matrix; the corresponding projected crossover errors for Geosat and T/P are 8 cm and 2.3 cm, respectively. The precision of our mean difference observations is about 3 cm for Geosat (approx. 24,000 observations), 1.5 cm for T/P (approx. 6,000 observations) and 5 cm for ERS 1 (approx. 44,000 observations). Thus, these “global” independent data should provide a valuable new source for improving geopotential models. Our results show the need for further correction of the low order JGM 2 geopotential as well as certain resonant orders for all 3 satellites.     

Galileo real-time orbit determination with multi-frequency raw observations

Real-time GNSS-based applications require corresponding real-time orbit products. While traditional GNSS orbits are generated with the dual-frequency IF (Ionosphere-Free) model, the increase of multi-frequency signal satellites brings new challenges for the data processing. Therefore, real-time orbit determination with the multi-frequency UC (Uncombined) model is introduced in this study considering its flexibility. With the derived mathematical model conforming to IGS (International GNSS Service) dual-frequency clock definition and one-week triple-frequency Galileo observation data from 90 IGS network stations, the convergence and accuracy of real-time orbits is assessed and the characteristics of satellite IFCB (Inter-Frequency Clock Bias) are analyzed. Results indicate that the model differences, including dual-frequency IF model, dual-frequency UC model and triple-frequency UC model, contribute to only cm-level differences with CODE (Center for Orbit Determination in Europe) final orbits after a convergence time of around 12 h. The constellation-mean RMS (Root Mean Square) differences of the converged real-time orbits with the CODE final orbits reaches about 5.0 cm, 7.0 cm and 5.0 cm for the radial, tangential and normal directions. The convergence of satellite IFCB is much faster than that of satellite orbit, which reflects a loose correlation between these two parameters. While the Galileo satellite IFCB are temporally stable, the modeling of satellite IFCB may be unreliable when over constrained and becomes even more unstable with commonly encountered datum changes. In summary, real-time GNSS orbit determination with multi-frequency raw observations is feasible and extendable with proper treatment of IFCB.     

Precise orbit determination and baseline consistency assessment for Swarm constellation

Precise orbit determination (POD) and precise baseline determination (PBD) of Swarm satellites with 4 years of data are investigated. Ambiguity resolution (AR) plays a crucial role in achieving the best orbit accuracy. Swarm POD and PBD based on single difference (SD) AR and traditional double difference (DD) AR methods are explored separately. Swarm antenna phase center variation (PCV) corrections are developed to further improve the orbit determination accuracy. The code multipath of C1C, C1W and C2W observations is first evaluated and clear variations in code noise related to different receiver settings are observed. Carrier phase residuals of different time periods and different loop tracking settings of receiver are studied to explore the effect of ionospheric scintillation on POD. The reduction of residuals in the polar and geomagnetic equator regions confirms the positive impact of the updated carrier tracking loops (TLs) on POD performance. The SD AR orbits and orbits with float ambiguity (FA) are compared with the Swarm precise science orbits (PSOs). An average improvement of 27 %, 4 % and 16 % is gained in along-track, cross-track and radial directions by fixing the ambiguity to integer. For Swarm-A/B and Swarm-B/C formations, specific days are selected to perform the DD AR-based POD during which the average distance of the formation satellites is less than 5000 km. Satellite laser ranging (SLR) observations are employed to validate the performance of FA, SD AR and DD AR orbits. The consistency between the SD AR orbits and SLR data is at a level of 10 mm which shows an improvement of 25 % when comparing with the FA results. An SLR residuals reduction of 15 % is also achieved by the DD AR solution for the selected days. Precise relative navigation is also an essential aspect for spacecraft formation flying missions. The closure error method is proposed to evaluate the baseline precision in three dimensions. A baseline precision of 1–3 mm for Swarm-A/C formation and 3–5 mm for Swarm-A/B and Swarm-B/C satellite pairs is verified by both the consistency check and closure error method.     

Comprehensive outage compensation of real-time orbit and clock corrections with broadcast ephemeris for ambiguity-fixed precise point positioning

The main challenge in real-time precise point positioning (PPP) is that the data outages or large time lags in receiving precise orbit and clock corrections greatly degrade the continuity and real-time performance of PPP positioning. To solve this problem, instead of directly predicting orbit and clock corrections in previous researches, this paper presents an alternative approach of generating combined corrections including orbit error, satellite clock and receiver-related error with broadcast ephemeris. Using ambiguities and satellite fractional-cycle biases (FCBs) of previous epoch and the short-term predicted tropospheric delay through linear extrapolation model (LEM), combined corrections at current epoch are retrieved and weighted with multiple reference stations, and further broadcast to user for continuous enhanced positioning during outages of orbit and clock corrections. To validate the proposed method, two reference station network with different inter-station distance from National Geodetic Survey (NGS) network are used for experiments with six different time lags (i.e., 5 s, 10 s, 15 s, 30 s, 45 s and 60 s), and one set of data collected by unmanned aerial vehicle (UAV) is also used. The performance of LEM is investigated, and the troposphere prediction accuracy of low elevation (e.g., 10–20degrees) satellites has been improved by 44.1% to 79.0%. The average accuracy of combined corrections before and after LEM is used is improved by 12.5% to 77.3%. Without LEM, an accuracy of 2–3 cm can be maintained only in case of small time lags, while the accuracies with LEM are all better than 2 cm in case of different time lags. The performance of simulated kinematic PPP at user end is assessed in terms of positioning accuracy and epoch fix rate. In case of different time lags, after LEM is used, the average accuracy in horizontal direction is better than 3 cm, and the accuracy in up direction is better than 5 cm. At the same time, the epoch fix rate has also increased to varying degrees. The results of the UAV data show that in real kinematic environment, the proposed method can still maintain a positioning accuracy of several centimeters in case of 20 s time lag.     

GPS single-frequency orbit determination for low Earth orbiting satellites

The determination of high-precision orbits for Low Earth Orbiting (LEO) satellites (e.g., CHAMP, GRACE, MetOp-A) is based on dual-frequency tracking data from on-board GPS (Global Positioning System) receivers. The two frequencies allow it to eliminate the first order ionosphere effects. Data screening and precise orbit determination (POD) procedures are optimized under the assumption of the availability of two frequencies.