Precise Satellite Orbit Research Articles

Research on the Impact of BDS-2/3 Receiver ISB on LEO Satellite POD

In recent years, the multi-GNSS positioning application is becoming more and more popular, same to the low Earth orbit (LEO) satellite precise orbit determination (POD) based on the onboard multi-GNSS measurements. The third-generation Beidou navigation satellite system (BDS-3) provides a new option to obtain the LEO satellite orbit solutions. However, the receiver intersystem bias (ISB) of different GNSS is unavoidable in multi-GNSS data processing. This paper’s main goal is absorption of the impact of the ISB between BDS-3 and BDS-2 on the LEO satellite POD. Taking GPS-based POD solutions for the reference orbit, this paper evaluates the orbit accuracy of BDS-2-based POD, BDS-3-based POD, BDS-2 and BDS-3 combined PODs with/without ISB. The BDS-3-based POD accuracy is 6.57 cm in the 3D direction, a 56% improvement over BDS-2-based POD. When the ISB between BDS-3 and BDS-2 is estimated, the BDS-2/3 combined POD accuracy of 5.37 cm in the 3D direction is better than that without ISB, which is a 64% improvement over BDS-2-based POD and 18% improvement over BDS-3-based POD. For GPS and BDS-2/3 combined POD, the GPS and BDS-3 joint POD solutions have the smallest RMS differences in overlapping consistency and smallest RMS differences compared to GPS-based POD. This study indicates that estimating the BDS-2/3 receiver ISB in BDS-2/3 joint POD could improve the orbit accuracy, and the GPS and BDS-3 joint POD solution is better than another combined POD. This paper will provide meaningful references for the LEO satellite multi-GNSS-based POD.

The Potential of LEO Satellite-Based Opportunistic Navigation for High Dynamic Applications.

Resilient navigation in Global Navigation Satellite System (GNSS)-degraded and -denied environments is becoming more and more required for many applications. It can typically be based on multi-sensor data fusion that relies on alternative technologies to GNSS. In this work, we studied the potential of a low earth orbit (LEO) satellite communication system for a high-dynamic application, when it is integrated with an inertial measurement unit (IMU) and magnetometers. We derived the influence of the main error sources that affect the LEO space vehicle (SV) Doppler-based navigation on both positioning and attitude estimations. This allowed us to determine the best, intermediate and worst cases of navigation performances. We show that while the positioning error is large due to large orbit errors or high SV clock drifts, it becomes competitive with that of an inertial navigation system (INS) based on a better quality IMU if precise satellite orbits are available. On the other hand, the attitude estimation tolerates large orbit errors and high SV clock drifts. The obtained results suggest that LEO SV signals, used as signals of opportunity for navigation, are an attractive alternative in GNSS-denied environments for high dynamic vehicles.

A variant of raw observation approach for BDS/GNSS precise point positioning with fast integer ambiguity resolution

The Precise Point Positioning (PPP) technique uses a single Global Navigation Satellite System (GNSS) receiver to collect carrier-phase and code observations and perform centimeter-accuracy positioning together with the precise satellite orbit and clock corrections provided. According to the observations used, there are basically two approaches, namely, the ionosphere-free combination approach and the raw observation approach. The former eliminates the ionosphere effects in the observation domain, while the latter estimates the ionosphere effects using uncombined and undifferenced observations, i.e., so-called raw observations. These traditional techniques do not fix carrier-phase ambiguities to integers, if the additional corrections of satellite hardware biases are not provided to the users. To derive the corrections of hardware biases in network side, the ionosphere-free combination operation is often used to obtain the ionosphere-free ambiguities from the L1 and L2 ones produced even with the raw observation approach in earlier studies. This contribution introduces a variant of the raw observation approach that does not use any ionosphere-free (or narrow-lane) combination operator to derive satellite hardware bias and compute PPP ambiguity float and fixed solution. The reparameterization and the manipulation of design matrix coefficients are described. A computational procedure is developed to derive the satellite hardware biases on WL and L1 directly. The PPP ambiguity-fixed solutions are obtained also directly with WL/L1 integer ambiguity resolutions. The proposed method is applied to process the data of a GNSS network covering a large part of China. We produce the satellite biases of BeiDou, GPS and Galileo. The results demonstrate that both accuracy and convergence are significantly improved with integer ambiguity resolution. The BeiDou contributions on accuracy and convergence are also assessed. It is disclosed for the first time that BeiDou only ambiguity-fixed solutions achieve the similar accuracy with that of GPS/Galileo combined, at least in mainland China. The numerical analysis demonstrates that the best solutions are achieved by GPS/Galileo/BeiDou solutions. The accuracy in horizontal components is better than 6 mm, and in the height component better than 20 mm (one sigma). The mean convergence time for reliable ambiguity-fixing is about 1.37 min with 0.12 min standard deviation among stations without using ionosphere corrections and the third frequency measurements. The contribution of BDS is numerically highlighted.

Optimization of ground tracking stations for BDS-3 satellite orbit determination

Abstract A precise satellite orbit is the basis for high-precision services for users, and the determination of high-precision satellite orbits depends on the reasonable distribution and volume of ground tracking stations (GTSs). In July 2020, the BeiDou global navigation satellite system (BDS-3) was completed and began to be operated globally. Based on the principle of dynamic orbit determination, we first developed an algorithm to determine the optimal distribution and number of GTSs for accurate satellite orbit determination. Subsequently, based on 10 GTSs located in China, the optimal distribution and number of GTSs with and without inter-satellite link (ISL) ranging observations were determined. Finally, real measurements of GTS and ISL ranging observation data were used to validate the GTS results yielded by the algorithm. Using 18 BDS-3 satellites, and based on non-ISL observations and 10 Chinese regional GTSs, we found that GTSs distributed near the equator contributed significantly to the accuracy of orbit determination for these satellites compared to other GTSs. Orbit determination results obtained from the measured data of the optimal GTSs were more accurate than those obtained from the measured data of uniformly distributed global GTSs. Upon the addition of 55 uniformly distributed GTSs worldwide, the orbit determination accuracy for BDS-3 satellites tended to plateau. Moreover, following the addition of ISL, although the distribution and number of GTSs was optimized using the proposed algorithm, the orbit determination results from the measured data revealed that a change in the distribution and number of GTSs had a limited effect on the BDS-3 orbit determination results.

Precise Point Positioning with Almost Fully Deployed BDS-3, BDS-2, GPS, GLONASS, Galileo and QZSS Using Precise Products from Different Analysis Centers

The space segment of all the five satellite systems capable of providing precise position services, namely BeiDou Navigation Satellite System (BDS) (including BDS-3 and BDS-2), Global Positioning System (GPS), GLObal NAvigation Satellite System (GLONASS), Galileo and Quasi-Zenith Satellite System (QZSS), has almost been fully deployed at present, and the number of available satellites is approximately 136. Currently, the precise satellite orbit and clock products from the analysis centers European Space Agency (ESA), GeoForschungsZentrum Potsdam (GFZ) and Wuhan University (WHU) can support all five satellite systems. Thus, it is necessary to investigate the positioning performance of a five-system integrated precise point positioning (PPP) (i.e., GRECJ-PPP) using the precise products from different analysis centers under the current constellation status. It should be noted that this study only focuses on the long-term performance of PPP based on daily observations. The static GRECJ-PPP can provide a convergence time of 5.9–6.9/2.6–3.1/6.3–7.1 min and a positioning accuracy of 0.2–0.3/0.2–0.3/1.0–1.1 cm in east/north/up directions, respectively, while the corresponding kinematic statistics are 6.8–8.6/3.3–4.0/7.8–8.1 min and 1.0–1.1/0.8/2.5–2.6 cm in three directions, respectively. For completeness, although the real-time precise products from the analysis center Centre National d’Etudes Spatiales (CNES) do not incorporate QZSS satellites, the performance of real-time PPP with the other four satellite systems (i.e., GREC-PPP) is also analyzed. The real-time GREC-PPP can achieve a static convergence time of 8.7/5.2/11.2 min, a static positioning accuracy of 0.6/0.8/1.3 cm, a kinematic convergence time of 11.5/6.9/13.0 min, and a kinematic positioning accuracy of 1.7/1.6/3.6 cm in the three directions, respectively. For comparison, the results of single-system and dual-system PPP are also provided. In addition, the consistency of the precise products from different analysis centers is characterized.

Ionosphere-weighted undifferenced and uncombined PPP-RTK: theoretical models and experimental results

Precise ionospheric information, as like precise satellite orbits, clocks, and code/phase biases, is a critical factor for achieving fast integer ambiguity resolution in precise point positioning (PPP-AR). This study develops an ionosphere-weighted (IW) undifferenced and uncombined PPP real-time kinematic (PPP-RTK) network model using code and phase observations. We introduce between-station single-differenced ionospheric delay pseudo-observations to take advantage of the similar characteristics of ionospheric delays between two receivers tracking the same satellite. The estimable ionospheric parameters are commonly affected by the differential code bias referring to a particular receiver assigned as pivot, which facilitates the ionospheric interpolation at the user side. Then, the kinematic positioning performance of the IW PPP-RTK user model is analyzed and compared with those of PPP-AR without ionospheric corrections, RTK, and IW-RTK models during low and high solar activity days. The results show that for the PPP-RTK model, the positioning errors converge to thresholds of 2 cm for the horizontal components and 5 cm for the vertical component within 20 epochs, and the positioning errors become stable after an initialization of 20 epochs with root-mean-squared (RMS) values of approximately 0.47, 0.58 and 1.66 cm for the east, north and up components, respectively, which are superior to those of the other three models. Owing to the high ionospheric disturbance influence, the RMS values of the east and up components increase by approximately double and the mean time-to-first-fix increases by 61.5% for the PPP-RTK case.

Modeling and Performance Evaluation of Precise Positioning and Time-Frequency Transfer with Galileo Five-Frequency Observations

The present Global Navigation Satellite System (GNSS) can provide at least double-frequency observations, and especially the Galileo Navigation Satellite System (Galileo) can provide five-frequency observations for all constellation satellites. In this contribution, precision point positioning (PPP) models with Galileo E1, E5a, E5b, E5 and E6 frequency observations are established, including a dual-frequency (DF) ionospheric-free (IF) combination model, triple-frequency (TF) IF combination model, quad-frequency (QF) IF combination model, four five-frequency (FF) IF com-bination models and an FF uncombined (UC) model. The observation data of five stations for seven days are selected from the multi-GNSS experiment (MGEX) network, forming four time-frequency links ranging from 454.6 km to 5991.2 km. The positioning and time-frequency transfer performances of Galileo multi-frequency PPP are compared and evaluated using GBM (which denotes precise satellite orbit and clock bias products provided by Geo Forschung Zentrum (GFZ)), WUM (which denotes precise satellite orbit and clock bias products provided by Wuhan University (WHU)) and GRG (which denotes precise satellite orbit and clock bias products provided by the Centre National d’Etudes Spatiales (CNES)) precise products. The results show that the performances of the DF, TF, QF and FF PPP models are basically the same, the frequency stabilities of most links can reach sub10−16 level at 120,000 s, and the average three-dimensional (3D) root mean square (RMS) of position and average frequency stability (120,000 s) can reach 1.82 cm and 1.18 × 10−15, respectively. The differences of 3D RMS among all models are within 0.17 cm, and the differences in frequency stabilities (in 120,000 s) among all models are within 0.08 × 10−15. Using the GRG precise product, the solution performance is slightly better than that of the GBM or WUM precise product, the average 3D RMS values obtained using the WUM and GRG precise products are 1.85 cm and 1.77 cm, respectively, and the average frequency stabilities at 120,000 s can reach 1.13 × 10−15 and 1.06 × 10−15, respectively.

Assessment of multi-GNSS precise orbit and clock products from different analysis centers based on precise point positioning

Performance of 24h static Precise Point Positioning (PPP) solutions based on multi-GNSS precise satellite orbit and clock products from four analysis centers and seven various constellation combinations was studied to evaluate their quality and characteristics. Data from ten European and four Chinese GNSS stations and 152 days long period from year 2020 were processed. Obtained coordinates were firstly compared with those provided by IGS final weekly combined solution. In Europe, the best agreement with this reference product was reached by solutions including Galileo signals, namely by a combination of GPS+GLONASS+Galileo systems with a mean RMS of 11 mm. This situation was different in China where inclusion of Galileo always led to worse results and the best agreement was achieved by a combination of GPS+GLONASS systems. Although product provided by German Research Center for Geosciences (GFZ) could be selected as the best performing over Europe and product by Center for Orbit Determination in Europe (CODE) over China, differences between individual precise products were mostly at a minimal level. Secondly, coordinates repeatability over the processed period was computed in order to assess the positioning stability. In this regard, the lowest values in both horizontal and vertical direction were reached by GPS+GLONASS solutions. From the perspective of precise products, the repeatability results were dependent on the selected constellation where mainly a specific behavior of product from Wuhan University (WUM) for Galileo system was observed.

Comparisons of CODE and CNES/CLS GPS satellite bias products and applications in Sentinel-3 satellite precise orbit determination

To resolve undifferenced GNSS phase ambiguities, dedicated satellite products are needed, such as satellite orbits, clock offsets and biases. The International GNSS Service CNES/CLS analysis center provides satellite (HMW) Hatch-Melbourne-Wübbena bias and dedicated satellite clock products (including satellite phase bias), while the CODE analysis center provides satellite OSB (observable-specific-bias) and integer clock products. The CNES/CLS GPS satellite HMW bias products are determined by the Hatch-Melbourne-Wübbena (HMW) linear combination and aggregate both code (C1W, C2W) and phase (L1W, L2W) biases. By forming the HMW linear combination of CODE OSB corrections on the same signals, we compare CODE satellite HMW biases to those from CNES/CLS. The fractional part of GPS satellite HMW biases from both analysis centers are very close to each other, with a mean Root-Mean-Square (RMS) of differences of 0.01 wide-lane cycles. A direct comparison of satellite narrow-lane biases is not easily possible since satellite narrow-lane biases are correlated with satellite orbit and clock products, as well as with integer wide-lane ambiguities. Moreover, CNES/CLS provides no satellite narrow-lane biases but incorporates them into satellite clock offsets. Therefore, we compute differences of GPS satellite orbits, clock offsets, integer wide-lane ambiguities and narrow-lane biases (only for CODE products) between CODE and CNES/CLS products. The total difference of these terms for each satellite represents the difference of the narrow-lane bias by subtracting certain integer narrow-lane cycles. We call this total difference “narrow-lane” bias difference. We find that 3% of the narrow-lane biases from these two analysis centers during the experimental time period have differences larger than 0.05 narrow-lane cycles. In fact, this is mainly caused by one Block IIA satellite since satellite clock offsets of the IIA satellite cannot be well determined during eclipsing seasons. To show the application of both types of GPS products, we apply them for Sentinel-3 satellite orbit determination. The wide-lane fixing rates using both products are more than 98%, while the narrow-lane fixing rates are more than 95%. Ambiguity-fixed Sentinel-3 satellite orbits show clear improvement over float solutions. RMS of 6-h orbit overlaps improves by about a factor of two. Also, we observe similar improvements by comparing our Sentinel-3 orbit solutions to the external combined products. Standard deviation value of Satellite Laser Ranging residuals is reduced by more than 10% for Sentinel-3A and more than 15% for Sentinel-3B satellite by fixing ambiguities to integer values.

Initial Assessment of BDS PPP-B2b Service: Precision of Orbit and Clock Corrections, and PPP Performance

On 31 July 2020, the Beidou global navigation satellite system (BDS-3) was officially announced as being commissioned. In addition to offering global positioning, navigation, and timing (PNT) services, BDS-3 also provides precise point positioning (PPP) augmentation services. The satellite orbit correction, clock correction and code bias correction of BDS-3 and other global navigation satellite systems (GNSS) are broadcast by the BDS-3 geostationary earth orbit (GEO) satellites through the PPP-B2b signal. The PPP-B2b service is available for users in China and the surrounding area. In this study, an initial assessment of the PPP-B2b service is presented, with collected 3-day PPP-B2b messages. Based on broadcast ephemeris and PPP-B2b messages, the precise satellite orbits and clock offsets can be recovered. This precision is evaluated with the precise ephemeris from the GeoForschungsZentrum Potsdam (GFZ) analysis center as references. The results indicate that the accuracy of BDS-3 satellite orbits in the direction of radial, along-track, and cross-track is 0.138, 0.131, and 0.145 m, respectively, and for GPS a corresponding accuracy of 0.104, 0.160, and 0.134 m, respectively, could be obtained. The precision of clock offsets can reach a level of several centimeters for both GPS and BDS-3. Both the performance of static PPP and kinematic PPP are evaluated using the observations from four international GNSS monitoring assessment service (iGMAS) stations. Regarding static PPP, the average convergence time is 17.7 min to achieve a horizontal positioning accuracy of better than 0.3 m, and a vertical positioning accuracy of better than 0.6 m. The average positioning accuracy in the direction of east, north, and up-directions are 2.4, 1.6, and 2.3 cm. As to kinematic PPP, the average RMS values of positioning errors in the direction of east, north, and up are 8.1 cm, 3.6 cm, and 8.0 cm after full convergence.

Enabling ambiguity resolution in CSRS‐PPP

<h3>Abstract</h3> Precise point positioning (PPP) uses precise satellite orbits, clock corrections and biases derived from a global network of reference stations to enable accurate positioning worldwide. Natural Resources Canada’s Canadian Spatial Reference System (CSRS) PPP is a free Web service offering automated PPP processing. A critical factor limiting the adoption of PPP in many applications is the convergence time needed to reach centimeter-level accuracies. To address this issue, CSRS-PPP now implements PPP with ambiguity resolution (PPP-AR). This feature required the development of new algorithms, such as sequential normal stacking for least-squares filtering/smoothing, and the weighted integer decision concept for ambiguity validation. New satellite product lines (ultra-rapid, rapid, final) also have been deployed to enable PPP-AR processing with various latencies. This analysis demonstrates that sub-centimeter horizontal accuracies can be obtained in less than one hour for both static and kinematic modes. Using product lines with longer latencies is beneficial, although improvements are typically within the reported uncertainties.

Estimation of fractional cycle bias for GPS/BDS-2/Galileo based on international GNSS monitoring and assessment system observations using the uncombined PPP model

The Fractional Cycle Bias (FCB) product is crucial for the Ambiguity Resolution (AR) in Precise Point Positioning (PPP). Different from the traditional method using the ionospheric-free ambiguity which is formed by the Wide Lane (WL) and Narrow Lane (NL) combinations, the uncombined PPP model is flexible and effective to generate the FCB products. This study presents the FCB estimation method based on the multi-Global Navigation Satellite System (GNSS) precise satellite orbit and clock corrections from the international GNSS Monitoring and Assessment System (iGMAS) observations using the uncombined PPP model. The dual-frequency raw ambiguities are combined by the integer coefficients (4,− 3) and (1,− 1) to directly estimate the FCBs. The details of FCB estimation are described with the Global Positioning System (GPS), BeiDou-2 Navigation Satellite System (BDS-2) and Galileo Navigation Satellite System (Galileo). For the estimated FCBs, the Root Mean Squares (RMSs) of the posterior residuals are smaller than 0.1 cycles, which indicates a high consistency for the float ambiguities. The stability of the WL FCBs series is better than 0.02 cycles for the three GNSS systems, while the STandard Deviation (STD) of the NL FCBs for BDS-2 is larger than 0.139 cycles. The combined FCBs have better stability than the raw series. With the multi-GNSS FCB products, the PPP AR for GPS/BDS-2/Galileo is demonstrated using the raw observations. For hourly static positioning results, the performance of the PPP AR with the three-system observations is improved by 42.6%, but only 13.1% for kinematic positioning results. The results indicate that precise and reliable positioning can be achieved with the PPP AR of GPS/BDS-2/Galileo, supported by multi-GNSS satellite orbit, clock, and FCB products based on iGMAS.

Considering inter-receiver pseudorange biases for BDS-2 precise orbit determination

The inter-receiver pseudorange biases exist between receivers equipping with different front-end designs and correlator types. It is distinguishable from differential code biases and would affect Global Navigation Satellite System (GNSS) estimations if it is not taken into account in data processing. In this contribution, the effects of inter-receiver pseudorange biases on the regional BeiDou navigation satellite system (BDS-2) satellite precise orbit determination (POD) will be investigated. For validation purposes, 35 globally distributed Multi-GNSS Experiment ground stations for which the receivers are from three manufacturers were used to determine the precise orbits of BDS-2 satellites from day of year 154 to 163, 2017. The accuracy of orbit overlap and satellite laser ranging (SLR) residual validation comparisons show that by implementing inter-receiver pseudorange bias corrections, the POD accuracies of the BDS-2 satellites can be effectively improved. The root mean square errors of 24-h precise orbit determination overlap corresponding to the radial, cross-track, and along-track components are improved by 1.4%, 2.7%, and 12.7%, respectively, after correcting the inter-receiver pseudorange biases. The standard deviations of the SLR residuals of satellite C01, C13, and C11 are reduced from 30.7, 7.1, and 3.5 cm to 30.2, 6.8, and 2.9 cm, respectively. The results also showed that inter-receiver pseudorange biases will cause an along-track bias in Geostationary Earth Orbit (GEO) satellite orbit determination. The performances of GEO POD in along-track component can be improved by considering the inter-receiver pseudorange biases.

Analysis of real-time multi-GNSS satellite products of Wuhan University for rapid response of precise positioning

When users need to quickly process GNSS data, they often need the satellite orbit and clock products with the minimum latency and the highest precision, and it is a good solution to receive the real-time satellite RTCM SSR correction stream to recover the precise satellite orbit and clock products in real time and then store them in an offline repository for rapid response of precise positioning. In this paper, the real-time multi-GNSS orbit and clock RTCM SSR correction stream broadcast by SSRC00WHU0 mountpoint of Wuhan University is used to recover precise satellite orbit and clock products in real time. First, the seven-day orbit files and clock files were obtained and stored locally, and compared with the final MGEX precise satellite orbit and clock products. The results show that the real-time orbit and clock products of GPS and Galileo satellites have the best accuracy, followed by GLONASS satellites and BDS satellites. The real-time orbit products can reach the accuracy level of 5 cm for GPS satellites, 8 cm for Galileo satellites, 15 cm for GLONASS satellites and 16 cm for BDS-3 satellites, and the real-time clock products can reach the accuracy level of 0.43 ns for GPS satellites, 0.44 ns for Galileo satellites, 0.91 ns for GLONASS satellites and 3.14 ns for BDS satellites. Then, the observation data of 20 IGS stations randomly distributed around the world from DOY 150 to 156 in 2021 were processed by static precise point positioning (PPP) mode using the recovered real-time products. The results show that the average positioning accuracy can reach 1.57 cm, 0.76 cm and 1.67 cm in east, north and up direction for static PPP, respectively. Finally, using the recovered real-time products and the final products, the GPS observation data collected in aviation were processed in pseudo real-time in a kinematic mode. The results show that the RMSs of positioning errors are 8.5 cm, 2.4 cm and 16.5 cm in the east, north and up direction, respectively. In addition, one-day multi-GNSS observation data at 20 IGS stations were processed in a kinematic PPP mode, and the results show that the average positioning accuracy is 3.11 cm, 2.04 cm and 4.94 cm in east, north and up directions.

Responses of Thermospheric Mass Densities to the October 2016 and September 2017 Geomagnetic Storms Revealed From Multiple Satellite Observations

AbstractIn this study, the thermospheric mass densities based on satellite Precise Orbit Determination (POD) data from Gravity Recovery and Climate Experiment (GRACE), Swarm‐A, and Swarm‐B were used to explore the thermospheric variations in response to the October 2016 and September 2017 geomagnetic storms which occurred around the equinox. Two of the three satellites were nearly coplanar and the third one flew at a separated orbital plane. Based on the nearly coplanar observations of GRACE and Swarm, the thermospheric mass densities showed different hemispheric asymmetries depending on altitudes. The observations from different local times (LTs) revealed that the density enhancements were similar between the two hemispheres when the LTs were 8–10/20–22 LTs. However, the enhancements were stronger in the southern hemisphere than those in the northern hemisphere at around 16 LT. Moreover, the density enhancements at low latitudes underwent significant day‐night variation as the daytime densities at low latitudes increased more rapidly and strongly than the nightside. Our results demonstrated that the satellite POD data could be used to retrieve high‐cadence thermospheric density to study the variations of the upper atmosphere.

Satellite precise orbit determination with ionospheric-free strategy using triple-frequency observations

Satellite precise orbit determination with ionospheric-free strategy using triple-frequency observations

Performance Assessment of PPP Surveys with Open Source Software Using the GNSS GPS–GLONASS–Galileo Constellations

In this work, the performance of the multi-GNSS (Global Navigation Satellite System) Precise Point Positioning (PPP) technique, in static mode, is analyzed. Specifically, GPS (Global Positioning System), GLONASS, and Galileo systems are considered, and quantifying the Galileo contribution is one of the main objectives. The open source software RTKLib is adopted to process the data, with precise satellite orbits and clocks from CNES (Centre National d’Etudes Spatiales) and CLS (Collecte Localisation Satellites) analysis centers for International GNSS Service (IGS). The Iono-free model is used to correct ionospheric errors, the GOT-4.7 model is used to correct tidal effects, and Differential Code Biases (DCB) are taken from the Deutsche Forschungsanstalt für Luftund Raumfahrt (DLR) center. Two different tropospheric models are tested: Saastamoinen and Estimate ZTD (Zenith Troposhperic Delay). For the proposed study, a dataset of 31 days from a permanent GNSS station, placed in Palermo (Italy), and a dataset of 10 days from a static geodetic receiver, placed nearby the station, have been collected and processed by the most used open source software in the geomatic community. The considered GNSS configurations are seven: GPS only, GLONASS only, Galileo only, GPS+GLONASS, GPS+Galileo, GLONASS+Galileo, and GPS+GLONASS+Galileo. The results show significant performance improvement of the GNSS combinations with respect to single GNSS cases.

Evidence for Drag Coefficient Modeling Errors near and Above the Oxygen-to-Helium Transition

The ability to model atmospheric drag is critical for precise satellite orbit prediction below 1000 km altitudes. Uncertainty in atmospheric drag comes primarily from estimates of the atmospheric mass density and the spacecraft drag coefficient. Mismodeling the drag coefficient introduces errors in densities derived from atmospheric drag that are then used to predict drag forces and satellite orbits. Drag coefficient models are based on assumptions about the energy and momentum exchange between the atmospheric gas and the satellite surface, and the associated interaction parameters are the main source of uncertainty. In this work, some of these assumptions are evaluated by comparing the aerodynamic drag on satellites of different shapes. Atmospheric densities derived for Gravity Recovery and Climate Experiment (GRACE) and a set of compact satellites within a scale height of GRACE are normalized to an atmospheric model and compared. Offsets in these derived densities can be attributed to drag coefficient modeling assumptions. Results indicate that current drag coefficient models lead to normalized derived density differences of up to in low-pressure, high-altitude atmospheres nearing the oxygen-to-helium transition region. Consequently, current drag coefficient assumptions may lead to drag-derived mass densities that are underestimated by up to 35% at and above 500 km altitudes.

Ambiguity of Residual Constraint-Based Precise Point Positioning with Partial Ambiguity Resolution under No Real-Time Network Corrections Using Real Global Positioning System (GPS) Data.

Although precise point positioning (PPP) is a well-established and promising technique with the use of precise satellite orbit and clock products, it costs a long convergence time to reach a centimeter-level positioning accuracy. The PPP with ambiguity resolution (PPP-AR) technique can improve convergence performance by resolving ambiguities after separating the fractional cycle bias (FCB). Now the FCB estimation is mainly realized by the regional or global operating reference station network. However, it does not work well in the areas where network resources are scarce. The contribution of this paper is to realize an ambiguity residual constraint-based PPP with partial ambiguity resolution (PPP-PARC) under no real-time network corrections to speed up the convergence, especially when the performance of the float solution is poor. More specifically, the update strategy of FCB estimation in a stand-alone receiver is proposed to realize the PPP-PAR. Thereafter, the solving process of FCB in a stand-alone receiver is summarized. Meanwhile, the influencing factors of the ambiguity success rate in the PPP-PAR without network corrections are analyzed. Meanwhile, the ambiguity residual constraint is added to adapt the particularity of the partial ambiguity-fixing without network corrections. Moreover, the positioning experiments with raw observation data at the Global Positioning System (GPS) globally distributed reference stations are conducted to determine the ambiguity residual threshold for post-processing and real-time scenarios. Finally, the positioning performance was verified by 22 GPS reference stations. The results show that convergence time is reduced by 15.8% and 26.4% in post-processing and real-time scenarios, respectively, when the float solution is unstable, compared with PPP using a float solution. However, if the float solution is stable, the PPP-PARC method has performance similar to the float solution. The method shows the significance of the PPP-PARC for future PPP applications in areas where network resource is deficient.

An Improved Method Using SINS/PPP Method for Land Vehicle Gravimetry

Differential GNSS has been successfully applied in the SINS/GNSS vehicle gravity measurement method over the past few decades. However, GNSS error source has the spatio-temporal correlation in the differential mode. The navigation resource utilization efficiency is degraded due to the limitation of the baseline distance and the satellite common view. Using only one satellite receiver with high precision satellite orbit parameters and clock parameters, establishing navigation error models and parameter estimation methods, and obtaining high-precision receiver dynamic positioning, Precise Point Positioning (PPP) is a promising non-differential mode GNSS technique. The advantages of PPP are that it is simple to operate, low in cost, and not limited by the requirements for establishing a base station. This paper presents an SINS/PPP method for land vehicle gravimetry. Based on the strapdown gravimeter SGA-WZ02 developed by the National University of Defense Technology (NUDT), a land vehicle gravimetry test was carried out on a road about 36 kilometres long. The test consists of four measuring lines back and forth in the north-south direction with an average speed of 40km/h. Using this method, the internal accuracy of four repeated lines is 0.52mGal/0.9km. Compared with the results obtained by traditional SINS/GNSS method, the internal accuracy is 0.51mGal/0.9km, which shows that the accuracy calculated by SINS/PPP method is comparable to the results calculated by SINS/DGNSS method. Practical gravimetry results indicate that the proposed SINS/PPP method in this paper can meet the requirements of vehicle gravimetry under ideal GNSS observation conditions, and the feasibility of PPP technology for vehicle gravimetry is verified. Finally, some discussions and suggestions about the applicability of the method and its further improvement are put forward.