Receiver Clock Offsets Research Articles

Regional multi-station real-time time transfer using an undifferenced multi-GNSS network solution

Real-time time transfer is the basis for the time synchronization and establishment and maintenance of time scales. In this contribution, we present a regional multi-station real-time time transfer approach, in which observations from multi-global navigation satellite system (GNSS) received at regional multi-station are integrated to conduct an undifferenced network solution. Consequently, the simultaneous estimation of receiver clock offsets for multiple stations becomes possible, enabling the execution of real-time time transfer. One week of observation data from five multi-GNSS Experiment (MGEX) stations located in Europe are selected to generate four links (distances from 919.7 to 2153.4 km), and four schemes are designed, i.e., GPS-only, BDS-3-only, Galileo-only, and GPS/BDS-3/Galileo (GCE) solutions, respectively. Experiment results show that the mean number of observations, time dilution of precision (TDOP) values, and standard deviation (STD) of clock offset difference time series between the Center for Orbit Determination in Europe (CODE) and the estimated solutions for four time links are 90, 76, 72, 239 and 0.34, 0.38, 0.39, 0.21 and 0.039, 0.050, 0.043, 0.036 ns for GPS-only, BDS-3-only, Galileo-only, and GCE solutions, respectively. When the averaging time is shorter than 7680 s, the frequency stability of GCE solutions shows the best performance. The mean frequency stability of four time links at 7680 s is 6.59 × 10–15,7.25 × 10–15, 6.88 × 10–15 and 5.96 × 10–15 for GPS-only, BDS-3-only, Galileo-only, and GCE solutions, respectively. The GCE solution shows the best performance among the four schemes in terms of the number of observations, TDOP, STD, and frequency stability. The experiment results demonstrate that this approach is suitable for regional multi-station real-time time transfer.

BDS-3 full-frequency precise point positioning: models and performance comparison

With the BDS-3 six-frequency integration, there are more choices to implement the precise point positioning (PPP) technology. To take full advantage of the multi-frequency combination, six typical BDS-3 six-frequency PPP models using uncombined observation (UC), five dual-frequency ionospheric-free (IF) combinations (IF2), four triple-frequency IF combinations (IF3), three four-frequency IF combinations (IF4), two five-frequency IF combinations (IF5), and a single six-frequency IF combination (IF6) were constructed and compared. The results indicate that the positioning accuracies of the six models are similar. The static positioning accuracies reach 4, 3–5, and 12–14 mm in the east, north, and up directions, respectively, while the kinematic positioning accuracies are 24–26, 16–17, and 42–43 mm, respectively. Regarding the convergence times, the UC model is slightly worse than the five IF combined models, except for some cases in the up direction. In the static mode, benefiting from the smallest noise amplification factor, the average convergence times of the IF6 model are the shortest, reaching 12.1, 5.5, and 13.4 min in the three directions, respectively, and are 7%, 15%, and 6% shorter than those of the UC model. In the kinematic mode, with the combination of more signals into a single IF combination, the noise level of the IF combined observables gradually decreases, but the convergence times gradually increase. The kinematic average convergence times of the IF2 model are 15.3, 3.6, and 18.0 min in the three directions, which are 6%, 22%, and 10% and 1%, 16%, and 20% shorter than those of the UC and IF6 models, respectively. In addition, the observation residuals, and the estimates of inter-frequency bias, tropospheric zenith wet delay, and receiver clock offsets from different models were compared and analyzed. The specific selection of the model should be based on actual situations.

Precise orbit determination for TH02-02 satellites based on BDS3 and GPS observations

The Tianhui-2 02 (TH02-02) satellite formation, as a supplement to the microwave mapping satellite system Tianhui-2 01 (TH02-01), is the first Interferometric Synthetic Aperture Radar (InSAR) satellite formation-flying system that supports the tracking of BeiDou global navigation Satellite system (BDS3) new B1C and B2a signals. Meanwhile, the twin TH02-02 satellites also support the tracking of Global Positioning System (GPS) L1&L2 and BDS B1I&B3I signals. As the spaceborne receiver employs two independent boards to track the Global Navigation Satellite System (GNSS) satellites, we design an orbit determination strategy by estimating independent receiver clock offsets epoch by epoch for each GNSS to realize the multi-GNSS data fusion from different boards. The performance of the spaceborne receiver is evaluated and the contribution of BDS3 to the kinematic and reduced-dynamic Precise Orbit Determination (POD) of TH02-02 satellites is investigated. The tracking data onboard shows that the average number of available BDS3 and GPS satellites are 8.7 and 9.1, respectively. The carrier-to-noise ratio and carrier phase noise of BDS3 B1C and B2a signals are comparable to those of GPS. However, strong azimuth-related systematic biases are recognized in the pseudorange multipath errors of B1C and B3I. The pseudorange noise of BDS3 signals is better than that of GPS after eliminating the multipath errors from specific signals. Taking the GPS-based reduced-dynamic orbit with single-receiver ambiguity fixing technique as a reference, the results of BDS3-only and BDS3 + GPS combined POD are assessed. The Root Mean Square (RMS) of orbit comparison of BDS3-based kinematic and reduced-dynamic POD with reference orbit are better than 7 cm and 3 cm in three-Dimensional direction (3D). The POD performance based on B1C&B2a data is comparable to that based on B1I&B3I. The precision of BDS3 + GPS combined kinematic orbit can reach up to 3 cm (3D RMS), which has a more than 25% improvement relative to the GPS-only solution. In addition, the consistency between the BDS3 + GPS combined reduced-dynamic orbit and the GPS-based ambiguity-fixed orbit is better than 1.5 cm (3D RMS).

UTC and GNSS system time access using PPP with broadcast ephemerides

The application of precise point positioning with broadcast ephemerides (PPP-BCE) is discussed as an alternative to the established all-in-view technique for multi-GNSS time transfer. It combines the use of broadcast ephemerides with low-noise carrier-phase observations for accessing GNSS system time scales and Coordinated Universal Time (UTC) with improved precision, and can be employed on stationary as well as mobile receivers in offline or real-time analyses. Using calibrated timing receivers, the method is shown to provide estimates of the GNSS-to-GNSS time offsets (XYTOs) with an accuracy at the 2 ns level. In the absence of prior calibrations, 0.5 ns consistency across different stations is achieved for GPS, Galileo, and BeiDou-3 after adjustment of systematic biases in comparison with calibrated reference stations or broadcast XYTO values. Furthermore, access to GNSS-specific UTC realizations can be obtained through predictions of the UTC offset from GNSS system time as provided in the broadcast ephemerides of individual constellations. The overall quality of the PPP-BCE-derived receiver clock offsets from UTC is assessed using calibrated receivers at various timing laboratories along with BIPM-provided UTC-UTC(k) measurements. Over the 1.5 years covered in the study, an accuracy of 1.8 ns for GPS and 2.5 ns for Galileo is demonstrated. For BeiDou, a slightly worse accuracy of 3 ns is obtained for a single timing laboratory over 9 months.

GNSS time and frequency transfers through national positioning, navigation and timing infrastructure

Abstract GNSS signals have been a practical time transfer tool to realise a Coordinated Universal Time (UTC) and set civilian clocks around the world with respect to this atomic time standard. UTC time scale is maintained by the International Bureau of Weights and Measurements (BIPM) adjusted to be close to a time scale based on the Earth’s rotation. In Thailand, the official atomic time clocks are maintained by the National Institute of Metrology Thailand (NIMT) to produce UTC(NIMT) and Thailand standard time which is always 7 hours ahead of UTC(NIMT) because of the time zone differences between Greenwich and Bangkok. National Positioning, Navigation and Timing (PNT) infrastructure comprises of GNSS geodetic receivers uniformly distributed to continually observe GNSS signals, mainly for geodetic survey applications both real-time and post-processing services. NIMT is involved in order to provide time link to UTC and to determine the characteristics of GNSS receiver internal clocks; namely, fractional frequency offset and frequency stabilities by applying the GNSS time transfer techniques of common-view algorithms. Monitored time differences with respect to UTC(NIMT) are achieved from selected 4 ground stations in different parts of the country with observations of 21 days in order to determine the frequency stability at 1-day and 7-day modes. GNSS standard log files; in RINEX format, at these receivers are transformed into a time transfer standard format; CGGTTS, used to compute the time differences between two stations, the fractional frequency offset and the frequency stability. Averaged fractional frequency offsets are 2.8 × 10 − 13 Hertz/Hertz 2.8\times {10^{-13}}\hspace{2.38387pt}\text{Hertz/Hertz} and computed Allan deviation is around 1.5 × 10 − 13 Hertz/Hertz 1.5\times {10^{-13}}\hspace{2.38387pt}\text{Hertz/Hertz} for an averaging time of 1 day. The comparison of the national time scale and receiver clock offsets of every receivers in this national GNSS PNT infrastructure could be accomplished through common-view time transfer using GNSS satellites to maintain the time link of geodetic active control points to UTC as well as to determine receiver internal clock characteristics.

Precise Orbit Determination and Maneuver Assessment for TH-2 Satellites Using Spaceborne GPS and BDS2 Observations

The TH-2 satellite system, including the TH-2A and TH-2B, is the first distributed interferometric synthetic aperture radar (InSAR) satellite system in China. During the in-orbit operation, the TH-2A satellite should perform three maneuvers per day to keep the formation flying geometry. We estimate those maneuvers in the precise orbit determination (POD) by the GPS and BDS2 measurements on board, respectively. The residuals of the POD show that the effects caused by orbital maneuvers can be well eliminated for both the GPS and BDS2 data. The precision of the BDS2-based POD is better than 8.0 cm in the three-dimensional direction (3D) compared with the orbit derived from the GPS observations. Such a precision level of the satellite orbit satisfies the InSAR mission requirement of the TH-2. In addition, the relative error of velocity changes is employed to evaluate the maneuver estimations by the POD using the regional navigation system of BDS2. The results show that the relative error of velocity changes between the GPS- and BDS2-based POD is less than 7.0%, which indicates that the maneuver performance extracted from the regional BDS2 data is as good as that extracted from the global GPS data. In the GNSS fused processing, we found that the independent receiver clock offsets should be taken into account, since the time tag corrections for the GPS and BDS2 observations collected on the TH-2 spaceborne receivers were different. The precision of the GPS and BDS2 (GC) combined single point positioning (SPP) can be improved by 12–14% compared with the GPS-only solution when the position dilution of precision (PDOP) of GPS exceeds three. The overlap comparisons of the GC combined orbits show that the internal orbit precision of the TH-2 satellites is better than 0.7 cm. However, the improvement of the GC combined POD result is only 3–4% with respect to the GPS-only solution, which is limited to the precision of the precise orbit and clock products of BDS2 at the present stage.

Functional model modification of precise point positioning considering the time-varying code biases of a receiver

Precise Point Positioning (PPP), initially developed for the analysis of the Global Positing System (GPS) data from a large geodetic network, gradually becomes an effective tool for positioning, timing, remote sensing of atmospheric water vapor, and monitoring of Earth’s ionospheric Total Electron Content (TEC). The previous studies implicitly assumed that the receiver code biases stay constant over time in formulating the functional model of PPP. In this contribution, it is shown this assumption is not always valid and can lead to the degradation of PPP performance, especially for Slant TEC (STEC) retrieval and timing. For this reason, the PPP functional model is modified by taking into account the time-varying receiver code biases of the two frequencies. It is different from the Modified Carrier-to-Code Leveling (MCCL) method which can only obtain the variations of Receiver Differential Code Biases (RDCBs), i.e., the difference between the two frequencies’ code biases. In the Modified PPP (MPPP) model, the temporal variations of the receiver code biases become estimable and their adverse impacts on PPP parameters, such as ambiguity parameters, receiver clock offsets, and ionospheric delays, are mitigated. This is confirmed by undertaking numerical tests based on the real dual-frequency GPS data from a set of global continuously operating reference stations. The results imply that the variations of receiver code biases exhibit a correlation with the ambient temperature. With the modified functional model, an improvement by 42% to 96% is achieved in the Differences of STEC (DSTEC) compared to the original PPP model with regard to the reference values of those derived from the Geometry-Free (GF) carrier phase observations. The medium and long term (1 × 104 to 1.5 × 104 s) frequency stability of receiver clocks are also significantly improved.

SUPREME: an open-source single-frequency uncombined precise point positioning software

With the rapid development of Global Navigation Satellite Systems (GNSS), precise point positioning (PPP) has been widely used for positioning, navigation, timing (PNT), and atmospheric sensing. Currently, the demand for low-cost single-frequency hardware is increasing. However, open-source single-frequency PPP (SFPPP) software, in particular those that employ uncombined GNSS observations, is scarce. In view of this fact, we developed an open-source software, called Single-frequency Uncombined PREcise point positioning for Multi-parameter Estimation (SUPREME), which can process multi-GNSS observations collected from a low-cost single-frequency receiver. It can simultaneously estimate receiver coordinates, receiver clock offsets, zenith tropospheric delays, and ionospheric delays utilizing a least-squares filter. SUPREME is developed in the C/C++ computer language; thus, it has good portability and cross-platform capability. The formatted output is also beneficial for the post-analysis of results. We evaluated SUPREME using several experiments based on real single-frequency data, and the results indicate that it provides high accuracy and robust performance.

Modeling and Analysis of BDS-2 and BDS-3 Combined Precise Time and Frequency Transfer Considering Stochastic Models of Inter-System Bias

BeiDou global navigation satellite system (BDS) began to provide positioning, navigation, and timing (PNT) services to global users officially on 31 July, 2020. BDS constellations consist of regional (BDS-2) and global navigation satellites (BDS-3). Due to the difference of modulations and characteristics for the BDS-2 and BDS-3 default civil service signals (B1I/B3I) and the increase of new signals (B1C/B2a) for BDS-3, a systemically bias exists in the receiver-end when receiving and processing BDS-2 and BDS-3 signals, which leads to the inter-system bias (ISB) between BDS-2 and BDS-3 on the receiver side. To fully utilize BDS, the BDS-2 and BDS-3 combined precise time and frequency transfer are investigated considering the effect of the ISB. Four kinds of ISB stochastic models are presented, which are ignoring ISB (ISBNO), estimating ISB as random constant (ISBCV), random walk process (ISBRW), and white noise process (ISBWN). The results demonstrate that the datum of receiver clock offsets can be unified and the ISB deduced datum confusion can be avoided by estimating the ISB. The ISBCV and ISBRW models are superior to ISBWN. For the BDS-2 and BDS-3 combined precise time and frequency transfer using ISBNO, ISBCV, ISBRW, and ISBWN, the stability of clock differences of old signals can be enhanced by 20.18%, 23.89%, 23.96%, and 11.46% over BDS-2-only, respectively. For new signals, the enhancements are −50.77%, 20.22%, 17.53%, and −3.69%, respectively. Moreover, ISBCV and ISBRW models have the better frequency transfer stability. Consequently, we recommended the optimal ISBCV or suboptimal ISBRW model for BDS-2 and BDS-3 combined precise time and frequency transfer when processing the old as well as the new signals.

Removing day-boundary discontinuities on GNSS clock estimates: methodology and results

Global navigation satellite system (GNSS) satellites are equipped with very stable atomic clocks that can be used for assessing the models and strategies involved in the estimation processes, where the clock estimates should present high stability. For instance, GNSS products (including satellite and receiver clocks) are computed on daily basis, i.e., with the data of each day being processed independently from other days. This choice produces the well-known day-boundary discontinuities (DBDs) on clock estimates that stem from the estimation process, rather than to the nature of the atomic clock itself. The aim of the present contribution is to propose a strategy to estimate the satellite and receiver clock offsets that is capable to reduce the DBDs observed in the products of different analysis centers (ACs) within the International GNSS Service (IGS), ultimately improving the accuracy of clock estimates. Our approach relies on the use of unambiguous, undifferenced and uncombined carrier phase measurements collected by a network of permanent receivers on ground. The strategy considers the carrier phase hardware delays and assumes their possible variations along time. Our daily data processing aims to maintaining the natural continuity over days of the carrier phase measurements after integer ambiguity resolution (IAR), even if IAR is performed on daily batches. We compare our clock estimations with those computed by different IGS ACs, evaluating the linear behavior of the satellite atomic clocks on the day change. The results show the removal of DBD on clock estimates computed with the continuous and unambiguous carrier phase measurements. This DBD improvement may benefit the statistical characterization of long-term phenomena correlated with the on-board clocks.

Higher order ionospheric delay and derivation of regional total electron content over Ethiopian global positioning system stations

The Global Positioning System (GPS) is a space-based radio positioning system which is capable of providing continuous position, velocity and time information to users anywhere on, or near, the surface of the Earth. The positional accuracy of GPS is limited by several sources of error, such as satellite and receiver clock offsets, signal propagation delays (due to the ionosphere and troposphere), multipath, receiver measurement noise, and instrument bias. The ionospheric delay is the predominant error source. The main objective of this work was to estimate the regional vertical Total Electron Content (vTEC) densities, using a linear combination of L1 and L2 carrier phase for higher order time delays at different thin-shell layers of the ionosphere (i.e. 60 km, 90 km, 150 km, 200 km and 450 km) over GPS stations in Ethiopia. Due to the high equatorial ionization anomaly and irregularity of the electron density distribution, we selected four GPS stations across the country. We studied longitudinal, latitudinal, and altitudinal variations in the ionosphere using GPS observables extracted by precise geodetic GAMIT-GLOBK software package. We obtained data from the 2013 to 2015 period for all stations. For daily data processing in GAMIT, we switched the International Geomagnetic Reference Field 2012 (IGRF-12) model (which consists of spherical harmonic coefficients) on and off, representing the Earth’s main field and its secular variation and ionospheric electron content along the signal path (available from the Centre for Orbit Determination in Europe (CODE)).Our results confirmed that there is latitudinal, longitudinal and altitudinal variation in the ionosphere. The density of total electron content and GPS positional error due to higher-order time delays have a positive correlation (more than 95%). The positional error, due to the higher order ionospheric delay, exceeds 4 mm for all GPS stations and reached up to 8 mm. Finally, we observed that the time delay due to the higher-order ionospheric effect in the L2 signal is twice that in the L1.We conclude that the GPS signal is affected by the higher order ionospheric delay by up to several centimetres due to its electron content and the Earth’s magnetic field.

MG-APP: an open-source software for multi-GNSS precise point positioning and application analysis

To meet the demands of research and precise point positioning (PPP) in a multi-GNSS environment, we developed a GNSS data processing software named multi-GNSS automatic precise positioning software (MG-APP). MG-APP is an open-source software that can be run on Windows/Linux/UNIX and other operating systems. It can simultaneously process GPS/GLONASS/BDS/Galileo observations using a Kalman filter or a square root information filter (SRIF). Compared to the Kalman filter, the SRIF has better numerical stability and maintains stable convergence even with a significant round-off error. MG-APP has a comprehensive and friendly graphical user interface that conveniently allows the user to select models and set parameters. It also contains several types of tropospheric and estimation models that make it easy to analyze the impact of different models and parameters on PPP data processing. After the data processing finishes, zenith tropospheric delays, receiver clock offsets, satellite ambiguity parameters, observation residuals, and other results will be saved into files. Users can further analyze the solution results and construct graphs easily.

Mitigation of Short-Term Temporal Variations of Receiver Code Bias to Achieve Increased Success Rate of Ambiguity Resolution in PPP

Ambiguity resolution (AR) is critical for achieving a fast, high-precision solution in precise point positioning (PPP). In the standard uncombined PPP (S-UPPP) method, ionosphere-free code biases are superimposed by ambiguity and receiver clock offsets to be estimated. However, besides the time-constant part of the receiver code bias, the complex and time-varying term in receivers destroy the stability of ambiguities and degrade the performance of the UPPP AR. The variation of receiver code bias can be confirmed by the analysis in terms of ionospheric observables, code multipath (MP) of the Melbourne–Wübbena (MW) combination and the ionosphere-free combination. Therefore, the effect of receiver code biases should be rigorously mitigated. We introduce a modified UPPP (M-UPPP) method to reduce the effects of receiver code biases in ambiguities and to decouple the correlation between receiver clock parameters, code biases, and ambiguities parameters. An extra receiver code bias is set to isolate the code biases from ambiguities. The more stable ambiguities without code biases are expected to achieve a higher success rate of ambiguity resolution and a shortened convergence time. The variations of the receiver code biases, which are the unmodeled errors in measurement residuals of the S-UPPP method, can be estimated in the M-UPPP method. The maximum variation of the code biases is up to 16 ns within two-hour data. In the M-UPPP method, the averaged epoch residuals for code and phase measurements recover their zero-mean features. For the ambiguity-fixed solutions in the M-UPPP method, the convergence times are 14 and 43 min with 17.7% and 69.2% improvements compared to that in the S-UPPP method which are 17 and 90 min under the 68% and 95% confidence levels.

Performance of Multi-GNSS Precise Point Positioning Time and Frequency Transfer with Clock Modeling

Thanks to the international GNSS service (IGS), which has provided multi-GNSS precise products, multi-GNSS precise point positioning (PPP) time and frequency transfer has of great interest in the timing community. Currently, multi-GNSS PPP time transfer is not investigated with different precise products. In addition, the correlation of the receiver clock offsets between adjacent epochs has not been studied in multi-GNSS PPP. In this work, multi-GNSS PPP time and frequency with different precise products is first compared in detail. A receiver clock offset model, considering the correlation of the receiver clock offsets between adjacent epochs using an a priori value, is then employed to improve multi-GNSS PPP time and frequency (scheme2). Our numerical analysis clarify how the approach performs for multi-GNSS PPP time and frequency transfer. Based on two commonly used multi-GNSS products and six GNSS stations, three conclusions are obtained straightforwardly. First, the GPS-only, Galileo-only, and multi-GNSS PPP solutions show similar performances using GBM and COD products, while BDS-only PPP using GBM products is better than that using COD products. Second, multi-GNSS time transfer outperforms single GNSS by increasing the number of available satellites and improving the time dilution of precision. For single-system and multi-GNSS PPP with GBM products, the maximum improvement in root mean square (RMS) values for multi-GNSS solutions are up to 7.4%, 94.0%, and 57.3% compared to GPS-only, BDS-only, and Galileo-only solutions, respectively. For stability, the maximum improvement of multi-GNSS is 20.3%, 84%, and 45.4% compared to GPS-only, BDS-only and Galileo-only solutions. Third, our approach contains less noise compared to the solutions with the white noise model, both for the single-system model and the multi-GNSS model. The RMS values of our approach are improved by 37.8–91.9%, 10.5–65.8%, 2.7–43.1%, and 26.6–86.0% for GPS-only, BDS-only, Galileo-only, and multi-GNSS solutions. For frequency stability, the improvement of scheme2 ranges from 0.2 to 51.6%, from 3 to 80.0%, from 0.2 to 70.8%, and from 0.1 to 51.5% for GPS-only, BDS-only, Galileo-only, and multi-GNSS PPP solutions compared to the solutions with the white noise model in the Eurasia links.

Enhancing real-time precise point positioning time and frequency transfer with receiver clock modeling

Thanks to the international GNSS service (IGS), which has provided an open-access real-time service (RTS) since 2013, real-time precise point positioning (RT-PPP) has become a major topic in the time community. Currently, a few scholars have studied RT-PPP time transfer, and the correlation of the receiver clock offsets between adjacent epochs have not been considered. We present a receiver clock offset model that considers the correlation of the receiver clock offsets between adjacent epochs using an a priori value. The clock offset is estimated using a between-epoch constraint model rather than a white noise model. This approach is based on two steps. First, the a priori noise variance is based on the Allan variance of the receiver clock offset derived from GPS PPP solutions with IGS final products. Second, by applying the between-epoch constraint model, the RT-PPP time transfer is achieved. Our numerical analyses clarify how the approach performs for RT-PPP time and frequency transfer. Based on five commonly used RTS products and six IGS stations, two conclusions are obtained straightforwardly. First, all RT-PPP solutions with different real-time products are capable of time transfer. The standard deviation (STD) values of the clock difference between the PPP solutions with respect to the IGS final clock products are less than 0.3 ns. Second, the STD values are reduced significantly by applying our approach. The reduction percent of STD values ranges from 4.0 to 35.5%. Moreover, the largest improvement ratio of frequency stability is 12 as compared to the solution of the white noise model. Note that the receiver clock offset from IGS final clock products is regarded as a reference.

Near real-time BDS GEO satellite orbit determination and maneuver analysis with reversed point positioning

The Geostationary Earth Orbit (GEO) satellite is a crucial part of the BeiDou Navigation Satellite System (BDS) constellation. However, due to various perturbation forces acting on the GEO satellite, it drifts gradually over time. Thus, frequent orbit maneuvers are required to maintain the satellite at its designed position. During the orbit maneuver and recovery periods, the orbit quality of the maneuvered satellite computed with broadcast navigation ephemeris will be significantly degraded. Furthermore, the conventional dynamic Precise Orbit Determination (POD) approach may not work well, because of a lack of publicly available satellite information for modeling the thrust forces. In this paper, a near real-time approach free of thrust forces modeling is proposed for BDS GEO satellite orbit determination and maneuver analysis based on the Reversed Point Positioning (RPP). First, the station coordinates and receiver clock offsets are estimated by GPS/BDS combined Single Point Positioning (SPP) with single-frequency phase-smoothed pseudorange observations. Then, with the fixed station coordinates and receiver clock offsets, the RPP method can be conducted to determine the GEO satellite orbits. When no orbit maneuvers occur, the proposed method can obtain orbit accuracies of 0.92, 2.74, and 8.30 m in the radial, along-track, and cross-track directions, respectively. The average orbit-only Signal-In-Space Range Error (SISRE) is 1.23 m, which is slightly poorer than that of the broadcast navigation ephemeris. Using four days of GEO maneuvered datasets, it is further demonstrated that the derived orbits can be employed to characterize the behaviors of GEO satellite maneuvers, such as the time span of the maneuver as well as the satellite thrusting accelerations. These results prove the efficiency of the proposed method for near real-time GEO satellite orbit determination during maneuvers.

NavIC receiver clock offsets estimation with common view master clock method

The current manuscript proposes a new methodology for receiver clock offset estimation in IRNSS (Indian Regional Navigation Satellite System) which is also known as NavIC (Navigation Indian Constellation). This new methodology has been designed by clubbing the master clock concept with the traditional common view time transfer method and therefore it has been named as Common View Master Clock Method (CVMCM). The proposed methodology is intended to share the reference time uniformly and precisely across all the receiver clocks of IRNSS. The IRNSS receivers equipped at IRIMS (IRNSS Range and Integrity Monitoring Stations) acquire IRNSS satellite signals and generate code and carrier phase measurements on L5 and S frequencies. For ease of convenience, this range measurements and broadcast navigation messages are converted to standard RINEX (Receiver Independent Exchange) format in the form of RINEX observation files and RINEX navigation files respectively. As IRNWT1 (IRNSS Network Time Facility Bangalore) has been directly fetched to IRIMS Bangalore we have chosen IRIMS Bangalore as the master (reference) station. This is followed by time offset estimation of all IRIMS with respect to IRIMS Bangalore using the CVMCM method. This proposed methodology reduces all the error sources in IRNSS signals and produces very accurate time offsets results for all IRIMS. This helps in maintaining IRNSS reference time very precisely across all IRIMS with a proper time steering, thereby revamping the process of time synchronization in NavIC. Analyses were performed which establishes the stability and credibility of our results. In the process, it also corrects almost all the error sources in NavIC signals.

GPS/GLONASS Combined Precise Point Positioning With the Modeling of Highly Stable Receiver Clock in the Application of Monitoring Active Seismic Deformation

AbstractThe high‐rate kinematic Precise Point Positioning (PPP) of the Global Navigation Satellite System has become an effective method for monitoring crustal deformation caused by earthquakes. In this contribution, the method of GPS/GLONASS PPP with the receiver clock modeling is applied in active seismic deformation monitoring for the first time. With the modeling method, the short‐term vertical positioning accuracy of 2–4 mm that usually cannot be obtained by standard PPP is achieved. Our PPP results confirm that the positioning accuracy is improved due to the increase of GLONASS observations compared to the GPS‐only solution. Based on the external seismic data and the high‐rate GPS/GLONASS data for the 2011 Japan earthquake and 2010 and 2015 Chile earthquakes, comparative analyses concerning receiver clock modeling are carried out. The results show that a high degree of decorrelation between the height position estimates and receiver clock offsets can be obtained by using the receiver clock modeling. The short‐term accuracy of the GPS‐based vertical displacements is improved to the level of about 4.4 mm, and the short‐term accuracy of better than 4 mm for the GPS/GLONASS‐combined vertical displacements is achievable. Furthermore, the weak vertical signals that are not detected by standard PPP can be captured with the modeling of highly stable receiver clock.

Precise Receiver Clock Offset Estimations According to Each Global Navigation Satellite Systems (GNSS) Timescales

Abstract Each GNSS constellation operates its own system times; namely, GPS system time (GPST), GLONASS system time (GLONASST), BeiDou system time (BDT) and Galileo system time (GST). They could be traced back to Coordinated Universal Time (UTC) scale and are aligned to GPST. This paper estimates the receiver clock offsets to three timescales: GPST, GLONASST and BDT. The two measurement scenarios use two identical multi-GNSS geodetic receivers connected to the same geodetic antenna through a splitter. One receiver is driven by its internal oscillators and another receiver is connected to the external frequency oscillators, caesium frequency standard, kept as the Thailand standard time scale at the National Institute of Metrology (Thailand) called UTC(NIMT). The three weeks data are observed at 30 seconds sample rate. The receiver clock offsets with respected to the three system time are estimated and analysed through the geodetic technique of static Precise Point Positioning (PPP) using a data processing software developed by Wuhan University - Positioning And Navigation Data Analyst (PANDA) software. The estimated receiver clock offsets are around 32, 33 and 18 nanoseconds from GPST, GLONASST and BDT respectively. This experiment is initially stated that each timescale is inter-operated with GPST and further measurements on receiver internal delay has to be determined for clock comparisons especially the high accuracy clock at timing laboratories.

Precise real-time navigation of LEO satellites using a single-frequency GPS receiver and ultra-rapid ephemerides

Precise (sub-meter level) real-time navigation using a space-capable single-frequency global positioning system (GPS) receiver and ultra-rapid (real-time) ephemerides from the international global navigation satellite systems service is proposed for low-Earth-orbiting (LEO) satellites. The C/A code and L1 carrier phase measurements are combined and single-differenced to eliminate first-order ionospheric effects and receiver clock offsets. A random-walk process is employed to model the phase ambiguities in order to absorb the time-varying and satellite-specific higher-order measurement errors as well as the GPS clock correction errors. A sequential Kalman filter which incorporates the known orbital dynamic model is developed to estimate orbital states and phase ambiguities without matrix inversion. Real flight data from the single-frequency GPS receiver onboard China's SJ-9A small satellite are processed to evaluate the orbit determination accuracy. Statistics from internal orbit assessments indicate that three-dimensional accuracies better than 0.50 m and 0.55 mm/s are achieved for position and velocity, respectively.