Satellite Clock Research Articles

MEVSİMSEL DEĞİŞİMLERİN HASSAS NOKTA KONUMLAMAYA ETKİSİ

Hassas Nokta Konumlama (Precise Point Positioning-PPP), tek bir GNSS alıcısıyla hassas uydu yörünge ve saat bilgilerini kullanarak santimetre doğruluğunda konum bilgisi sağlayan bir yöntemdir. Son zamanlarda bu yöntem pek çok bilimsel çalışmaya konu olmaktadır. Bu çalışmada, mevsimlerin PPP konum belirleme doğruluğu üzerindeki etkisini araştırmak amacıyla kuzey yarım kürede yer alan yüksek enlem (KIR8 (İsveç), NYA2 (Norveç)), orta enlem (ANKR(Türkiye), DLF1(Hollanda)) ve ekvatoral bölgede (NKLG(Gabon), SIN1(Singapur)) bulunan Uluslararası GNSS Servisi (International GNSS Service: IGS) istasyonları seçilmiştir. Seçilen istasyonlara ait 365 gün 24 saat 30 saniyelik RINEX verileri çözümlerde kullanılmak üzere elde edilmiştir. 01.12.2019-30.11.2020 tarihleri arasında elde edilen veriler çözümlerin yapılabildiği web tabanlı PPP servislerinden CSRS-PPP, MagicGNSS ve APPS ile değerlendirilmiştir. Web tabanlı servislerden elde edilen koordinatların hassasiyetlerini araştırmak amacıyla her ay için ortalama koordinat değerleri kullanılarak karesel ortalama hatalar (KOH) hesaplanmış, daha sonra mevsimlere bağlı doğrulukları ortaya koymak için istasyonların IGS’den temin edilen bilinen koordinatları kullanılarak konum ortalama hataları hesaplanmıştır. Aynı istasyonlar ve servisler için farklı mevsimlerde elde edilen konum ortalama hataları Bartlett testi ile karşılaştırılmıştır. Karşılaştırma sonunda ANKR istasyonu hariç diğer istasyonlarda konum ortalama hatalarının uyuşum içinde olduğu, konum doğruluklarının mevsimlerden ziyade kullanılan servislere bağlı olduğu ve en iyi sonuçların MagicGNSS ile elde edildiği görülmüştür.

PPP-RTK considering the ionosphere uncertainty with cross-validation

With the high-precision products of satellite orbit and clock, uncalibrated phase delay, and the atmosphere delay corrections, Precise Point Positioning (PPP) based on a Real-Time Kinematic (RTK) network is possible to rapidly achieve centimeter-level positioning accuracy. In the ionosphere-weighted PPP–RTK model, not only the a priori value of ionosphere but also its precision affect the convergence and accuracy of positioning. This study proposes a method to determine the precision of the interpolated slant ionospheric delay by cross-validation. The new method takes the high temporal and spatial variation into consideration. A distance-dependent function is built to represent the stochastic model of the slant ionospheric delay derived from each reference station, and an error model is built for each reference station on a five-minute piecewise basis. The user can interpolate ionospheric delay correction and the corresponding precision with an error function related to the distance and time of each reference station. With the European Reference Frame (EUREF) Permanent GNSS (Global Navigation Satellite Systems) network (EPN), and SONEL (Système d'Observation du Niveau des Eaux Littorales) GNSS stations covering most of Europe, the effectiveness of our wide-area ionosphere constraint method for PPP-RTK is validated, compared with the method with a fixed ionosphere precision threshold. It is shown that although the Root Mean Square (RMS) of the interpolated ionosphere error is within 5 cm in most of the areas, it exceeds 10 cm for some areas with sparse reference stations during some periods of time. The convergence time of the 90th percentile is 4.0 and 20.5 min for horizontal and vertical directions using Global Positioning System (GPS) kinematic solution, respectively, with the proposed method. This convergence is faster than those with the fixed ionosphere precision values of 1, 8, and 30 cm. The improvement with respect to the latter three solutions ranges from 10 to 60%. After integrating the Galileo navigation satellite system (Galileo), the convergence time of the 90th percentile for combined kinematic solutions is 2.0 and 9.0 min, with an improvement of 50.0% and 56.1% for horizontal and vertical directions, respectively, compared with the GPS-only solution. The average convergence time of GPS PPP-RTK for horizontal and vertical directions are 2.0 and 5.0 min, and those of GPS + Galileo PPP-RTK are 1.4 and 3.0 min, respectively.

Prediction of GPS Satellite Clock Offset Based on an Improved Particle Swarm Algorithm Optimized BP Neural Network

Satellite clock offset is an important factor affecting the accuracy of real-time precise point positioning (RT-PPP). Due to missing real-time service (RTS) products provided by the International GNSS Service (IGS) or network faults, users may not obtain effective real-time corrections, resulting in the unavailability of RT-PPP. Considering this issue, an improved back propagation (BP) neural network optimized by heterogeneous comprehensive learning and dynamic multi-swarm particle swarm optimizer (HPSO-BP) is proposed for clock offset prediction. The new model uses the particle swarm optimizer to optimize the initial parameters of the BP neural network, which can avoid the instability and over-fitting problems of the traditional BP neural network. IGS RTS product data is selected for the experimental analysis; the results demonstrate that the average prediction precision of the HPSO-BP model for 20-min and 60-min is better than 0.15 ns, improving by approximately 85% compared to traditional models including the linear polynomial (LP) model, the quadratic polynomial (QP) model, the gray system model (GM (1,1)), and the ARMA time series model. It indicates that the HPSO-BP model has reasonable practicability and stability in the short-term satellite clock offset prediction, and its prediction performance is superior to traditional models. Therefore, in practical applications, the clock offset products predicted by the HPSO-BP model can meet the centimeter-level positioning accuracy requirements of RT-PPP.

Enhancing Short-Term Prediction of BDS-3 Satellite Clock Bias Based with BSO Optimized BP Neural Network

The satellite clock bias (SCB) prediction plays an important role in high-accuracy and real-time navigation and positioning. When predicting the SCB, the performance of the BP neural network is affected by the local optimum due to inaccurate initial parameters. Therefore, we propose an improved BP neural network based on the beetle swarm optimization (BSO-BP) algorithm to improve the performance of SCB prediction in third-generation Beidou satellite navigation system (BDS-3). The proposed model takes advantage of group learning strategy to optimize the initialization parameters of the BP neural network and obtains globally optimized parameters. In order to verify the proposed BSO-BP model, 15 BDS satellites are analyzed in terms of prediction accuracy and stability of SCB. The experimental results show that when predicting 1 hour SCB based on a 12 hours SCB data, the prediction accuracy of the BSO-BP model is the best, with an average accuracy of 0.064 ns. As compared with the LP, QP, and GM models, the average prediction accuracy of the proposed BSO-BP model increases by about 72.6%, 43.4%, and 86%, respectively. As the prediction time increases, the influence of the inaccurate initial parameters on SCB prediction gradually decreases, and the prediction accuracy improves. The proposed BSO-BP model has the best accuracy and stability when predicting the 1 h SCB based on the same data. The prediction stability of the proposed BSO-BP model improves by more than 36% as compared with LP, QP, and GM models. In addition, the prediction accuracies of PHM clock and Rb-II clock improved by more than 47%, as compared with that of the Rb clock. Therefore, the overall performance of the atomic clock based on BDS-3 is better than BDS-2. The positioning accuracy of the BSO-BP model can reach the centimeter level in east, north, and up directions.

Double difference method with zero and short base length carrier phase measurements for Navigation with Indian Constellation satellites L5 (1176.45 MHz) signal quality analysis

SummaryThe carrier phase (CP) measurements should be unambiguous to achieve the enhanced accuracy of Global Navigation Satellite System (GNSS) services. However, all the real‐time CP measurements are manipulated by different errors, namely, satellite and receiver clock error, ionosphere delay, troposphere delay, integer ambiguity, etc. Even after removing or minimizing all these errors, the CP measurements are influenced by multipath error and receiver hardware residual or bias. In this research article, a double difference (DD) method is proposed to estimate residual or bias in CP observations of Navigation with Indian Constellation (NavIC). The proposed method abolishes all the common errors and provides bias. However, the CP measurement with a bit of bias value can be considered a high‐quality signal. Here, we investigate the quality of NavIC satellites L5 (1176.45 MHz) signal with real‐time measurements obtained through zero base length (ZBL) and short base length (SBL) experiments conducted at Kurnool (15.79°N, 78.07°E), India. The results show that the CP measurement bias of the L5 signal is within the range ±0.338 and ±1.688 m, respectively, for stationary and moving receivers. The bias was enhanced to 3.71 m for the SBL measurements. The results also demonstrate that the bias is low when carrier to noise (C/No) is high, and its range is nearly the same for all the days. This research would be helpful to estimate the bias that improves accuracy of precise point positioning (PPP) applications.

Principle and performance of BDSBAS and PPP-B2b of BDS-3

Within the framework of differential augmentation, this paper introduces the basic technical framework and performance of the BeiDou Global Navigation Satellite System (BDS-3) Satellite-Based Augmentation System (BDSBAS), including orbit products, satellite clock offset products, ionosphere and its integrity performance. The basic principle of BDS-3 Precise Point Positioning (PPP-B2b) is expounded, the similarities and differences between the PPP service provided by BDS-3 and International Global Navigation Satellite System (GNSS) Service (IGS) are discussed, and the limitations of PPP-B2b are analyzed. Since both the BDSBAS and PPP-B2b utilize a ground monitoring station network to determine the satellite orbits and clock offset corrections, and broadcast differential corrections through the three Geostationary Orbit (GEO) satellites of BDS-3, the feasibility of the co-construction of BDSBAS and PPP-B2b is analyzed, strategies for the infrastructure sharing and correction broadcasting are presented, and the influences of BDSBAS correction broadcasting strategy adjustment are evaluated. In addition, it assesses the possibility of broadcasting differential corrections through the Inclined Geosynchronous Orbit (IGSO) satellites of BDS-3, and the feasibility of augmenting satellite navigation with Low Earth Orbit (LEO) satellites.

Analysis of BDS-3 Onboard Clocks Based on GFZ Precise Clock Products

The characteristics and performance of satellite clocks are important to the positioning, navigation, and timing (PNT) services of Global Navigation Satellite System (GNSS) users. Although China’s BeiDou-3 Navigation Satellite System (BDS-3) has been fully operational for more than one year, there is still a lack of comprehensive research on the onboard clocks of the entire BDS-3 constellation. In this study, the precise clock products of GeoForschungsZentrum (GFZ) from day-of-year (DOY) 1, 2021 to DOY 300, 2021 were used to analyze the characteristics and performance of BDS-3 onboard clocks from the following aspects: clock bias, frequency, drift rate, fitting residuals, periodicity, and frequency stability. Compared with BDS-2, the clock quality of BDS-3 satellites has been greatly improved, but there are still jumps in the clock offsets and frequency series of BDS-3 clocks. The drift rate of BDS-3 clocks varies within the range between −2×10−18 and 2×10−18 s/s2. The daily model fitting residuals of passive hydrogen masers (PHM) on BDS-3 medium Earth orbit (MEO), inclined geosynchronous orbit (IGSO), and geostationary (GEO) satellites are 0.15, 0.28, and 0.46 ns, respectively. The overlapping Allan deviation (OADEV) of BDS-3 MEO clocks is 4.0 × 10−14 s/s at a time interval of 1000 s. The PHMs on BDS-3 MEO satellites exhibit fewer periodic signals than those of Rb clocks. In addition, the precise clock offsets of the BDS-3 PHMs carried on the MEO, IGSO, and GEO satellites show different periodicities, which are similar to those of the corresponding types of BDS-2 satellites.

Modeling wide-area tropospheric delay corrections for fast PPP ambiguity resolution

The performance of precise point positioning (PPP) has been significantly improved thanks to the continuous improvements in satellite orbit, clock, and ambiguity resolution (AR) technologies, but the convergence speed remains a limiting factor in real-time PPP applications. To improve the PPP precision and convergence time, tropospheric delays from a regional network can be modeled to provide precise correction for users. We focus on the precise modeling of zenith wet delay (ZWD) over a wide area with large altitude variations for improving PPP-AR. By exploiting the water vapor exponential vertical decrease, we develop a modified optimal fitting coefficients (MOFC) model based on the traditional optimal fitting coefficients (OFC) model. The proposed MOFC model provides a precision better than 1.5 cm under sparse inter-station distances over the Europe region, with a significant improvement of 70% for high-altitude stations compared to the OFC model. The MOFC model with different densities of reference stations is further evaluated in GPS and Galileo kinematic PPP-AR solutions. Compared to the PPP-AR solutions without tropospheric delay augmentation, the positioning precision of those with 100-km inter-station spacing MOFC and OFC is improved by 25.7% and 17.8%, respectively, and the corresponding time to first fix (TTFF) is improved by 36.9% and 33.0% in the high-altitude areas. On the other hand, the OFC model only slightly improves the TTFF and positioning accuracy when using the 200 km inter-station spacing modeling and even degrades the positioning for high-altitude stations, whereas using the MOFC model, the PPP-AR solutions always improve. Moreover, the positioning precision improvement of MOFC compared with OFC is about 22.1%, 21.7%, and 25.7% for the Galileo-only, GPS-only, and GPS + Galileo PPP-AR solutions, respectively.

Evaluation and mitigation of the influence of pseudorange biases on GNSS satellite clock offset estimation

The pseudorange bias inconsistencies are notably originating primarily from the individual chip shape distortions in the ranging signals, these distortions cause different shifts of the correlator’s tracking point for receivers, as a result giving rise to a different pseudorange bias for each pseudorange observation. The different bias should be properly dealt with in the process of satellite clock offset estimation when receivers of mixed types are used. In this work, using observations from 140 international global navigation satellite system (GNSS) service stations, the pseudorange bias was calculated, and the effect of inconsistent biases on satellite clock offset estimation from different receiver networks was investigated. The inconsistencies between the GPS satellites were ranging from −6 ns to 4 ns. For GALILEO and BDS, the biases are significant, ranging from −20 ns to 40 ns and −60 ns to 40 ns, respectively. The biases of the individual satellites are receiver-related and statistically stable from day to day. The influence of pseudorange bias was strikingly noticeable, and can improve the accuracy of the estimated clock offset by several ps for GPS; and by more than 15 ps for GALILEO and BDS after considering bias inconsistencies. Furthermore, owing to the pseudorange bias correction, the convergence and positioning performance have improved significantly, with an improvement of more than 12 % for the static precise point position (PPP), and more than 10 % for the kinematic PPP.

High-Rate One-Hourly Updated Ultra-Rapid Multi-GNSS Satellite Clock Offsets Estimation and Its Application in Real-Time Precise Point Positioning

The requirement of timeliness is increasing while obtaining precise tempo-spatial information with the development of global navigation satellite systems (GNSSs). Due to the poor network environment and communication conditions in some regions or application scenarios, it is difficult for users to receive real-time (RT) precise products. The hourly updated ultra-rapid products with low latency and high accuracy are of great interest in GNSS real-time and near-real-time fields. However, it is difficult to achieve the high-rate one-hourly updated precise clock estimation (PCE); since many ambiguity parameters need to be estimated, the computation is time-consuming. At present, the highest time resolution of ultra-rapid clock offsets is 15 min. The low samplings affect the prediction accuracy of clock offsets and the precise point positioning (PPP) performances. To meet these requirements, we proposed an efficient method and design a new framework for high-rate one-hourly updated ultra-rapid PCE. We modified the epoch-difference (ED) PCE model in the parameter estimation. According to the characteristics of the modified ED PCE model, the Open Multi-Processing (OpenMP) and Intel Math Kernel Library (MKL) technologies are used to construct a parallel system to realize the parallelism among satellites, epochs, and stations. The comprehensive assessment in the precision of clock offsets and PPP performances is conducted. The result demonstrates that the one-hourly updated multi-GNSS clock offsets with 30 s sampling can be obtained within 20 min. The estimated clock offsets accuracy increases with the improvement of the time resolution. The STD and RMS are improved by (0.97 to 9.09% and 0.12 to 5.56%) in the observation session, (2.82 to 23.08% and 0.95 to 9.09%) in the first hour of the prediction session, and (0.11 to 3.85% and 0.12 to 4.19%) in the second hour of the prediction session compared with low-rate products, respectively. The high-rate one-hourly updated ultra-rapid clock offsets significantly improves the RT-PPP performances. The positioning accuracy can be improved by 1.52~25.74%, and the convergence time can be improved by 21.96~65.75%. The RT-PPP performances are basically the same as GeoForschungsZentrum Potsdam (GFZ) rapid products and slightly better than the Center National d’Etudes Spatiales (CNES) RT products (CLK93). The one-hourly updated ultra-rapid products with low latency, high accuracy, and not limited by network conditions can be well applied to real-time or near real-time applications and research.

GNSS observable-specific phase biases for all-frequency PPP ambiguity resolution

An unwritten rule to resolve GNSS ambiguities in precise point positioning (PPP-AR) is that users should follow faithfully the frequency choices and observable combinations mandated by satellite clock and phase bias providers. Switching to other frequencies of measurements requires that the satellite clocks be converted, albeit in a roundabout way, to agree with the new frequencies of code biases. Satellite phase biases, on the other hand, are prescribed conventionally as wide-lane and narrow-lane combinations, which prevents users from resolving other phase combinations in the case of multi-frequency observables. We therefore develop an approach to compute observable-specific phase biases (phase OSBs) in concert with the legacy, but ambiguity-fixed, satellite clocks to enable PPP-AR over any frequency choices and observable combinations at the user end, i.e., all-frequency PPP-AR. In particular, the phase OSBs on the baseline frequencies (e.g., L1/L2 for GPS and E1/E5a for Galileo) are estimated by decoupling the code OSBs pre-aligned with the satellite clocks; then satellite clocks are re-estimated by holding pre-resolved undifferenced ambiguities and phase OSBs on the baseline frequencies; finally, all third-frequency phase OSBs are determined by introducing the ambiguity-fixed satellite clocks above. We used a global network of multi-frequency GPS/Galileo data over a month to verify this approach. In dual-frequency PPP-AR using GPS L1/L2, L1/L5, Galileo E1/E5a, E1/E5b, E1/E5 and E1/E6 signals, over 95% of wide-lane and narrow-lane ambiguity residuals were within ±0.25 and ±0.15 cycles, respectively, after the code and phase OSB corrections on raw GNSS measurements. As a result, the ambiguity fixing rates reached around 95% in all PPP-AR tests, though it was only the satellite clocks aligned with the GPS L1/L2 and Galileo E1/E5a pseudorange that were applied throughout. We stress that the key to computing such phase OSBs for all-frequency PPP-AR is that the code OSBs have the same bias datum as that of the satellite clocks.

Undifferenced Kinematic Precise Orbit Determination of Swarm and GRACE-FO Satellites from GNSS Observations.

Low Earth Orbit (LEO) satellites can be used for remote sensing and gravity field recovery, while precise orbit determination (POD) is vital for LEO satellite applications. However, there are some systematic errors when using the LEO satellite orbits released by different agencies in multi-satellite-based applications, e.g., Swarm and Gravity Recovery and Climate Experiment-Follow-On (GRACE-FO), as different GNSS precise orbit and clock products are used as well as processing strategies and software. In this paper, we performed undifferenced kinematic PODs for Swarm and GRACE-FO satellites simultaneously over a total of 14 days by using consistent International Global Navigation Satellite System (GNSS) Service (IGS) precise orbit and clock products. The processing strategy based on an undifferenced ionosphere-free combination and a least squares method was applied for Swarm and GRACE-FO satellites. Furthermore, the quality control for the kinematic orbits was adopted to mitigate abrupt position offsets. Moreover, the accuracy of the kinematic orbits solution was evaluated by carrier phase residual analysis and Satellite Laser Ranging (SLR) observations, as well as comparison with official orbits. The results show that the kinematic orbits solution is better than 4 cm, according to the SLR validation. With quality control, the accuracy of the kinematic orbit solution is improved by 2.49 % for the Swarm-C satellite and 6.98 % for the GRACE-D satellite when compared with their precise orbits. By analyzing the accuracy of the undifferenced kinematic orbit solution, the reliability of the LEO orbit determination is presented in terms of processing strategies and quality control procedures.

Comprehensive Analyses of PPP-B2b Performance in China and Surrounding Areas

BeiDou Global Navigation Satellite System (BDS-3) provides a regional Precise Point Positioning (PPP) service, called PPP-B2b, for users in China and surrounding areas through B2b signal transmitted from its three geostationary earth orbit (GEO) satellites. The information broadcasted by the B2b signal include satellite orbit corrections, satellite clock offset corrections, and differential code bias (DCB) corrections of BDS-3 satellites. In this study, the accuracies of PPP-B2b corrections along with real-time PPP performance are comprehensively evaluated referenced to precise orbit and clock products from GFZ and the precise DCB products from CAS. The result indicates that the accuracy of the BDS-3 broadcast orbit is similar to that of the PPP-B2b real-time orbit. The PPP-B2b clock offset correction improved the satellite clock offset precision of the BDS-3 broadcast ephemeris. The Signal-in-Space Range Error (SISRE) of broadcast ephemeris and PPP-B2b are calculated, which are 0.536 and 1.24 m, respectively. The large SISRE value of PPP-B2b is caused by the satellite-specified systematic bias to IGS final products. The positioning performance evaluation of real-time PPP with B2b service is carried out and compared with the real-time product provided by Wuhan University (WHU) based on the eight IGS MGEX stations in China and surrounding countries. The positioning accuracy of static positioning mode with PPP-B2b service achieved centimeter-level accuracy in the selected station, and that of kinematic positioning mode achieved decimeter-level accuracy. The availability rate of PPP-B2b corrections in the surrounding area of China, however, degrades from 88.76% to 60.91% in the selected stations. The accuracy of the PPP solution using PPP-B2b correction is better than that of using WHU real-time product within China. The positioning performance of stations located at the boundary of the PPP-B2b service area, however, is affected by the number of PPP-B2b available satellites. The positioning accuracy in kinematic positioning mode is worse than that of using WHU real-time precise product.

Ready for Real Time: Performance of Global Navigation Satellite System in 2019 Mw 7.1 Ridgecrest, California, Rapid Response Products

Abstract Global Navigation Satellite Systems (GNSSs) have undergone notable advancement in the last few decades, leading to the availability of a dataset with capabilities well beyond its original intended purpose. The proliferation of high-rate (1 Hz or greater) GNSS receivers in areas of seismological interest now allows for routine consideration of dynamic earthquake ground motions, with centimeter-level displacement accuracy via precise point positioning methods. Real-time (RT) GNSS observations, from stations that are both telemetered and processed to displacement with minimal latency, have lower accuracy compared to post-processed (PP) GNSS displacements due to imprecise knowledge of atmospheric conditions, satellite clocks, and satellite orbits in RT. Whether the quality of RT high-rate GNSS is sufficient for use in rapid response products remains to be thoroughly examined. Here, we highlight RT GNSS displacement time series processed during the 2019 Mw 7.1 Ridgecrest, California, earthquake in the context of common rapid-response products, magnitude estimation, and kinematic fault-slip models. We discuss how these data can be used to supplement RT seismic data for rapid characterization of significant earthquakes. We find that kinematic fault-slip models using RT GNSS data retain the general spatiotemporal characteristics of those with PP data, with subtle differences in size and amplitude of modeled slip asperities. We demonstrate the effect of these rapid seismic source models using RT GNSS data on the U.S. Geological Survey product ShakeMap—a downstream ground-motion prediction algorithm informed by the rupture dimensions estimated in the slip model. Discrepancies in the ShakeMap estimate are minor, within ±12% change, with the most severe variation at the fault edges. Our analysis suggests that, when used in conjunction with available seismic data sources, RT GNSS is sufficient and valuable for rapid earthquake characterization.

Short-term satellite clock bias forecast based on complementary ensemble empirical mode decomposition and quadratic polynomial

The nonlinear and nonstationary characteristics of satellite clock bias (SCB) have a harmful effect on the accuracy and stability of SCB forecast. To eliminate the influence of nonlinearity and non-stationarity, a hybrid forecast model was constructed that combines complementary ensemble empirical mode decomposition (CEEMD) and quadratic polynomial (QP), called CEEMD-QP. First, the SCB sequence is decomposed into several intrinsic mode function (IMF) components and one residual term by CEEMD. Second, permutation entropy (PE) and the correlation coefficient are used to quantitatively determine the IMF component with more noise and weak correlation with the original SCB signal. Finally, the SCB is reconstructed with the IMFs and residual components, and QP model is used to fit and forecast the clock bias. We adapt the observation part of ultra-rapid precise SCB data of GPS provided by IGS to forecast experiments. The results show that the CEEMD-QP method has obvious advantages of forecast accuracy and stability in short-term forecast.

Analysis and improvement of the Bancroft algorithm for GNSS satellite orbit determination

Satellite orbit information is crucial for ensuring that global navigation satellite systems (GNSSs) provide appropriate positioning, navigation and timing services. Typically, users can obtain access to orbit information of a specific accuracy level from navigation messages or precise ephemeris products. Without this information, a system will not be able to provide normal service. In response to this problem, initial orbit information of a certain level of precision must be obtained to support subsequent applications, such as broadcasting or precise ephemeris calculations, thereby ensuring the successful subsequent operation of the navigation system. One of two ways to calculate the initial orbit of a GNSS satellite is to utilize ground tracking stations to observe satellite vector information in the geocentric inertial system; the second way is to utilize GNSS range observations and known orbit information from other satellites. For the second approach, some researchers use the Bancroft algorithm combined with receiver clock offset to determine the initial orbit of GNSS satellites. Because this method requires an additional known receiver clock offset, we study the dependence of the Bancroft algorithm on clock offset in GNSS orbit determination. By assessing the impact of errors of different magnitude on the accuracy of the orbit results, we obtain experimental conclusions. After comprehensively analyzing various errors, we determine the accuracy level that the Bancroft algorithm can achieve for orbit determination without considering receiver clock correction. Dual-frequency and single-frequency pseudorange data from International GNSS Service stations are used in orbit determination experiments. When a small receiver clock offset is considered and no correction is made, the deviations in the calculated satellite positions in three dimensions are approximately 979.3 and 1118.1 m (dual and single frequency); with a satellite clock offset, these values are approximately 928.8 and 1062.7 m (dual and single frequency).

Real-Time Precise GPS Orbit and Clock Estimation With a Quasi-Orbit-Fixed Solar Radiation Pressure Model

<h3>Abstract</h3> Real-time precise global navigation satellite system (GNSS) orbit and clock products play a key role for real-time GNSS-based applications, both in the scientific and industrial communities. Different from the typical two-step procedure to generate orbit and clock solutions separately, we estimate the real-time orbit and clock products simultaneously using a Kalman filter. For this purpose, we developed a GNSS data processing software that can run in pseudo-real-time mode with RINEX files and is ready to run in real-time mode once given the real-time observation stream. Meanwhile, a quasi-orbit-fixed solar radiation pressure (SRP) model is developed. In order to verify the performance of the software and the new SRP model, several experiments with a global network of 60 tracking stations over a time span of three months were conducted to generate real-time Global Positioning System (GPS) orbit and clock products. Then, the results were assessed in terms of accuracy and efficiency, both critical for real-time precise GNSS applications. Compared to the International GNSS Service (IGS) final orbits, the real-time GPS orbit accuracy was 2.82 cm, 5.45 cm, and 5.47 cm in the radial, along-track, and cross-track components, respectively. The precision of the clock product in terms of standard deviation (STD) value was about 0.1 ns. Moreover, the average execution time per epoch was usually less than 1.0 s, which ensures the high efficiency of the processing.

An Evaluation Method of Gnss Satellite Clock In-Orbit with Periodic Terms Deducted

An Evaluation Method of Gnss Satellite Clock In-Orbit with Periodic Terms Deducted

INVESTIGATION OF THE ABSOLUTENESS OF TIME

In classical physics, time is considered absolute. It is believed that all processes, regardless of their complexity, do not affect the flow of time&#x0D; The theory of relativity determines that the flow of time for bodies depends both on the speed of movement of bodies and on the magnitude of the gravitational potential. It is believed that time in space orbit passes slower due to the high speed of the spacecraft, and faster due to the lower gravitational potential than on the surface of the Earth. Currently, the dependence of time on the magnitude of the gravitational potential and velocity (relativistic effect) is taken into account in global positioning systems.&#x0D; However, studying the relativistic effect, scientists have made a wrong interpretation of the difference between the clock frequency of an orbiting satellite and the clock frequency on the Earth's surface. All further studies to explain the relativistic effect were carried out according to a similar scenario, that is, only the difference in clock frequencies under conditions of different gravitational potentials was investigated.&#x0D; While conducting theoretical research, I found that the frequency of the signal changes along the way from the satellite to the receiver due to the influence of Earth's gravity. It was found that the readings of two high-precision clocks located at different heights will not differ after any period of time,&#x0D; that is, it is shown that the flow of time does not depend on the gravitational potential. It is proposed to conduct full-scale experiments, during which some high-precision clocks are sent aboard the space station, while others remain in the laboratory on the surface of the earth. It is expected that the readings of the satellite clock will be absolutely identical to the readings of the clock in the Earth laboratory.

Evaluation of BDS-2 and BDS-3 Satellite Atomic Clock Products and Their Effects on Positioning

The BeiDou Navigation Satellite System (BDS) has completed third phase construction and currently provides global services, with a mixed constellation of BDS-2 and BDS-3. The newly launched BDS-3 satellites are equipped with rubidium and passive hydrogen maser (PHM) atomic clocks. The performance of atomic clocks is one of the cores of satellite navigation system, which will affect the performance of positioning, navigation and timing (PNT). In this paper, we systematically analyze the characteristics of BDS-2 and BDS-3 atomic clocks, based on more than one year of precise satellite clock products and broadcast ephemeris. Firstly, the results of overlapping Allan variations demonstrate that BDS-3 Rb and PHM clocks improve better in stability than BDS-2 Rb clock and are comparable to GPS IIF Rb and Galileo PHM clocks. Accordingly, the STDs of BDS-3 broadcast satellite clock are better than GPS and BDS-2, which are at the same level with that of Galileo. Secondly, the inter-system bias (ISB) between BDS-2 and BDS-3 is analyzed by satellite clock datum comparison and precise point positioning (PPP). Surprisingly, the discrepancy between BDS-2 and BDS-3 satellite clock datum has a great difference between products that could reach up to about 10 ns for WHU satellite clock products and broadcast ephemeris. Moreover, the ISBs between BDS-2 and BDS-3 satellite clocks are quite stable over one-year periods. Thirdly, due to the improved stability of BDS-3 atomic clock, the 68% positioning accuracy is better than 0.65 m at 10 min for BDS-3 PPP, based on broadcast ephemeris. Besides, the non-negligible bias between BDS-2 and BDS-3 will greatly affect the BDS precise data processing. The accuracy of positioning is greatly improved when considering the ISB.