Satellite Clock Offsets Research Articles

Real-Time Estimation of BDS-3 Satellite Clock Offset with Ambiguity Resolution Using B1C/B2a Signals

The third generation of the BeiDou navigation satellite system (BDS-3) can transmit five-frequency signals. The real-time satellite clock offset of BDS-3 is typically generated utilizing the B1I/B3I combination with the ambiguity-float solutions. By conducting the ambiguity resolution (AR), the reliability of the satellite clock offset can be improved. However, the performance of BDS-3 ambiguity-fixed real-time satellite clock offset with B1C/B2a signals remains unknown and unrevealed. In this contribution, the performance of the BDS-3 ambiguity-fixed satellite clock offset with the new B1C/B2a signals is investigated. One week of observation data from 85 stations was used to perform ambiguity-fixed satellite clock offset estimation. For B1I/B3I and B1C/B2a signals, the wide-lane (WL) uncalibrated phase delay (UPD) on the satellite end is fairly stable for one day, while the narrow-lane (NL) UPD standard deviation (STD) amounts to 0.122 and 0.081 cycles, respectively. The mean ambiguity fixing rate is 80.7% and 78.0% for these two signal combinations, and the time to first fix (TTFF) for the B1C/B2a signals is remarkably shorter than that of the B1I/B3I signals. The STDs of the ambiguity-float and -fixed satellite clock offsets are 0.033 and 0.026 ns, respectively, for the B1I/B3I combination, and it is reduced to 0.024 and 0.023 ns for B1C/B2a signals, respectively. Using the estimated UPD and clock offset products, the positioning performance of the kinematic Precise Point Positioning (PPP)-AR results amounts to 1.56, 1.23, and 4.46 cm in the east, north, and up directions for B1I/B3I signals, respectively. It is improved to 1.36, 1.16, and 4.25 cm using the products estimated with the B1C/B2a signals, with improvements of 12.8%, 5.7%, and 4.7% in three directions, respectively. The experiments showed that the performances of the ambiguity-fixed satellite clock offsets and the PPP-AR results using B1C/B2a signals are better than those of B1I/B3I.

A method to assess the quality of GNSS satellite phase bias products

As part of the International GNSS Service (IGS), several analysis centers provide GPS and Galileo satellite phase bias products to support precise point positioning with ambiguity resolution (PPP-AR). Due to the high correlation with satellite orbits and clock offsets, it is difficult to assess directly the precision of satellite phase bias products. Once outliers exist in satellite phase biases, PPP-AR results are no longer reliable and the combination of satellite phase bias products from IGS analysis centers also gets difficult. In this contribution, we propose a method independent of ground measurements to detect outliers in satellite phase biases by computing the total Difference of satellite Orbits, Clock offsets and narrow-lane Biases at the midnight epoch between two consecutive days. Results over 180 days show that about 0.2, 1.1, 2.0 and 0.1% of the total DOCB values for GPS satellites exceed 0.15 narrow-lane cycles for CODE final, CODE rapid, CNES/CLS final and WUHN rapid satellite products, respectively, while the same outlier-ratios for Galileo satellites are 0.1, 0.9, 0.4 and 0.1%, respectively. As an important contribution to the orbit, clock and bias combination task, we check the consistency of satellite phase bias products between two analysis centers before and after removing these detected outliers from individual analysis centers. It is convincing that the number of large differences of satellite phase biases between two analysis centers is notably reduced.

An un-differenced epoch-piecewise parallel estimation of the GNSS satellite clock offsets

Precise Point Positioning (PPP) requires a satellite clock product with an interval of 30-s. It is indispensable to re-estimate the high sampling product after orbit determination. However, as the number of navigation satellites increases, their generation efficiency is severely affected. Therefore, an un-differenced epoch-piecewise parallel clock offset estimation method is proposed. Based on 120 stations, the 30-s clocks of 118 satellites were parallel estimated by four blocks within 19 min with a 3.5 times improved efficiency. The standard deviations between the estimated clock and the released products are 0.06, 0.06, 0.29, 0.10, and 0.15 ns for GPS, Galileo, GLONASS, BDS2, and BDS3 MEO satellites, respectively. When the 30-s interval clock products are used than 300-s, the convergence time of kinematic PPP for the BDS/Galileo and GPS/BDS/Galileo/GLONASS improves by 22 % and 33 %, respectively, while the three-dimensional RMS decreases by 5 mm (10 %) and 12 mm (28 %), respectively.

PPP-RTK with Rapid Convergence Based on SSR Corrections and Its Application in Transportation

Real-time Kinematic (RTK) positioning provides centimeter-level positioning accuracy within several seconds, but it has to rely on a nearby base station. Although Precise Point Positioning (PPP) supplies precise positions with one receiver, its convergence time takes several tens of minutes, which makes PPP not well suited for real-time kinematic applications where a rapid convergence is required. PPP-RTK integrates the benefits of PPP and RTK, which actually is PPP augmented by a ground GNSS network. The satellite orbit, clock offsets, signal biases, ionospheric and tropospheric corrections are determined based on this GNSS network, modeled as state space information and transmitted to PPP users. By applying these State Space Representation (SSR) corrections, a real-time kinematic PPP-RTK approach is developed and implemented, which can instantly resolve the ambiguities to integers and realize rapid convergence. In a static scenario, it realized an instant ambiguity resolution and a rapid convergence within 2 s in more than 90% of 120 hourly sessions. The PPP-RTK has been applied and evaluated in a kinematic scenario on the highway. The horizontal positioning errors are almost lower than 0.1 m except for the time of passing through bridges. After passing bridges, the PPP-RTK successfully resolved ambiguities within 2 s in 90.6% of the cases and achieved convergence in horizontal within 5 s in more than 90% of the cases. The PPP-RTK with a precision of 0.1 m and rapid convergence of several seconds benefits the precise navigation of automobile on the highway, which will support the development of autonomous driving in future.

A Real-Time Linear Prediction Algorithm for Detecting Abnormal BDS-2/BDS-3 Satellite Clock Offsets

Due to space environment interference, imperfect data processing model, and the performance of atomic clocks, real-time satellite clock products often contain outliers or irregular biases. We propose a real-time linear moving short-term prediction algorithm to predict clock offsets and detect abnormalities. The proposed algorithm mainly includes phase/frequency anomaly detection and real-time prediction part. Both the phase and frequency domains are used to detect abnormal clock offsets with previous epochs for building the clock prediction model accurately. The real-time moving prediction module utilizes the high short-term prediction performance to check the clock abnormality. The performance of the algorithm is then evaluated for all satellites with real-time estimated satellite clock offsets. To verify the feasibility and effectiveness of the proposed linear moving model and algorithm, the results of the grey model GM(1,1) and the ARIMA model are also compared. The experimental results indicated that the algorithm can detect clock outliers, frequency modulation, and phase jumps, and the linear model has a better clock performance improvement. After the abnormalities are removed with the proposed algorithm, the average STD accuracy of the real-time clock offsets for all satellites is improved by 15.5%, compared to an improvement of 11.4% by the GM(1,1) model and 11.5% by the ARIMA model. The PPP results demonstrate that the proposed clock prediction algorithm improves the positioning accuracy by 8.1%, 13.3%, and 16.9% in the east, north, and up components, respectively.

PPP/INS Tight Integration with BDS−3 PPP−B2b Service in the Urban Environment

To provide continuous and reliable real-time precise positioning services in challenging environments and poor internet conditions, the real-time precise corrections of the BeiDou global navigation satellite system (BDS-3) PPP-B2b signal are utilized to correct the satellite orbit errors and clock offsets. In addition to this, using the complementary characteristics of the inertial navigation system (INS) and the global navigation satellite system (GNSS), a PPP-B2b/INS tight integration model is established. With observation data collected in an urban environment, the results show that PPP-B2b/INS tight integration can ensure a decimeter-level positioning accuracy; the positioning accuracies of the E, N, and U components are 0.292, 0.115, and 0.155 m, respectively, which can provide a continuous and secure position during short interruptions in the GNSS. However, there is still a gap of about 1 dm compared with the three-dimensional (3D) positioning accuracy obtained from Deutsche GeoForschungsZentrum (GFZ) real-time products, and a gap of about 2 dm compared with the GFZ post-precise products. Using a tactical inertial measurement unit (IMU), the velocimetry accuracies of the tightly integrated PPP-B2b/INS in the E, N, and U components are all about 0.3 cm/s, and the attitude accuracy of yaw is about 0.1 deg, while the pitch and roll show a superior performance of less than 0.01 deg. The accuracies of the velocity and attitude mainly depend on the performance of the IMU in the tight integration mode, and there is no significant difference between using real-time products and post products. The performance of the microelectromechanical system (MEMS) IMU and tactical IMU is also compared, and the positioning, velocimetry, and attitude determinations with the MEMS IMU are significantly worsened.

Analysis of BDS-3 Real-Time Satellite Clock Offset Estimated in Global and Asia-Pacific and the Corresponding PPP Performances

The quality of satellite clock offset affects the performances of positioning, navigation and timing services, and thus it is essential to the Global Navigation Satellite System (GNSS). This research focuses on the estimation of BeiDou Navigation Satellite System (BDS) real-time precise satellite clock offset by using GNSS stations located in the Global and Asia-Pacific region based on the mixed-difference model. The precision of the estimated BDS clock corrections is then analyzed with the classification of the orbit types, satellite generations, and atomic clock types. The results show that the precision of the BDS clock offset estimated in the Asia-Pacific for Geosynchronous Earth Orbit (GEO), Inclined Geosynchronous Satellite Orbit (IGSO) and Medium Earth Orbit (MEO) satellites are 0.204 ns, 0.077 ns and 0.085 ns, respectively, as compared to those of clock offsets estimated in globally distributed stations. The average precision of the BDS-3 satellites clock offset estimated in global region is 0.074 ns, which is much better than the 0.130 ns of BDS-2. Furthermore, analyzing the characteristics of the corresponding atomic clocks can explain the performance of the estimated satellite clock offset, and the stability and accuracy of various parameters of the Passive Hydrogen Maser (PHM) atomic clocks are better than those of Rubidium (Rb) atomic clocks. In the positioning domain, the real-time clocks estimated in the global/Asia-Pacific have been applied to BDS kinematic Precise Point Positioning (PPP) in different regions. The Root Mean Square (RMS) of positioning results in global real-time kinematic PPP is within 4 cm in the horizontal direction and about 6 cm in the vertical direction. Hence, the BDS real-time clock offset can supply the centimeter-level positioning demand around the world.

Analysis of Galileo five-frequency precise satellite clock estimation models and its effect on multi-frequency PPP

The Global Navigation Satellite System (GNSS) multi-frequency observations are widely used in positioning applications, while precise orbit determination and precise clock estimation (PCE) techniques typically employ dual-frequency undifferenced (UD) ionospheric-free (IF) observations from global networks. To fully utilize the multi-frequency GNSS observations for generating satellite products at the server-end, we develop some new five-frequency PCE models based on Galileo data, which are five-frequency uncombined FFUC model, FFIF0 model combining the E1/E5a, E1/E5b, E1/E5 and E1/E6 IF observables, FFIF1 model combining E1/E5a and E1/E5a/E5b/E5/E6 IF observables, respectively. The traditional dual-frequency UD IF and triple-frequency PCE models are also introduced for comparison. The new multi-frequency PCE models can not only make full use of the modern GNSS multi-frequency observations, but also obtain satellite clock offsets and inter-frequency clock bias (IFCB) at the same time, which can better support multi-frequency precise point positioning (PPP) applications. The multi-frequency models can improve the stability of GNSS satellite clock estimation, the precision of satellite clock offsets can be improved by 8–12% for triple-frequency models, and 19–27% for five-frequency PCE models compared with the traditional dual-frequency IF model. The PPP positioning accuracy using only multi-frequency satellite clock offsets can be improved by 7–18% for dual-frequency PPP, 8–15% for triple-frequency PPP, 4–16% for five-frequency PPP. The positioning accuracy can be further improved by 11–28% for triple-frequency PPP and 7–20% for five-frequency PPP. Therefore, the new multi-frequency PCE models are demonstrated to support PPP applications with better performance.

High-Accuracy Clock Offsets Estimation Strategy of BDS-3 Using Multi-Source Observations

Satellite clock offsets are the critical parameters for The Global Navigation Satellite Systems (GNSSs) to provide position and timing (PNT) service. Unlike other GNSSs, BDS-3 uses the two-way superimposition strategy to measure satellite clock offsets. However, affected by some deficiencies of the two-way superimposition strategy, the accuracy of BDS-3 clock offsets parameters is 1.29 ns (RMS), which is the main bottleneck for BDS-3 to improve its space signal accuracy. After analyzing problems in the clock offsets measurement process of BDS-3, the paper proposes a new strategy to real-time estimate high-accuracy satellite clock offsets. The clock offsets estimated by the new strategy show a good consistency with GBM clock offsets. The averaged STD of their differences in MEO is 0.14 ns, and the clock offsets estimated by the new strategy present less fluctuation in the 1-day fitting residuals. Applying the new clock offsets to prediction, BDS-3 can reduce its clock offsets errors from 1.05 ns to 0.29 ns (RMS), about 72%. The above results indicate that the new clock offsets estimated strategy can improve the accuracy of clock offsets parameters of BDS-3 effectively.

Real-time ocean precise point positioning with BDS-3 service signal PPP-B2b

For ocean high-precision positioning, the Real-Time Kinematic (RTK) technique exists disadvantages since the positioning accuracy will deteriorate with the baseline elongating. The real-time Precise Point Positioning (PPP) based on Real-Time Service (RTS) may be difficult to operate on ocean since the internet-based communication is unavailable. As an alternative, the PPP-B2b service provided by BeiDou Global Navigation Satellite System (BDS-3) is considered free from these limiting requirements, and it can realize real-time PPP for users in China and surrounding areas. This research focuses on a real-time PPP with BDS-3 service signal PPP‑B2b in ocean high-precision positioning application. The real-time satellite orbit and clock are recovered, and the accuracy are evaluated with collected 10-day PPP-B2b messages. The results indicate that the accuracy of PPP-B2b satellite orbit is better than 0.1 m in the radial component and the satellite clock offsets achieve an accuracy of better than 0.2 ns for both BDS-3 and Global Positioning System (GPS). The land simulated real-time kinematic PPP experiment using 7 International GNSS Service (IGS) stations observations yielded the three-dimensional (3D) positioning accuracy of 11.6 cm for BDS-3 only and 8.3 cm for GPS + BDS-3. Finally, an ocean real-time kinematic PPP positioning experiment is carried out and the data quality of ocean observations are analyzed. The ocean real-time PPP with PPP-B2b corrections achieves the 3D Root Mean Square (RMS) of 21.3 cm for BDS-3-only and 18.2 cm for GPS + BDS-3, which indicates that the PPP-B2b service provided by BDS-3 is prospective in location-based ocean application.

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.

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.

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.

A Method to Accelerate the Convergence of Satellite Clock Offset Estimation Considering the Time-Varying Code Biases

Continuous and stable precision satellite clock offsets are an important guarantee for real-time precise point positioning (PPP). However, in real-time PPP, the estimation of a satellite clock is often interrupted for various reasons such as network fluctuations, which leads to a long time for clocks to converge again. Typically, code biases are assumed to stay constant over time in clock estimation according to the current literature. In this contribution, it is shown that this assumption reduces the convergence speed of estimation, and the satellite clocks are still unstable for several hours after convergence. For this reason, we study the influence of different code bias extraction schemes, that is, taking code biases as constants, extracting satellite code biases (SCBs), extracting receiver code biases (RCBs) and simultaneously extracting SCBs and RCBs, on satellite clock estimation. Results show that, the time-varying SCBs are the main factors leading to the instability of satellite clocks, and considering SCBs in the estimation can significantly accelerate the filter convergence and improve the stability of clocks. Then, the products generated by introducing SCBs in the clock estimation based on undifferenced observations are applied to PPP experiments. Compared with the original undifferenced model, clocks estimated using the new method can significantly accelerate the convergence speed of PPP and improve the positioning accuracy, which illustrates that our estimated clocks are effective and superior.

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.

An efficient clock offset datum switching compensation method for BDS real-time satellite clock offset estimation

The quality of real-time satellite clock offsets products is one of the key elements for real-time satellite clock performance monitoring and real-time precise point positioning (PPP). However, impacted by the station location, environment, communication equipment, receiver performance, network delay, temporary modem failure or other reasons, the observation data of clock offset datum receiver occasionally outage, resulting in all satellite clocks offset cannot be estimated. In this contribution, an efficient clock offset datum switching compensation method for BDS real-time satellite clock offset estimation is proposed. One hundred stations distributed around the world, from day of year (DOY) 074 to 075 in 2019 are used to estimate BDS real-time satellite clock offset. Four schemes: clock offset datum switching without compensation (S1), clock offset datum switching with satellite clock offset jump compensation (S2), clock offset datum switching with satellite clock offset jump and receiver clock drift compensation (S3, the proposed method), clock offset datum without switching (S4), are used to validate the proposed method. By using the proposed method, the satellite clock offset jump can be eliminated and the satellite clock offset consistency can be maintained. The satellite clock offsets STD for S1, S2, S3 and S4 are 0.184, 0.183, 0.183 and 0.150 ns, respectively. The fitting precision of S1, S2, S3 and S4 are 70907.344, 0.731, 0.502 and 0.543 ns, respectively. The frequency stability of S3 shows the best performance among S2, S3 and S4 when the averaging interval time is 10,000 and 20,000 s, which can be attributed to the effectiveness of proposed method and frequency stability difference of clock offset datum receiver. The fitting precision and frequency stability cannot be reflected correctly by clock offset due to the satellite clock offset jump in S1. For precise point positioning (PPP), the coordinates jump and re-convergence can be eliminated by using the proposed method. Thus, this method can provide a reference for obtaining real-time, continuous and reliable BDS satellite clock offset products.

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.

An Improved Multi-Satellite Method for Evaluating Real-Time BDS Satellite Clock Offset Products

Two methods are widely used for evaluating the precision of satellite clock products, namely the single-satellite method (SSM) and the multi-satellite method (MSM). In the satellite clock product evaluation, an important issue is how to eliminate the timescale difference. The SSM selects a reference satellite to eliminate the timescale difference by between-satellite differencing, but its evaluation results are susceptible to the gross errors in the referenced satellite clock offsets. In the MSM, the timescale difference is first estimated and then removed. Unlike the GPS, the BeiDou Navigation Satellite System (BDS) consists of three types of satellites, namely geosynchronous earth orbit (GEO), inclined geosynchronous orbit (IGSO), and medium earth orbit (MEO) satellites. The three types of satellites have uneven orbital accuracy. In the generation of satellite clock products, the orbital errors are partly assimilated into the clock offsets. If neglecting the orbital accuracy difference of the three types of BeiDou satellites, the MSM will obtain biased estimates of the timescale difference and finally affect the clock product evaluation. In this study, an improved multi-satellite method (IMSM) is proposed for evaluating the real-time BDS clock products by removing the assimilated orbital errors of the three types of BDS satellites when estimating the timescale difference. Three real-time BDS clock products disseminated by three different International GNSS Service (IGS) analysis centers, namely CLK16, CLK20, and CLK93, over a period of two months are used to validate this method. The results indicate that the assimilated orbital errors have a significant impact on the estimation of the timescale difference. Subsequently, the IMSM is compared with the SSM in which the referenced satellite is rigorously chosen, and their RMS difference is only 0.08 ns, which suggests that the evaluation results obtained by the IMSM are accurate. Compared with the traditional MSM, the IMSM improves the RMS by 0.16, 0.11, and 0.07 ns for CLK16, CLK20, and CLK93, respectively. Finally, three real-time BDS clock products are evaluated using the proposed method, and results reveal a significant precision difference among them.

Анализ влияния эфемеридно-временной информации на точность решения навигационной задачи по сигналам системы ГЛОНАСС

The Global Navigation Satellite System has a huge impact on both the public and private sectors, including the social-economic development, it has many applications and is an integral part of many domains. The application of the satellite navigation systems remains the most relevant in the field of transport, including land, air and maritime transport. The GLONASS system consists of three segments and the operation of the entire system depends on functioning of each component, but primarily, the accuracy of measurements depends on the basis forming of the control segment and management, responsible for forming ephemeris-time information. In the work, the influence of ephemeris-time information on the accuracy of solving the navigation problem by the signals of the GLONASS satellite navigation system has been analyzed. The influence of both ephemeris information and the frequency information, and of the time corrections has been individually studied. The accuracy of the ephemeris-time information is especially important when solving the navigation problem by highly precise positioning method. For the analysis the following scenarios of the navigation problem solving have been formed: using high-precision and broadcast ephemeris-time information, a combination of broadcast (high-precision) ephemeris-time information, and high-precision (broadcast) satellite clock offsets and two scenarios with simulation of the calculation of the relative correction to the radio signal carrier frequency. Based on the study results it has been concluded that the contribution of the frequency-time corrections to the error of location determination is of the greatest importance and a huge impact on the error location, while the errors of the ephemeris information are insignificant

Evaluation of BDS-3 Orbit Determination Strategies Using Ground-Tracking and Inter-Satellite Link Observation

Dual one-way inter-satellite link (ISL) pseudoranges of BDS-3 satellites can be introduced as an additional measurement along with L-band pseudoranges and phases to improve the accuracy of precise orbit determination (POD). In the existing research, although the clock-free or geometry-free ISL observables are derived from the raw two one-way pseudoranges, only the clock-free observables are adopted for the ISL joint POD (Joint 1 POD) without considering the geometric-free observables. An improved joint (Joint 2 POD) strategy making full use of the clock-free and geometry-free observables is applied in this contribution. The orbits of ground-only POD, ISL-only POD, Joint 1 POD, and Joint 2 POD are comprehensively compared by the orbit overlapping differences, the Satellite Laser Ranging (SLR) residuals, and the characteristics of the satellite clock offsets estimated simultaneously. The comparisons prove that the performance of the Joint 2 POD strategy is better than that of the other three POD strategies regardless of the types of satellites. Moreover, this paper discusses ISL’s contribution to the station selection strategy in terms of the number and distribution. The experimental results show that, when there are more than 20 stations, each additional 10 stations contributes to a maximum of 7.5%, 3.9%, and 2.8% improvement on MEO, IGSO, and GEO satellites 3D accuracy, respectively. When the number of stations reaches 50, the precise orbits achieve similar accuracy to the results using 80 stations. In addition, after adding ISL data, the orbits estimated using 10 regional stations and 10 global stations are greatly improved, and the accuracy between them is only 0.9 cm in 3D errors.