Broadcast Ephemeris Research Articles

Precise coseismic displacements from the GPS variometric approach using different precise products: Application to the 2008 MW 7.9 Wenchuan earthquake

The Global Positioning System (GPS) variometric approach has emerged as an attractive alternative to traditional well-developed positioning techniques including relative positioning and precise point positioning. Previous studies have demonstrated the capability of the variometric approach to retrieve coseismic displacements at centimeter-level precision, in a real-time manner using only readily available broadcast ephemeris. This study presents the first results comparing the performance of the variometric approach by using a variety of precise satellite orbit and clock products. Totally six kinds of products are included in our evaluation, namely the broadcast, IGS (International GNSS Service) ultra-rapid (predicted), ultra-rapid (observed), rapid, final (30-s clock) and CODE (Center for Orbit Determination in Europe) final (5-s clock) products. Static and dynamic experiments are conducted using 1-Hz GPS data covering a relatively large area in China during the 2008 Wenchuan MW 7.9 earthquake. After removing the linear trend, the displacements using broadcast, ultra-rapid (predicted), ultra-rapid (observed) and rapid products reach nearly equivalent precisions at centimeter level. By using final and CODE final products, the precision of displacements can be significantly improved from 1.9–2.0 cm to 0.4–0.7 cm horizontally, and from 6.0–6.2 cm to 1.0–1.7 cm vertically for the dynamic experiments. The displacements using the CODE final products achieve the best precision, improved by more than 40% compared to those using the IGS final products. With the availability of IGS high-rate real-time precise products, this approach is promising to capture coseismic displacements more precisely in real time, which is crucial for earthquake and tsunami early warning.

SIS accuracy and service performance of the BDS-3 basic system

On December 27, 2018, the basic system of the third-generation BeiDou navigation satellite system (BDS-3) completed the deployment of its constellation of 18 MEO networking satellites as well as the construction of the operation control system (OCS) and began to provide basic navigation services to users worldwide. Compared with BDS-2, BDS-3 aims to offer users better navigation signals and higher precision with a series of new technologies. For example, the spaceborne atomic clock of BDS-3 is upgraded for higher performance, the Ka-band inter-satellite link is adopted for inter-satellite ranging and communication, and new B1C and B2a signals are broadcast in addition to B1I and B3I signals (compatible with BDS-2). In addition, a 9-parameter model based on a spherical harmonic function is employed for ionospheric delay corrections. Using the observation data from 18 satellites of the basic system, this paper conducts a comprehensive evaluation of the pseudorange measurement characteristics, signal-in-space (SIS) accuracy of navigation messages and global service capability of BDS-3. The results indicate that the pseudorange measurement multipath effect and observation noise of BDS-3 satellites are better than those of BDS-2; additionally, with the support of inter-satellite links, the user range error (URE) of the BDS-3 satellite broadcast ephemeris is better than 10 cm, the precision of the broadcast clock parameter is better than 1.5 ns, and the SIS accuracy is better than 0.6 m overall. Different from the traditional Klobuchar model, the BeiDou global broadcast ionospheric delay correction model (BDGIM) can provide ionospheric delay corrections better than 70% for worldwide single-frequency users. The service capability evaluation of the basic system consists mainly of the accuracy improvement of the B1I and B3I signals according to BDS-2 as well as the global positioning accuracy of the new signals. These results prove that the BDS-3 basic system has achieved the design goal; that is, both the horizontal and the vertical global positioning accuracies are better than 10 m (95%). In the future, 6 MEO satellites as well as 3 GEO satellites and 3 IGSO satellites for regional enhancement purposes will be deployed for full operation; consequently, BDS-3 will definitely provide a higher SIS accuracy and better service capability.

Calibration and Impact of BeiDou Satellite-Dependent Timing Group Delay Bias

The accuracy of the timing group delay (TGD) transmitted in the broadcast ephemeris is an important factor that affects the service performance of a GNSS system. In this contribution, an apparent bias is found by comparing the orbit and clock difference using half-year data of the BeiDou navigation satellite system (BDS) broadcast ephemeris and precise post-processed products. The bias differs at each satellite on each frequency and shows a general systematic difference between BDS-2 and BDS-3. We attribute this to the satellite-dependent TGD bias of the BDS broadcast ephemeris, which is subsequently calibrated. Moreover, to calibrate the bias independently, a network solution strategy is proposed based on 87 globally distributed multi-GNSS experiment (MGEX) stations spanning 25 weeks. The estimated bias shows good agreement with the values observed from the orbit and clock comparison. For the validation of the bias, we compared the signal-in-space range error (SISRE) performance with and without the TGD bias correction. The results show that the SISRE of the BDS improved from 0.71, 0.81, and 1.40 m to 0.64, 0.66, and 0.64 m in the B1I, B3I, and B1I/B3I frequencies. For BDS-3, the SISRE is well within 0.50 m after the bias correction. To further validate the bias, a week’s data were collected at 97 globally distributed MGEX stations. When the TGD bias is corrected, the root mean square (RMS) of single point positioning (SPP) can be improved by 5.6, 8.4, and 21.6% in the B1I, B3I, and B1I/B3I frequencies. Meanwhile, the SISRE and SPP assessment results also indicate that the TGD bias should be corrected by each satellite rather than only corrected between BDS-2 and BDS-3.

Assisted cold start method for GPS receiver with artificial neural network-based satellite orbit prediction

Traditional GPS receivers usually take a long time to obtain their first position solution in the cold start mode. This paper presents a method for assisting the cold start of GPS receivers by autonomous satellite orbit prediction. In this method, the time-consuming broadcast ephemeris collection process in a traditional cold start is replaced by orbit prediction to obtain the satellite position information required for positioning. Thus, the time to first fix of the receiver can be reduced significantly. In addition, since the traditional orbit prediction algorithms based solely on physics-based models have limited accuracy, a hybrid model composed of dynamic models and artificial neural network models for orbit prediction is proposed to improve the accuracy of the orbit prediction. Taking GPS PRN1 as an example, the simulation results show that, in 75% of cases, the satellite position error after 7 days’ prediction with the dynamic models is less than 162.84 m, but this value can be reduced to 46.06 m with the proposed hybrid model; the improvement rate achieved is approximately 71.71%. Some positioning experiments with simulated satellite signals were conducted to assess the first-fix accuracy of a GPS receiver with the proposed satellite orbit prediction function. The results of this study offer insights for the design of advanced assisted GPS receivers.

Satellite selection methods for multi-constellation advanced RAIM

The increased number of potential threat modes under multi-constellation advanced receiver autonomy integrity monitoring (ARAIM) requires an increase in the number of subsets and a correspondingly high computational load. A new satellite selection method based on integrity support message (ISM) parameters is proposed and compared with GDOP-based selection. The performance was tested on five days of data measurements from 21 multi-global navigation satellite system experiment (MGEX) stations distributed around the world, as well as simulation using the broadcast ephemeris. The results show that the proposed ISM-based satellite selection method is highly compatible with the baseline ARAIM. This method could reduce the computational times by about 60–70% quickly, with minimising vertical protection level (VPL) loss, which was consistently within 1 m, even a reduced VPL value in some epochs, and resulting in an improved availability. The simulation results were similar to the MGEX data. It appears that the application of ISM-based satellite selection can effectively reduce computational burden with a minimal impact on availability.

A flexible strategy for handling the datum and initial bias in real-time GNSS satellite clock estimation

Investigations have been focused on improving the precision of real-time GNSS satellite clock corrections. There is a little literature analyzing the characteristics and impacts of the clock datum and initial clock biases (ICBs). We illustrated the clock anomaly caused by the two factors and proposed a new strategy flexible for global and regional clock estimation based on the mixed-difference observation method. First, we analyzed the clock datum of the final and real-time clocks. Results show that the variation in the clock datum can be up to 500 ns per day depending on the datum definition strategy. The variations can lead to large inconsistencies in the datum for the re-convergence of estimated satellite clocks when using the mixed-difference clock estimation method. To resolve the problem, we propose a new method for the epoch-by-epoch datum definition, which can screen out any outliers in broadcast ephemeris in real time, and particularly suitable for the real-time clock estimation. Second, we analyzed ICB jumps in real-time clock corrections, which can degrade the accuracy of precise point positioning. We propose a short-term prediction of clock corrections for bridging ICBs with the precision better than 0.1 ns for stable satellite clocks within a gap of 1–3 min. The prediction can decrease the magnitude of ICB jumps and thus improve a user solution. Considering the prediction of clocks, high precision cannot be guaranteed for all conditions, we thus recommend broadcasting a discontinuity flag for real-time service, so the re-convergence of ICB can be identified by users for resetting carrier-phase ambiguities.

Apparent clock and TGD biases between BDS-2 and BDS-3

With the official commencement of the BDS-3 service, the BeiDou navigation satellite system (BDS) has become a global navigation satellite system. The characteristics of the new BDS-3 satellites, including code bias, are worth investigating. An apparent pair of clock and timing group delay (TGD) biases between BDS-2 and BDS-3 are found when assessing the BDS signal-in-space range error (SISRE) with 5-months of data spanning day of year (DOY) 6 to 145 in 2019, which results from the system bias between the broadcast ephemeris and the precise products provided by Wuhan University and the Chinese Academy of Science. The biases of the broadcast ephemeris are therefore calibrated when aligning to precise products. When these biases are corrected, the overall performance of the BDS SISRE decreases from 1.41 to 0.84 m for the B1I/B3I frequency. To further investigate the biases, we analyze 68 multi-GNSS experiment stations equipped with different receivers based on raw pseudorange measurements. It is found that the clock bias seems similar at each receiver, while the TGD bias from B3I to B1I depends on receiver type, with a value of − 0.48, − 0.98, and − 1.60 m for Javad, Trimble, and Septentrio receiver, respectively. The estimated average clock and TGD biases show good agreement with that from broadcast ephemeris and precise product comparison. When the calibrated clock and TGD biases are corrected in the BDS-3 satellites, the SPP performance improves from 0.3 to 31.8%, depending on frequency and receiver type. For real-time kinematic positioning, when the clock and TGD biases are corrected, the ratio value for ambiguity resolution increases and the fixing rate also improves from 59.79 to 74.44% at B1I frequency.

Initial assessment of BDS-3 preliminary system signal-in-space range error

The basic constellation of the BeiDou global satellite navigation system (BDS-3) had been successfully completed by the end of 2018. It included 18 medium earth orbit satellites and 1 geostationary orbit satellite. An initial assessment of BDS-3 broadcast orbit and clock accuracy based on 55 days of broadcast message data is presented in this contribution. Satellite positions and clock offsets derived from broadcast ephemeris are compared with precise orbit determination orbits and clock offsets. Furthermore, the corresponding signal-in-space range error (SISRE), which is of most interest to navigation users, is computed. Thanks to the new inter-satellite link payloads on BDS-3 satellites, the statistics of age-of-data-ephemeris and age-of-data-clock demonstrate that more than 98% of ephemerides and 93% of clock parameters are updated within only one hour. Experimental results show that the 3D root mean square (RMS) of broadcast orbit errors is less than 0.6 m for the overall constellation. The broadcast orbit is also assessed by satellite laser ranging measurements, giving an RMS of 7.3 cm. The orbit-only SISRE is about 0.1 m. With respect to clock errors, the timescale differences between two clock products are eliminated to assess the accuracy of broadcast clock offsets. The standard deviation value of 0.25 m shows a good performance, but the RMS value is regrettably nearly 0.5 m due to a nonzero mean bias. RMS of BDS-3 SISRE amounts to approximately 0.5 m, which is largely attributed to clock errors. Finally, a positioning experiment is conducted to analyze the accuracy of single point positioning (SPP). With 95% confidence level, the horizontal accuracy is less than 5 m, and the vertical accuracy is close to 6 m. Considering that the nonzero mean bias in clock errors may affect the performance of SPP, we correct the nonzero mean value by a satellite-specific constant to analyze the influence of clock bias on the SPP performance. The results show that improvement in the 3D position accuracy can be up to 11%, especially in the up direction.

Real-time single-frequency pseudorange positioning in China based on regional satellite clock and ionospheric models

Improving performance of single-point positioning (SPP) with single-frequency pseudorange measurement is important for users equipped with mass-market or low-cost receivers. Considering a regional single-frequency SPP service is available, it is not necessary to realize precise orbit determination for single-frequency SPP. Instead, the ionospheric modeling is of utmost importance. Based on BDS/GPS broadcast ephemeris, we establish a regional satellite clock model (CLK) and two regional ionospheric models in China using 155 reference stations and investigate their efficiency in improving the performance of BDS/GPS SPP with additional 499 reference stations. Two ionospheric models are established based on different total electron content (TEC) observables; one is the low-order spherical harmonic function model (SHF) with vertical TEC observables and the other is the satellite-based ionospheric model (SIM) with slant TEC observables. It is demonstrated that the SIM model performs better than SHF model as it avoids the error due to the ionospheric mapping function. Overall, the positioning results with CLK + SIM perform the best for BDS-only, GPS-only, and BDS/GPS SPP. Compared to the positioning results with the broadcast ephemeris and the Klobuchar model, the SPP positioning accuracy with the CLK + SIM model improves by about 50% on average. By using the improved model CLK + SIM, the BDS/GPS SPP positioning accuracy is better than 1.5 m and 2.0 m at the 95% confidence level in the horizontal and vertical directions, respectively. Also, by comparing the SPP performance with IGS final products, including the GeoForschungsZentrum precise orbits and clock products and Center for Orbit Determination in Europe final GIMs, the proposed model in this study performs better than that with the IGS final products in terms of positioning accuracy and model complexity.

Comparison of Satellite Repeat Shift Time for GPS, BDS, and Galileo Navigation Systems by Three Methods

The characteristic of the satellite repeat shift time can reflect the status of the satellite operation, and is also one of the key factors of the sidereal filtering multipath correction. Although some methods have been developed to calculate the repeat shift time, few efforts have been made to analyze and compare the performance of this feature for the GPS (Global Positioning System), BDS (BeiDou System), and Galileo in depth. Hence, three methods used for calculating the repeat shift time are presented, and used to compare and analyze the three global systems in depth, named the broadcast ephemeris method (BEM), correlation coefficient method (CCM), and aspect repeat time method (ARTM). The experiment results show that the repeat shift time of each satellite is different. Also, the difference between the maximum and minimum varies from different systems. The maximum difference is about 25 s for the BDS IGSO (Inclined Geosynchronous Orbit) and the minimum is merely 10 s for the GPS system. Furthermore, for the same satellite, the shift time calculated by the three methods is almost identical, and the maximum difference is only about 7 s between the CCM and the ARTM method for the BDS MEO (Medium Earth Orbit) satellite. Although the repeat shift time is different daily for the same satellite and the same method, the changes are very small. Moreover, in terms of the STD (Standard Deviation) of the BS (between satellites) and MS (mean shift for the same satellite), the GPS system is the best, the performance of the BDS system is medium, and the Galileo performs slightly worse than the GPS and BDS.

Precise Orbit Determination for BeiDou GEO/IGSO Satellites during Orbit Maneuvering with Pseudo-Stochastic Pulses

In order to provide better service for the Asia-Pacific region, the BeiDou navigation satellite system (BDS) is designed as a constellation containing medium earth orbit (MEO), geostationary earth orbit (GEO), and inclined geosynchronous orbit (IGSO). However, the multi-orbit configuration brings great challenges for orbit determination. When orbit maneuvering, the orbital elements of the maneuvered satellites from broadcast ephemeris are unusable for several hours, which makes it difficult to estimate the initial orbit in the process of precise orbit determination. In addition, the maneuvered force information is unknown, which brings systematic orbit integral errors. In order to avoid these errors, observation data are removed from the iterative adjustment. For the above reasons, the precise orbit products of maneuvered satellites are missing from IGS (international GNSS (Global Navigation Satellite System) service) and iGMAS (international GNSS monitoring and assessment system). This study proposes a method to determine the precise orbits of maneuvered satellites for BeiDou GEO and IGSO. The initial orbits of maneuvered satellites could be backward forecasted according to the precise orbit products. The systematic errors caused by unmodeled maneuvered force are absorbed by estimated pseudo-stochastic pulses. The proposed method for determining the precise orbits of maneuvered satellites is validated by analyzing data of stations from the Multi-GNSS Experiment (MGEX). The results show that the precise orbits of maneuvered satellites can be estimated correctly when orbit maneuvering, which could supplement the precise products from the analysis centers of IGS and iGMAS. It can significantly improve the integrality and continuity of the precise products and subsequently provide better precise products for users.

Self‐assisted first‐fix method for GPS receiver with autonomous short‐term ephemeris prediction

The time needed to get the first position is one of the key parameters to assess the performance of a global position system (GPS) receiver. Here, the authors present an autonomous satellite orbit prediction algorithm to provide usable ephemeris before the broadcast ephemeris is completely collected. Experimental results show that, with the ephemeris prediction algorithm, the TTFF of the receiver saves ∼74% in cold start mode. Furthermore, the accuracy of the presented algorithm is improved by using an empirical SRP model with parameters depending on the angle between the Sun and the satellite's orbital plane. Simulation results show that, for GPS PRN 5, when the SRP model with constant parameters is used to extrapolate the orbit for 5 days, only 43% of the position error is within 10 m, but this percentage can reach to 87% using the SRP model presented here. In addition, some single point positioning experiments with simulated satellite signals and real satellite signals are conducted to analyse the positioning results of the receiver with ephemeris prediction. The experimental results verify the effectiveness of the proposed algorithm.

Real‐time BDS signal‐in‐space anomaly detection method considering receiver anomalies

Signal-in-space user range error (SIS URE) can reach tens of meters or even tens of thousands of meters, and this may introduce hazardous misleading information (HMI) to real-time navigation and positioning. Monitoring of real-time SIS anomalies could improve the reliability of navigation and location services for end-users. For BeiDou satellites, the user range accuracy (URA) index currently broadcasted by navigation ephemeris does not reflect the true variation of URE. The anomaly detection method employed uses priori information from precise ephemerides, remains difficult for real-time detection. Additionally, the existing SIS anomalies detection method for BeiDou satellites does not exclude the influence of receiver anomalies. To address these problems, a method for calculating the instantaneous URE (IURE) was developed, and the empirical threshold was obtained by statistically analysing IURE before detecting SIS anomalies. Data of 14 stations from the Multi-GNSS Experiment (MGEX) and the international GNSS Monitoring & Assessment System (iGMAS) in the Asia-Pacific region were selected for detecting anomalies. Results were analysed in combination with the broadcast ephemeris health status indicator and the precise ephemeris detection results to verify the effectiveness of the method. It shows that the proposed method can accurately detect the starting and ending times of SIS anomalies.

Accuracy analysis of GPS broadcast ephemeris in the 2036th GPS week

Satellite orbit error is one of main sources in Global Positioning System (GPS) receiver positioning error. Using broadcast ephemeris in navigation message, the receiver can calculate spatial position of GPS satellites, then combine pseudorange measurements and achieve positioning solution. In this work, taking broadcast ephemeris in the 2036th GPS week as an example, orbital position of the satellite with the pseudo-random-noise (PRN) code 4 is calculated. Furthermore, using GPS precision ephemeris as a reference, orbital error of the broadcast ephemeris for the PRN 4 satellite is investigated. The results show that the maximum difference of the satellite in three directions is 36 meters, 57 meters and 39 meters, respectively. The three-dimension distance deviating from precision ephemeris is at most 61 meters. The maximum deviation occurs only during certain time periods in the whole GPS week.

The Carrier Phase Time Transfer with Broadcast Ephemeris

Time transfer method PPP is restricted by the real-time and precision of IGS production, and the real-time application have not been widely implemented. Standard Point Positioning(SPP) can satisfy the application for the real-time customer, but the precision is low and is not satisfy the high precision customer. So a new algorithm which have real-time and high precision performance is given. The algorithm dose not need the external orbit and clock error, and can be used for the real-time time transfer because of getting rid of the reliance on IGS production. In this paper, the analysis for the new algorithm is given by using the real measurement data. The results show that the algorithm could improve the time transfer results and frequency stability significantly; the time transfer precision of the new algorithm relative to SPP is improved from 10 ns to 1-2 ns, and dose not need the external precise ephemeris production; the new algorithm can be realized in the receiver conveniently.

Space State Representation Corrections as an Aid in Pseudolite Positioning.

In the presented study, the authors deal with the problem of transmission of pseudolite coordinates to the receiver. Nowadays, there is no uniquely specified method that would provide data about the position of the pseudolite to the GNSS receiver. There is also no technical standard that defines the explicit way of performing such transmission. Solutions presented in the literature are usually tailored to the described system, which is then suited to the specific situation. The article shows that the universal methods, involving the modification of transmitted broadcast ephemeris data, cannot be universally used. The modifications could not have been introduced due to the low resolution of the quantities that are transmitted in the ephemeris data, in relation to the values that would have to be sent by the pseudolite. To overcome the implementation problems, the authors propose two solutions. The first solution presented is the modification of the RTCM SSR frame. This approach allows replacing one of the existing satellites in space with the pseudolite, while the second method involves the use of new RTCM frame for sending the pseudolite position. Finally, a numerical example of the proposed solutions is presented. At the end of the manuscript, their advantages and implementation possibilities are discussed.

Evaluation of Signal-in-Space Continuity and Availability for BeiDou Satellite Considering Failures

Signal-in-space (SIS) continuity and availability are important indicators of performance assessment for Global Navigation Satellite Systems (GNSSs). The BeiDou Navigation Satellite System (BDS) Open Service Performance Standard (BDS-OS-PS-1.0) has been released, and the corresponding public performance indicators have been provided, but the actual SIS performance is uncertain to users. SIS continuity and availability are primarily related to unscheduled outages (failures). Therefore, based on the existing failure classification system and actual operation modes, four types of failure modes are first analysed: long-term failure related to satellite service period, maintenance failure related to satellite manoeuvring, short-term failure associated with random repairable anomalies and equivalent failure corresponding to a combination of the above three types of failures. Second, based on the failure classification and selected precise and broadcast ephemerides from 2015–2016, the Mean Time Between Failure (MTBF) and Mean Time To Repair (MTTR) of each failure type are obtained using appropriate detection methods. Finally, using a corresponding assessment model, the SIS continuity and availability of BeiDou are calculated for individual and equivalent failure cases, and these are compared with the provided index in the BDS Open Service Performance Standard.

Performance of Galileo-only dual-frequency absolute positioning using the fully serviceable Galileo constellation

The recent development of the Galileo space segment and the accompanying support of the International GNSS Service (IGS) allows for worldwide Galileo-only positioning. In this study, different techniques of dual-frequency absolute positioning using the fully serviceable Galileo constellation are evaluated for the first time and compared to the performance of GPS positioning. The daily static positioning based on the broadcast ephemeris using Galileo pseudoranges is significantly more accurate than the corresponding GPS solutions, obtaining the accuracy of a few decimeters. In the kinematic mode, the accuracy is better than 10 m and 20 m for the horizontal and vertical components, respectively, which is comparable to that of GPS. Precise absolute positioning using pseudorange and carrier phase Galileo observations combined with IGS Real-Time Service (RTS) or Multi-GNSS Experiment products is not yet as good as the corresponding GPS solutions. In the static mode, the root mean squared error (RMSE) between estimated and reference coordinates does not exceed 0.05 m and 0.06 m for the horizontal and vertical components, respectively. In the kinematic mode, the respective accuracies are better than 0.17 m and 0.21 m. Moreover, we show that both GPS and Galileo pseudorange solutions benefit from the RTS when compared to the broadcast solutions with the improvement in the accuracy between 10 and 59%. Remarkable results are achieved for Galileo Precise Point Positioning (PPP) solutions based on the broadcast ephemeris. In the static mode, the RMSE is 0.07 and 0.10 m for the horizontal and vertical components which is three and two times better, respectively, then the corresponding solutions based on GPS.

BDS-3 Time Group Delay and Its Effect on Standard Point Positioning

The development of the BeiDou navigation system (BDS) is divided into three phases: The demonstration system (BDS-1), the regional system (BDS-2) and the global BeiDou navigation system (BDS-3). At present, the construction of the global BeiDou navigation system (BDS-3) constellation network is progressing very smoothly. The signal design and functionality of BDS-3 are different from those of BDS-1 and BDS-2. The BDS-3 satellite not only broadcasts B1I (1561.098 MHz) and B3I (1268.52 MHz) signals but also broadcasts new signals B1C (1575.42 MHz) and B2a (1176.45 MHz). In this work, six tracking stations of the international GNSS monitoring and assessment system (iGMAS) were selected, and 41 consecutive days of observation data, were collected. To fully exploit the code observations of BDS-2 and BDS-3, the time group delay (TGD) correction model of BDS-2 and BDS-3 are described in detail. To further verify the efficacy of the broadcast TGD parameters in the broadcast ephemeris, the standard point positioning (SPP) of all the signals from BDS-2 and BDS-3 with and without TGD correction was studied. The experiments showed that the B1I SPP accuracy of BDS-2 was increased by approximately 50% in both the horizontal and vertical components, and B1I/B3I were improved by approximately 70% in the horizontal component and 47.4% in the vertical component with TGD correction. The root mean square (RMS) value of B1I and B1C from BDS-3 with TGD correction was enhanced by approximately 60%–70% in the horizontal component and by approximately 50% in the vertical component. The B2a-based SPP was increased by 60.2% and 64.4% in the east and north components, respectively, and the up component was increased by approximately 19.8%. For the B1I/B3I and B1C/B2a dual-frequency positioning accuracy with TGD correction, the improvement in the horizontal component ranges from 62.1% to 75.0%, and the vertical component was improved by approximately 45%. Furthermore, the positioning accuracy of the BDS-2 + BDS-3 combination constellation was obviously higher than that of BDS-2 or BDS-3.

VPPP Algorithms with Multiple Antennas by Applying MADOCA Products

According to our previous research works, we present the algorithms of the VPPP (Very Precise Point Positions) using multiple GNSS antennas with known distances each other. VPPP algorithms contain the very precise GNSS positioning as well as the so-called GNSS Gyro by estimating the multiple baseline vectors from the reference antenna to other antennas. In this paper, we attempt to implement the satellite orbits and clocks correction data from the MADOCA Products which had been developed by JAXA, into our VPPP algorithms. Further, finally, we show the positioning accuracy as well as the estimation accuracy of the Euler's angles in the GNSS Gyro, in comparison with using the so-called GPS broadcast ephemeris.