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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.

For more than 20 years, precise point positioning (PPP) has been a well-established technique for carrier phase-based navigation. Traditionally, it relies on precise orbit and clock products to achieve accuracies in the order of centimeters. With the modernization of legacy GNSS constellations and the introduction of new systems such as Galileo, a continued reduction in the signal-in-space range error (SISRE) can be observed. Supported by this fact, we analyze the feasibility and performance of PPP with broadcast ephemerides and observations of Galileo and GPS. Two different functional models for compensation of SISREs are assessed: process noise in the ambiguity states and the explicit estimation of a SISRE state for each channel. Tests performed with permanent reference stations show that the position can be estimated in kinematic conditions with an average three-dimensional (3D) root mean square (RMS) error of 29 cm for Galileo and 63 cm for GPS. Dual-constellation solutions can further improve the accuracy to 25 cm. Compared to standard algorithms without SISRE compensation, the proposed PPP approaches offer a 40% performance improvement for Galileo and 70% for GPS when working with broadcast ephemerides. An additional test with observations taken on a boat ride yielded 3D RMS accuracy of 39 cm for Galileo, 41 cm for GPS, and 27 cm for dual-constellation processing compared to a real-time kinematic reference solution. Compared to the use of process noise in the phase ambiguity estimation, the explicit estimation of SISRE states yields a slightly improved robustness and accuracy at the expense of increased algorithmic complexity. Overall, the test results demonstrate that the application of broadcast ephemerides in a PPP model is feasible with modern GNSS constellations and able to reach accuracies in the order of few decimeters when using proper SISRE compensation techniques.

With the official announcement of open service since the end of 2018, the BeiDou navigation satellite system (BDS) has started to provide global positioning, navigation and timing (PNT) services. Thus, it is worth assessing the positioning service of new BDS satellites and signals. In this paper, we comprehensively assess the system status and the global positioning performance of BDS regarding single point positioning (SPP) and real-time kinematic (RTK) performance. Results show that the signal in space range error (SISRE) of BDS-3 satellites is superior to that of BDS-2 satellites, showing an overall accuracy of 0.71 m versus 0.97 m, which is competitive with GPS and Galileo. With the contribution of BDS-3, the number of global average visible satellites has increased from 5.1 to 10.7, which provides a mean global position dilution of precision (PDOP) value better than 6 at 99.88% and the mean availability of basic PNT performance is also improved from 35.25% to 98.84%. One week of statistical results from 54 globally distributed international GNSS service (IGS) stations show that the root mean square (RMS) of SPP accuracy is 1.1 m in horizontal and 2.2 m in vertical, which is at the same level of GPS. The new B1c and B2a signals show a smaller observation noise than B1I, and SPP performance of B1c is similar to that of B1I. However, the positioning precision is slightly worse at the B2a frequency, which may be due to the inaccurate BDS ionosphere correction. As for short baseline RTK, baseline accuracy is also improved due to the increased number of new BDS satellites.

The availability of orbit information with high precision and low latency is a key requirement for many Earth‐observation missions, predominantly in the field of radio occultation. Traditionally, precise orbit determination solutions of low‐Earth orbit (LEO) satellites are obtained offline on ground after downloading GNSS measurements and auxiliary spacecraft data to the processing center. The latency of this processing depends on the frequency of LEO downlink contacts and the availability of precise GNSS orbit and clock products required for the orbit determination process. These dependencies can be removed by computing the precise orbit determination solution on board the satellite using GNSS broadcast ephemerides. In this study, both real data and simulated measurements from a representative LEO satellite are processed in a flight‐proven Kalman‐filter algorithm. The paper studies the use of GPS, Galileo and BeiDou‐3 for real‐time orbit determination in different combinations with simulated measurements. Results show that use of dual‐frequency observations and broadcast ephemerides of Galileo and BeiDou‐3 leads to a significant reduction of 3D rms orbit errors compared to GPS‐only processing. An onboard navigation accuracy of about one decimeter can be achieved without external augmentation data, which opens up new prospects for conducting relevant parts of the science data processing in future space missions directly on board a LEO satellite.

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.

The effects of solar, geomagnetic, and ionospheric anomalies on satellite communication are inextricable. Range Error (RE) is the most common fault that is faced by the navigational receivers during solar flares. Since RE always depends on the Total Electron Content (TEC) available across the satellite ray path, a prediction model capable of predicting the TEC in advance will be an excellent deterrent during adverse space weather conditions. In this research, Cokriging based Surrogate Model (COKSM) is constructed for predicting the TEC variations that occurred during the month of January 2022 to April 2022 over Hyderabad region. The input data used in the construction of the model includes F 10.7 radio flux, Sunspot number (SSN), Geomagnetic index Kp and Ap along with Vertical TEC (VTEC) data collected from Hyderabad station located in 17.31° N latitude and 78.55° E longitude. The data is collected in hourly averaged resolution for a period of 120 days covering January to April 2022. The variations in Ionospheric TEC due to solar flares and geomagnetic anomalies that occurred during the selected observation dates are principally analyzed in order to evaluate the prediction capability of the COKSM program during adverse conditions. The performance of the model is evaluated using metrics like Root Mean Square Percentage error (RMSPE), Correlation Coefficient (ρ), CHI-Squared goodness of fit test and R-squared. The results that are plotted as a linear regression scatter plot clearly shows that with very small residuals the proposed prediction model is performing well for TEC prediction. The overall RE predicted by the model is within the scale of 1–12 meters. The error parameters calculated between true TEC and predicted TEC is found out to be in the scale of 0.88 to 5.06% for RMSPE, 0.9308 to 0.9981 for correlation coefficient, 4.97 to 107.94 (TECU) for chi squared and 0.78 to 0.98 (TECU) for R squared.

Positioning, navigation and time are the cornerstones of satellite navigation. These aspects are frequently affected by ionospheric variations caused by solar flares (SF). In this study, we have attempted to predict the range error (RE) caused by ionospheric delay in Global Positioning System (GPS) signals during six different X-class SF that occurred in the 25th solar cycle using two different approaches, namely, a recurrent neural network (RNN) and the ordinary Kriging-based surrogate model (OKSM). The total electron content (TEC) collected from Hyderabad station along with other input parameter includes the Planetary A and K index ( Ap and Kp ), solar sunspot number (SSN), disturbance storm time index ( Dst ), and radio flux measured at 10.7 cm ( F 10.7) were used for prediction. The OKSM uses the previous six days of datasets to predict the RE on the seventh day, whereas the RNN model uses the previous 45 days of datasets to predict the RE on the 46th day. The performance of both models is evaluated using statistical parameters such as root mean square error (RMSE), normalized root mean square error (NRMSE), Pearson’s correlation coefficient (CC), and symmetric mean absolute percentage error (sMAPE). The results indicate that the OKSM performs well in adverse space weather conditions when compared to RNN.

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.

Traditional intersatellite communications for shared timing information rely on microwave transceivers such as those in Milstar, AEHF, and Iridium constellations. With extensive space heritage and well-established engineering and performance specifications, these methods have typified the field of high-performance satellite synchronization for decades, recently introduced into active GNSS satellite constellations such as BeiDou. Optical crosslinks, currently investigated as an augmentation or alternative to traditional microwave-based methods, can provide enhanced precision to intersatellite ranging and time transfer, performing beyond one-way or uplink/downlink microwave-based communications. The challenges of time transfer through optical links and crosslinks can significantly impact the systems architecture, optical terminal complexity, and agreements on international standards. Orders-of-magnitude precision enhancement can enable novel timing and ranging technologies allowing for advanced navigation capabilities. Additionally, basic scientific studies with a fleet of synchronized satellites could inform fundamental physics studies on a truly global scale. We evaluate the benefits, drawbacks, and potential applications of satellite synchronization through microwave and optical crosslinks for shared timing and ephemeris data in support of enhanced constellation state estimation and reduced range error. The risks and value associated with these technologies are also discussed with an emphasis on challenges for aerospace.

Users of the Global Positioning System (GPS) utilize the Ionospheric Correction Algorithm (ICA) also known as Klobuchar model for correcting ionospheric signal delay or range error. Recently, we developed an ionosphere correction algorithm called NTCM-Klobpar model for single frequency GNSS applications. The model is driven by a parameter computed from GPS Klobuchar model and consecutively can be used instead of the GPS Klobuchar model for ionospheric corrections. In the presented work we compare the positioning solutions obtained using NTCM-Klobpar with those using the Klobuchar model. Our investigation using worldwide ground GPS data from a quiet and a perturbed ionospheric and geomagnetic activity period of 17 days each shows that the 24-hour prediction performance of the NTCM-Klobpar is better than the GPS Klobuchar model in global average. The root mean squared deviation of the 3D position errors are found to be about 0.24 and 0.45 m less for the NTCM-Klobpar compared to the GPS Klobuchar model during quiet and perturbed condition, respectively. The presented algorithm has the potential to continuously improve the accuracy of GPS single frequency mass market devices with only little software modification.