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The Beidou-3 system (BDS-3) satellites are deployed, equipped with an inter-satellite link (ISL) payload, so that the satellite–satellite or satellite-ground time synchronization is available. The satellite-ground link (GSL) can be used in conjunction with the ISL if proper attention is paid to all corrections and the biases are fitted. We execute methods to synchronize the clocks of BDS-3 satellites to an accurate reference clock on the ground, by estimating relative clock offsets obtained via Ka-band GSL observations. We solve for the relative biases using the closure properties of the redundant biases and the Ka-band (Ka-mode) satellite-ground two-way data. We find the biases, relative to the GSL hardware delay, are relatively stable in the short term. This makes it feasible to estimate them as a constant every few hours, and the standard deviation of the hardware delay estimations within 24 h is slightly less than 0.7 ns. The frequency stability of Ka-mode estimated clock offset shows a negative short-term performance because of the dominant effect of the white phase noise in the relative clock offsets from the Ka-mode, but the long-term performance seems to be improved to a higher level. The time synchronization accuracy of Ka-mode is proven to be better than 0.3 ns (RMS), whereas the accuracy for the high-orbit satellite is slightly worse. [ABSTRACT FROM AUTHOR]

The Chinese BeiDou global satellite system (BDS-3) and regional system (BDS-2) are predicted to coexist over the next decade. Intersystem biases (ISBs) in BDS-2/BDS-3 play a key role in maintaining the consistency and continuity from the BDS-2 to BDS-3 time transfer. Here, we discuss the temporal characteristics, parameter composition, generation mechanism, and the effect of ISBs in BDS-2/BDS-3 on time and frequency transfer. The satellite orbits and clock products from three international GNSS service analysis centers, namely Wuhan University (WUM, China), GeoForschungsZentrum Potsdam (GFZ, Germany), and the Center for Orbit Determination in Europe (CODE), were employed to investigate the time-transfer stability of ISBs when BDS-2 and BDS-3 were used in combination. We analyzed the intrinsic characteristics of ISBs, the receiver types, antennas, and frequency standards. Our first results showed that ISBs are stable for different analysis center products, although the mean values of daily results differed markedly for the three analysis centers. With respect to the relationship between station attribution and ISB difference for a time link, the receiver type, antenna, and frequency standard influence the ISB differences in time and frequency transfer. The effect of three ISB stochastic models was evaluated with respect to time and frequency transfer. The "walk" and "constant" schemes were slightly superior to "noise", with the improvement in their frequency stability being approximately 5% compared with that of "noise". [ABSTRACT FROM AUTHOR]

A quality evaluation of precise products for BDS-3 constellations is presented for the first time in this contribution. Then, the tropospheric delay retrieval and positioning performance of BDS-3 precise point positioning (PPP) solutions using the precise products (gbm, wum, iac, sha, cnt) with observations from 24 stations from DOY 280 to 317 in 2020 was comprehensively investigated. The orbit comparisons present consistencies of 0.09–0.22 m for the C19–C37 satellites and of 0.5–1.2 m for the C38–C46 satellites among the final products. The standard deviation (STD) values of the clock differences of iac showed the best agreement with those of gbm, followed by wum, sha. The clock differences performance of cnt was the worst. For BDS-3 PPP solutions with five Analysis centers (ACs) products, the median convergence times of static PPP mode incorporating the gbm, wum, iac, sha, and cnt products were 31.0, 33.5, 34.5, 37.8, and 72.0 min, respectively; the median convergence times of kinematic PPP model incorporating the same products were 40.5, 41.0, 50.5, 55.0, and 94.0 min, respectively. The positioning accuracies in the static and kinematic modes were approximately 1–4 cm, 2–6 cm in the horizontal and vertical components, respectively. With the final products in kinematic mode, the performance of PPP with real-time products (cnt) is poorer than all PPP with final products. The median of ZTD accuracies of the five products gbm, wum, iac, sha, and cnt were 7.84, 7.58, 7.04, 7.19, and 10.1 mm, respectively, and the accuracy differences were very small among five AC products (gbm, wum, iac, sha). [ABSTRACT FROM AUTHOR]

• GTS distribution of orbit determination can be optimized by the proposed algorithm. • GTS saturated number for orbit determination can be got by the proposed algorithm. • ISL can weaken the influence of GTS distribution and number on orbit determination. A precise satellite orbit is the basis for high-precision services for users, and the determination of high-precision satellite orbits depends on the reasonable distribution and volume of ground tracking stations (GTSs). In July 2020, the BeiDou global navigation satellite system (BDS-3) was completed and began to be operated globally. Based on the principle of dynamic orbit determination, we first developed an algorithm to determine the optimal distribution and number of GTSs for accurate satellite orbit determination. Subsequently, based on 10 GTSs located in China, the optimal distribution and number of GTSs with and without inter-satellite link (ISL) ranging observations were determined. Finally, real measurements of GTS and ISL ranging observation data were used to validate the GTS results yielded by the algorithm. Using 18 BDS-3 satellites, and based on non-ISL observations and 10 Chinese regional GTSs, we found that GTSs distributed near the equator contributed significantly to the accuracy of orbit determination for these satellites compared to other GTSs. Orbit determination results obtained from the measured data of the optimal GTSs were more accurate than those obtained from the measured data of uniformly distributed global GTSs. Upon the addition of 55 uniformly distributed GTSs worldwide, the orbit determination accuracy for BDS-3 satellites tended to plateau. Moreover, following the addition of ISL, although the distribution and number of GTSs was optimized using the proposed algorithm, the orbit determination results from the measured data revealed that a change in the distribution and number of GTSs had a limited effect on the BDS-3 orbit determination results. [ABSTRACT FROM AUTHOR]

• Under regional GTS, ISL significantly improves BDS-3 orbit determination accuracy. • The initial weight ratio has little effect on the result when VCE algorithm is used. • VCE algorithm has contribute to fusion data processing of L-band and Ka-band. The BeiDou global navigation satellite system (BDS-3) has established the Ka-band inter-satellite link (ISL) to realize a two-way ranging function between satellites, which provides a new observation technology for the orbit determination of BDS-3 satellites. Therefore, this study presents a BDS satellite orbit determination model based on ground tracking station (GTS) observations and ISL ranging observations firstly to analyze the impact of the ISL ranging observations on the orbit determination of BDS-3 satellites. Subsequently, considering the data fusion processing, the variance component estimation (VCE) algorithm is applied to the parameter estimation process of the satellite orbit determination. Finally, using the measured data from China's regional GTS observations and BDS-3 ISL ranging observations, the effects of ISL ranging observations on the orbit determination accuracy of BDS-3 satellites are analyzed. Moreover, the impact of the VCE algorithm on the fusion data processing is evaluated from the aspects of orbit determination accuracy, Ka-band hardware delay parameter stability, and ISL ranging observation residuals. The results show that for China's regional GTSs, the addition of BDS-3 ISL ranging observations can significantly improve the orbit determination accuracy of BDS-3 satellites. The observed orbit determination accuracy of satellite radial component is improved from 48 cm to 4.1 cm. In addition, when the initial weight ratio between GTS observations and ISL ranging observations is not appropriate, the various indicators which include orbit determination accuracy, ISL hardware delay, and ISL observation residuals were observed to have improved after the adjustment of the VCE algorithm. These results validate the effectiveness of the VCE algorithm for the fusion data processing of the GTS observations and ISL ranging observations. [ABSTRACT FROM AUTHOR]

• We analyze the time synchronization performance within the BDS-3 ISL system using real data (one month) • A two-way time synchronization method with error correction models is utilized. • The one-way ranging accuracy of BDS-3 ISLs is consistently better than 7 cm, and the calculated clock-free observables better than 5 cm. • Correcting various errors is crucial for improving synchronization to sub-ns levels. • The overall time synchronization accuracy between satellites achieved is better than 0.4 ns, with most BDS-3 satellites showing comprehensive synchronization accuracy of better than 0.3 ns. • The results verify the effectiveness of the BDS-3 ISL system for high-precision timekeeping. Time synchronization through inter-satellite link (ISL) observations is crucial for enabling autonomous navigation in global navigation satellite systems. This study investigates the time synchronization performance within China's BeiDou Navigation Satellite System (BDS) using ISL measurements from 29 BDS-3 constellation satellites. A dedicated two-way time synchronization method is detailed, emphasizing its uniqueness and precision in ensuring accurate time synchronization. The study also delves into the application of various error corrections, encompassing time delay induced by motion, relativistic effects, and hardware delays. Ranging results show accuracies around 7 cm for one-way ISLs. The impact of error corrections is quantified, with the time delay error caused by motion exhibiting the most significant influence on synchronization accuracy. Using one month of BDS-3 ISL data, time synchronization accuracies better than 0.4 ns are consistently achieved between all satellites after implementing comprehensive error mitigation. The results indicate the robust performance of the BDS-3 ISL system for high-precision timekeeping, supporting autonomous orbit determination and navigation without relying on ground monitoring. These findings demonstrate the effectiveness of using ISLs for GNSS satellites and provide valuable insights for advancing satellite navigation capabilities. [ABSTRACT FROM AUTHOR]