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The BeiDou Navigation Satellite System (BDS) broadcasts the BDS Klobuchar model (BDSK) for ionospheric delay correction in both BDS-2 regional service phase and BDS-3 global service phase. Unlike the GPS Klobuchar model, the BDSK model adopts a simple "symmetrical strategy" due to the limited ionospheric input data within China, which results in inaccurate total electron content (TEC) estimation in the southern hemisphere. Besides, the "high latitude anomaly" occurs in the BDSK model due to the lack of latitude limitation strategy, which deteriorates the accuracy of the BDSK model in the southern hemisphere further. To solve this problem, we propose a revised BDS Klobuchar model (RBDK), in which the "non-symmetrical strategy" is adopted in the southern hemisphere and an amplitude constraint is introduced at high latitudes. For comparison, the fitted BDS Klobuchar model (BDFK) that is estimated using the same ionospheric input data and constraint algorithm for the RBDK model but with the "symmetrical strategy" is also included. First, we conduct a comparative analysis of the time series of the eight parameters for the BDSK, BDFK and RBDK models in 2021. The parameters of the BDFK and RBDK models are more stable, and there will be no abnormal jumping phenomenon that occurs in the BDSK model. Then, the performance of the broadcast BDSK model, the fitted BDFK model and the proposed RBDK model during the whole year of 2021 are evaluated by comparing them with the high-precision global ionospheric map (GIM) of the International GNSS Service (IGS). In the southern hemisphere, the root mean square (RMS) values of the BDSK and BDFK are 6.5 and 5.8 TEC unit (TECU), respectively, while that of the RBDK is 4.6 TECU, showing improvements of 29% and 21%, respectively. At high latitudes in the northern hemisphere, the RMS value of the BDSK is 7.6 TECU, while they are only 3.7 TECU for the RBDK and BDFK when the amplitude constraint is introduced. Final, we select 16 IGS stations to validate the performance of the BDSK, BDFK and RBDK models in the standard point positioning (SPP) domain in 2021. The average SPP accuracy of the BDSK is 8.88 m at 6 high-latitude stations, while they are 5.48 m for the RBDK and BDFK, showing significant improvement of 38%. Excluding the high-latitude stations, the SPP accuracy of the RBDK outperforms the BDFK and BDSK by 14% and 18%, respectively, at stations in the southern hemisphere. As expected, the proposed RBDK model shows significantly better performance in the southern hemisphere and at high latitudes in contrast to the broadcast BDSK model. [ABSTRACT FROM AUTHOR]

The continuously developing Global Navigation Satellite Systems (GNSS), in particular with the latest operational BDS and Galileo, provide good opportunities to enhance the performance of precise positioning. This study evaluates the performance of high-rate precise point positioning (PPP) applied for seismogeodesy with very recent BDS and Galileo. The static experiments with 20-Hz GNSS data show that Galileo and BDS-3/BDS-2 achieve comparable performances, with average 3D RMS values of 0.6–1.3 cm and 0.8–1.2 cm, respectively. In the dynamic experiments, we use a single-axis earthquake simulator of Quanser Shake Table II to simulate seismic waveforms of real earthquakes and collect 20-Hz GNSS data to evaluate the PPP performance. Taking the displacements recorded by the embedded encoder of the shake table as the truth, the accuracies of PPP displacements during the seismic events are 4–8 mm for GPS, 6–9 mm for BDS-2, and 3–6 mm for Galileo and BDS-3/BDS-2. By combining BDS-3 with BDS-2, the positioning accuracy of BDS is improved by 50% with respect to BDS-2 only. Galileo and BDS-3/BDS-2 perform slightly better than GPS, which is likely because the two latest operational systems use the more precise passive hydrogen maser clocks and have lower signal-in-space range error. The multi-GNSS solutions with GPS + Galileo + BDS-3/BDS-2 further improve the accuracy reaching 2–5 mm. We also identify a scale factor in the high-rate PPP displacements, which is probably induced by the dynamic stress error and related to the oscillating frequency. The scale factor reaches the maximum of 1.71 at an oscillating frequency around 2.5 Hz and then descends as the frequency increases. The improved performance of high-rate PPP augmented by the recent BDS-3 and Galileo is helpful to improve the practical level of high-rate GNSS in seismogeodesy and expand its applications to many other high-rate and high-accuracy applications. [ABSTRACT FROM AUTHOR]

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 M W 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. [ABSTRACT FROM AUTHOR]

Precise point positioning with ambiguity resolution (PPP-AR) is a useful tool for high-precision geodetic and geophysical applications, while phase bias products are the prerequisite to implement PPP-AR. Wuhan University has been providing the final (the best operationally post-processing solution based) phase clock/bias products with a latency of two weeks since March of 2019, while a dedicated open-source software package PRIDE PPP-AR is released to leverage these products for high-precision positioning. In order to satisfy some both time and precision critical applications, such as rapid earthquake response, Wuhan University also released rapid (with comparable quality but with much shorter delivery latency) phase clock/bias products with a latency of less than 24 h and updated PRIDE PPP-AR in July 2019. We first introduce the phase clock/bias generation and validation schemes and the maintenance of routine products provision. Then, with 14 days (July 2 to July 15 in 2019) of GPS data collected from 146 globally distributed IGS (International GNSS Service) stations, we evaluated the positioning performance of the rapid products with respect to their final counterparts. It is found that positioning precision of PPP-AR using rapid products is comparable to that using final products, especially in kinematic positioning mode. When rapid products are used, the RMS of PPP-AR in static mode with respect to IGS weekly solutions can reach 1.7 mm, 1.8 mm and 5.5 mm in the east, north and up components, respectively. Furthermore, the RMS of epoch-wise positions with respect to daily solutions for the east, north and up components are 0.51 cm, 0.57 cm and 1.51 cm for PPP-AR with rapid products in kinematic mode. It demonstrates that the rapid phase clock/bias products can sufficiently meet the precision requirement of most geodetic and geophysical applications yet with much shorter time delay. Finally, we study the July 6th M7.1 2019 Ridgecrest, California earthquake using the rapid phase clock/bias products and demonstrate their comparable performance against the final products. [ABSTRACT FROM AUTHOR]