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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]

Global Positioning System technique has been widely used to estimate ocean tide loading displacements, but classical harmonic analysis with satellite modulation typically disregards the effects of hundreds of minor tides within the same tidal species of major tides. We present an improved harmonic analysis of eight major tidal constituents (M2, S2, N2, K2, K1, O1, P1 and Q1) that are adjusted by more adjacent minor tides in semidiurnal and diurnal species than the usual satellite modulation approach, through the tidal admittance interpolation. Our results show that this approach allows for a more reliable determination of GPS-observed N2, Q1, P1 and S2 constituents in the northwest European shelf than the classical method, as demonstrated by a comparison with FES2014b and TPXO9-Atlas ocean tide model predictions. The advantages of our method are more pronounced in the harmonic analysis of GPS time series of short duration (1–2 years) than long duration. These improvements mainly depend on some inferred minor tides with larger equilibrium amplitudes, which provide effective admittance constraints to major tidal estimation. Among the major tidal estimates, the most significant improvement is seen for the N2 constituent (with the maximum improvement of 9.9%, 9.0% and 9.7% for the up, east and north components in terms of agreement with FES2014b model predictions), particularly along the Wadden Sea coast where significant satellite modulation deviations occur. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • An adaptive and data-driven method for denoising high rate GNSS is introduced. • It is based on Complete Ensemble EMD and Multiscale Multiway PCA. • It can significantly eliminate the white noise and colored noise in the GNSS data. • It can be well suitable for nonlinear and nonstationary time series. Abstract In order to improve the possibility of correct interpretation of some geophysical phenomena such seismology, it is important to reduce systematic errors such as common mode error (CME) and multipath errors, and to improve the accuracy of high-rate (1–5 Hz) displacements. This paper focuses on accuracy enhancement and noise assessment of high-rate Global Navigation Satellite System (GNSS) position time series of regional network of GNSS stations. Complete ensemble empirical mode decomposition-based multiscale multiway principal component analysis (C-MSMPCA) denoising method is introduced to denoise the high-rate (1–5 Hz) GNSS position time series, whose performance was compared with those of modified sidereal filtering (MSF), stacking filtering, PCA and the recently developed multiscale multiway PCA (MSMPCA). It turns out that C-MSMPCA can significantly eliminate the high-frequency random noise and remove the low-frequency CME, and other systematic errors such as multipath errors. Furthermore, for denoising high-rate GNSS time series, C-MSMPCA is more precise than the other denoising methods. Irrespective of sampling rates and data processing strategies, C-MSMPCA can respectively reach the accuracy of submillimeter- and millimeter-levels on the horizontal and vertical components of high-rate GNSS displacements. Spectral analysis on the 1 Hz coordinate time series from the Sichuan GNSS Continuous Observing Network of China suggests that Gauss-Markov process is an adequate noise model for the noise characteristics of the filtered GNSS data using MSMPCA and C-MSMPCA. The CME magnitudes of MSMPCA are 2.61, 2.55, and 6.72 mm (east, north, and vertical), and those of C-MSMPCA are 2.69, 2.80, and 7.80 mm, respectively. [ABSTRACT FROM AUTHOR]