Journal of Geodesy最新文献

The paper deals with the linearized Molodensky problem, when data are supposed to be square integrable on the telluroid S, proving that a solution exists, is unique and is stable in a space of harmonic functions with square integrable gradient on S. A similar theorem has already been proved by Sansò and Venuti (J Geod 82:909–916, 2008). Yet the result basically requires that S should have an inclination of less than (60^circ ) with respect to the vertical, or better to the radial direction. This constraint could result in a severe regularization for the telluroid specially in mountainous areas. The paper revises the result in an effort to improve the above estimates, essentially showing that the inclination of S could go up to (75^circ ). At the same time, the proof is made precise mathematically and hopefully more readable in the geodetic community.

Global Navigation Satellite Systems (GNSS) enable the determination of station displacements, which are essential to understanding geophysical processes and establishing terrestrial reference frames. Unfortunately, GNSS station position time series exhibit spatially and temporally correlated noise, hindering their contribution to geophysical and geodetic applications. While temporal correlations are commonly accounted for, a strategy for modeling spatial correlations is still lacking. Therefore, this study proposes a diagnosis of the spatial correlations of the white and flicker noise components of GNSS position time series, using the global Nevada Geodetic Laboratory dataset. This analysis reveals different spatial correlation patterns for white and flicker noise and the superposition of three distinct spatial correlation regimes (large-scale, short-scale and station-specific), providing insight into the noise sources. We show, in particular, that about 70% of flicker noise corresponds to large-scale variations possibly attributable to orbit modeling errors. We also evidence an increase in the spatial correlations of white noise at distances below 50 km, most pronounced in the vertical component, where 50% of the white noise appears to be driven by short-scale effects—possibly tropospheric delay mismodeling.

Multipath remains one of the major challenges in high-precision GNSS positioning. The multipath hemispherical map (MHM) based on satellites’ location repeatability in space is a popular method to mitigate GNSS multipath effects, but its performance depends on the availability of sufficient satellite orbital tracks in the skyplot. For instance, for BDS-3 medium Earth orbiters and Galileo satellites with 7-day and 10-day orbital repeat times, respectively, the skyplot of their orbital tracks will be too sparse to cover the shifting orbital tracks on the succeeding days, if only a few days of observations are used to construct MHMs. In this study, we establish an interoperable MHM using the overlap frequency signals of GPS, Galileo and BDS-3 (i.e., GPS L1/L5, Galileo E1/E5a and BDS-3 B1C/B2a). We compared the performance of GPS/Galileo/BDS-3 MHM (i.e., MP_GEC) and single-constellation MHMs (i.e., MP_G, MP_E and MP_C). The mean reduction rates of the L1/E1/B1C and L5/E5a/B2a carrier-phase residuals for the MP_GEC applied to GPS, Galileo and BDS-3 are 36% and 48%, respectively, which are 10–30% points larger compared to the MP_G, MP_E and MP_C. The MP_GEC constructed using 4 days of observations reduced the Galileo RMS positioning errors by 26%, 31% and 29% for the east, north, and up components, respectively, showing improvements of about 16, 18 and 17% points compared to the MP_E, and even approaching the RMS errors of the MP_E constructed using 10 days of observations. The results show that the interoperable GPS/Galileo/BDS-3 MHM is able to improve the spatial resolution, modeling efficiency and correction performance in mitigating multipath effects for high-precision GNSS positioning.

The ionosphere crucially impacts on Global Navigation Satellite System (GNSS) positioning accuracy and integrity. Recently some network-based methods have shown the potential to construct a regional/global vertical total electron content (VTEC) or grid ionospheric vertical delay (GIVD) map for accuracy augmentation purposes. However, how to use these advanced methods for integrity augmentation has not been adequately investigated. The authors have investigated a regional ionospheric integrity monitoring strategy based on the radial basis function neural network (RBF-NN), using GNSS TEC observations. Similar to the SBAS approach, the GIVD map is constructed so as to enhance positioning accuracy, and the corresponding grid ionospheric vertical error (GIVE) map is constructed for protection level calculation to enhance positioning integrity. To reduce the GIVD residuals and the GIVE values, the local ionospheric spatial activity index (LISAI) is proposed as an indicator of local ionospheric spatial activity level. The RBF-NN structure parameters are able to be adaptively determined via hierarchical clustering. Modeling results in the China region have verified that the proposed GIVD modeling method is slightly better than the classical WAAS-Kriging method. The proposed GIVE modeling method significantly outperforms WAAS-Kriging, achieving an improvement of around 46% and 25% during the ionospheric calm and active periods, respectively.

Reliable integer ambiguity resolution (IAR) is essential for carrier phase-based centimeter-level accurate positioning using global navigation satellite systems (GNSSs). In all IAR methods, the best integer equivariant (BIE) estimator is optimal in the sense of minimizing the mean-squared errors. However, the BIE estimator comprises an enumeration in the integer space of ambiguities, and its complexity grows exponentially with the number of ambiguities. Moreover, in a complex urban environment, the positioning performance of the BIE estimator is also reduced due to larger observation errors and even outliers. To address this problem, an efficient and reliable IAR method is proposed in this paper, which consists of two major steps. First, we apply the vectorial integer bootstrapping (VIB) (Teunissen et al. in J Geod 95(9):1–14, 2021) by implementing BIE in each sequential block-by-block integer estimation to improve computation efficiency, which is denoted as VIB-BIE. Second, a measure, named the acceptable probability (ACP), is defined to control the reliability of VIB-BIE estimation. Both simulated and real multi-GNSS data are employed to evaluate the performance of the proposed method and conventional BIE. The results show that the flexibility and efficiency of IAR are both improved by VIB-BIE. In a complex urban environment, the ACP-based VIB-BIE outperforms the BIE in terms of IAR reliability and positioning accuracy. Compared to the BIE, the positioning accuracies are improved by 42.4%, 34.2%, and 31.8% in the east, north, and upward directions, respectively.

One of the most challenging environments for accurate geoid models is in high, rugged mountain areas. Orthometric heights derived from GNSS and a geoid model can easily have errors at the decimeter level. To investigate the effect of geoid model variability on the elevations of peaks in high, rugged mountain areas, this paper is focused on the “Fourteeners” of Colorado, USA (a group of about 60 peaks that are above 14,000 feet = 4267.2 m). Airborne LiDAR data are used to determine geometric (ellipsoidal) heights, which first requires removing a hybrid geoid model, as the LiDAR data is originally provided as orthometric heights. We quantify a significant improvement when using these derived ellipsoidal heights compared with the original orthometric heights: from ± 0.074 to ± 0.054 m (RMSE), an improvement of 28%. Next, a mean geoid model is determined with a relative accuracy of ± 0.06 to 0.08 m and used as a “stand in” realization of the future, official geopotential datum of the USA, NAPGD2022. Using the LiDAR ellipsoidal heights and geoid model, elevations (and uncertainties) for each of the Fourteener summits are determined and found to be, on average, 1.6 m lower than currently published values. This is a much larger change than the 0.5 m decrease expected from the new datum shift alone. The bulk of the difference is due to the original treatments of the vertical angle, triangulation data. A reanalysis of 32 of the 60 peaks shows that the historic data were indeed too high by about 1.0 m or more. Ultimately, no peak falls below the 14,000-foot level nor are any peaks elevated above this level.

We investigate using the GIRAFE cold-atom gravimeter during an airborne gravity survey for improving gravity field and quasigeoid modelling. The study is conducted over the Bay of Biscay, France. Geoid/quasigeoid determination is usually a major challenge over such coastal areas due to scarce and inconsistent gravity data. In a first step, the GIRAFE dataset is analysed and compared with available surface gravity data as well as with global altimetry models from UCSD and DTU. The comparisons indicate that the DTU model is better than the UCSD model within around 10 km from the coastline. Furthermore, recent satellite altimeter missions significantly improve the altimetry models in coastal areas. A significant bias (− 4.00 mGal) in shipborne data is also found from this comparison. In a second step, eight quasigeoid solutions are calculated to evaluate the contribution of GIRAFE data. This contribution reaches 3 cm in terms of height anomaly for DTU21 while being much larger for UCSDv31 and shipborne data. Finally, the quasigeoid solutions are validated using GNSS-levelling data. The results indicate that using GIRAFE data improves by approximately 50% the quality of quasigeoid models over land near the coast. The highest accuracy, around 1 cm, is achieved when GIRAFE data are merged with refined gravity data. Importantly, the standard deviation is just 1.2 cm when compared with GNSS-levelling points if using only GIRAFE data over marine areas, which is very close to the 1 cm goal of geoid/quasigeoid model determination in modern geodesy. This study thus confirms the benefits of performing airborne gravity survey using quantum sensors.

The Atmosphere and Ocean non-tidal De-aliasing Level-1B (AOD1B) product is widely used in precise orbit determination and satellite gravimetry to correct for transient effects of atmosphere–ocean mass variability that would otherwise alias into monthly mean global gravity fields. The most recent release is based on the global ERA5 reanalysis and ECMWF operational data together with simulations from the general ocean circulation model MPIOM consistently forced with fields from the corresponding atmospheric dataset. As background models are inevitably imperfect, residual errors will consequently propagate into the resulting geodetic products. Accounting for uncertainties of the background model data in a statistical sense, however, has been shown before to be a useful approach to mitigate the impact of residual errors leading to temporal aliasing artefacts. In light of the changes made in the new release RL07 of AOD1B, previous uncertainty assessments are deemed too pessimistic and thus need to be revisited. We here present an analysis of the residual errors in AOD1B RL07 based on ensemble statistics derived from different atmospheric reanalyses, including ERA5, MERRA2 and JRA55. For the oceans, we investigate the impact of both the forced and intrinsic variability through differences in MPIOM simulation experiments. The atmospheric and oceanic information is then combined to produce a new time-series of true errors, called AOe07, which is applicable in combination with AOD1B RL07. AOe07 is further complemented by a new spatial error variance–covariance matrix. Results from gravity field recovery simulation experiments for the planned Mass-Change and Geosciences International Constellation (MAGIC) based on GFZ’s EPOS software demonstrate improvements that can be expected from rigorously implementing the newly available stochastic information from AOD1B RL07 into the gravity field estimation process.

Diurnal tidal oscillations in the coupled atmosphere–ocean system generate important contributions to the Earth’s free core nutation (FCN) and annual and sub-annual components of forced nutation in the celestial pole offsets. The determination of FCN parameters cannot avoid the influence of geophysical fluid excitation neither with the direct analysis of FCN signal (direct approaches) nor with the resonance analysis of forced nutation (resonance approaches). There is a significant difference in the FCN parameters obtained with resonance and direct approaches from celestial pole offsets observed through very long baseline interferometry (VLBI). The source of the difference between the two lacks quantitative analysis, which causes difficulties in interpreting the validity of the derived FCN parameters. Using both approaches, we conducted a simulation of celestial pole offsets to quantitatively demonstrate how geophysical fluid excitation affects the determination of FCN parameters from VLBI observations. Using the same excitation source, the FCN period obtained by the direct approach deviated from the set value (430.21 d) by more than 10 d, while the FCN period obtained by the resonance approach showed no deviation from the set value by more than 1 d. The results indicate that the resonance approach more accurately reflects the intrinsic period of the FCN. The impact of atmospheric and oceanic contributions on the determination of the FCN period with the resonance approach was within 2 d. Numerical simulation shows that discrepancies in FCN parameters caused by geophysical excitation were nonnegligible in constructing accurate FCN models.