Journal of Geodesy最新文献

In this contribution, we introduce, in analogy to penalized ambiguity resolution, the concept of penalized misclosure space partitioning, with the goal of directing the performance of the DIA-estimator towards its application-dependent tolerable risk objectives. We assign penalty functions to each of the decision regions in misclosure space and use the distribution of the misclosure vector to determine the optimal partitioning by minimizing the mean penalty. As each minimum mean penalty partitioning depends on the given penalty functions, different choices can be made, in dependence of the application. For the DIA-estimator, we introduce a special set of penalty functions that penalize its unwanted outcomes. It is shown how this set allows one to construct the optimal DIA-estimator, being the estimator that within its class has the largest probability of lying inside a user specified tolerance region. Further elaboration shows how these penalty functions are driven by the influential biases of the different hypotheses and how they can be used operationally. Hereby the option is included of extending the misclosure partitioning with an additional undecided region to accommodate situations when it will be hard to discriminate between some of the hypotheses or when identification is unconvincing. By extending the analogy with integer ambiguity resolution to that of integer-equivariant ambiguity resolution, we also introduce the maximum probability estimator within the similar larger class.

Traditionally, GNSS space-based and ground-based estimates of tropospheric conditions are performed separately. It leads to limitations in the horizontal (e.g., a single space-based radio occultation profile covers a 300 km slice of the troposphere) and vertical resolution (e.g., ground-based estimates of troposphere conditions have spacing equal to stations’ distribution) of the tropospheric products. The first stage to achieve an integrated model is to create an effective 3D ray-tracing algorithm for the satellite-to-satellite (radio occultation) path reconstruction. We verify the consistency of the simulated data with the RO observations from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC-1) Data Analysis and Archive Center (CDAAC) in terms of excess phase and bending angle. The results show that our solution provides an effective RO excess phase, with a relative error varying from 35% at the height of 25–30 km (1.0–1.5 m) to 0.5% at heights 5–10 km (0.1–1 m) and 14 to 2% at heights below 5 km (2–14 m). The bending angle retrieval on simulated data attained for high-resolution ray-tracing, bias lower than 2% with respect to the observed bending angle. The optimal solution takes about 1 s for one transmitter–receiver pair with a tangent point below 5 km altitude. The high-resolution processing solution takes 3 times longer.

In this study, a novel two-scale spherical radial basis function (SRBF) modeling method is proposed for regional gravity field determination. First, satellite-only global gravity field models (GGMs) are combined with airborne gravity data at medium-frequency bands, and a series of combined gravity field models based on band-limited SRBFs are established for the mountainous areas of California and Oregon. The combined gravity field models are then compared with the airborne-only gravity field models. The results show that the combined models exhibit standard deviation (STD) values of 0.106–0.120 m in terms of geoid height differences w.r.t. the global positioning system (GPS)/leveling data, while the corresponding airborne-only models yield STD values of 0.126–0.131 m. The STD values of the combined models are reduced by 0.9–2.0 cm, which implies a potential benefit for the medium-frequency gravity field modeling by combining GGM and airborne gravity data. Second, after removing the low-frequency and medium-frequency gravity field signals as well as the residual terrain model signals from gravity data, a second SRBF modeling process is implemented using multisource residual gravity data. Subsequently, a high-resolution two-scale SRBF gravity field model is constructed for the mountainous areas of California and Oregon. The results indicate that the STD of geoid height differences for the two-scale SRBF model w.r.t. the GPS/leveling data is 0.098 m, with reductions of 3.0–6.2 cm compared to the models based on the single-scale SRBF modeling method. These findings indicate the effectiveness of the two-scale SRBF modeling method for refining the regional gravity field model in complex areas.

To accommodate the presence of bounded biases in mixed-integer models, Khodabandeh (2022) extended integer estimation theory by introducing a new admissible integer estimator. The estimator follows the principle of integer least squares estimation and is computed via the integer search method of BEAT. In this contribution, we present the probability distributions of a class of estimators to which the proposed bias-constrained integer least squares estimation belongs. Some important interferometric measuring systems, whose estimation problems can be covered by BEAT, are identified. To show the proposed estimator at work, we apply BEAT to the problem of GLONASS single-differenced (SD) ambiguity resolution. Numerical results of several short-baseline datasets are presented to illustrate why one can achieve more accurate positioning solutions when considering between-receiver SD ambiguity resolution for the cases where carrier phase data are captured on frequency-varying signals with bounded SD receiver phase delays.

The Sentinel-6 Michael Freilich altimetry mission flies two GNSS receivers: a primary multi-GNSS (GPS plus Galileo) PODRIX receiver and a GPS-only TriG receiver. Each of these receivers is independently capable of supporting the precise orbit determination (POD) requirement for < 1.5 cm radial rms error. In this study, we characterize the performance of single-receiver solutions and evaluate the benefits of a combined TriG and PODRIX orbit solution. The availability of both sets of receiver observations revealed a 10 mm in-track difference between orbit solutions derived independently from TriG and PODRIX tracking data. Based on satellite laser ranging (SLR) residuals, this bias has been isolated to an apparent inconsistency between the estimated TriG receiver clock and observation time-tags of approximately 1.3 (mu hbox {s}), which is equivalent to a common range error of roughly 400 m in the TriG observations. After applying this calibration, the TriG and PODRIX displayed similar performance in terms of orbit overlap precision. PODRIX-Galileo observations showed lower code and phase tracking residual rms values compared to the GPS observations. Overall, processing the calibrated TriG and PODRIX observations separately results in highly accurate orbit solutions with radial orbit accuracies better than 1 cm rms as indicated by one-way SLR residual rms of 7.2 mm or better for each solution. Orbit solution accuracy is slightly improved by processing both TriG and PODRIX observations together, resulting in one-way SLR residual rms of 7.0 mm.

This study proposes a model using 5G time-of-arrival data to assist global navigation satellite system precise point positioning ambiguity resolution. Specifically, the model addresses the problem of PPP requiring a long convergence time in partially satellite-occluded GNSS environments, such as urban canyons. First, we apply the ionosphere-free PPP model to estimate uncalibrated phase delays. Next, we combine real 5G data with GNSS data to determine whether introducing 5G observations will decrease the convergence time of the PPP solution. Experimental results reveal that the 5G-assisted PPP model can effectively improve the convergence efficiency of the float solution, lower the fixed time, and achieve greater positional reliability. Notably, the combination of GPS, BDS, and 5G with a sampling interval of 1 s obtains a fixed solution in an average of 1.12 min. Moreover, 5G-assisted GNSS positioning effectively compensates for partial satellite occlusion, optimizes the PDOP value, and speeds up ambiguity fixing. The introduction of three and more 5G base stations helps to obtain fixed solutions within 9 min when it is difficult to obtain fixed solutions relying only on GNSS. Our findings have important implications for improving the widespread applicability and effectiveness of satellite-based navigation systems in light of increasing urbanization and the rise of signal-occluding environments.

In high-precision space geodetic techniques data processing, the mapping function (MF) is a key factor in mapping the radio waves from the zenith direction down to the signal incoming direction. Existing MF products, either site-wise Vienna Mapping Function (VMF1 and VMF3) or grid-wise VMF1 and VMF3, are only available at the Earth surface. For overhead areas, height correction is always required, which is becoming increasingly important with growing airborne aircraft activity. In this contribution, we introduce a novel method aimed at providing a large number of MFs to the user in a simple and efficient manner, while minimizing the loss of precision. The approach effectively represents the vertical profile of the MFs from the Earth's surface up to altitudes of 14 km. In addition, the new model corrects for height in the assessment using the fifth generation of the European Centre for Medium-Range Weather Forecasts ReAnalysis (ERA5) ray tracing calculations for a global 5° × 5° grid with 54 layers in the vertical direction, a total of 8 azimuths in the plane, and 7 elevation angles, for each day in 2021. Specifically, for both polynomial and exponential model of order 2 and 3, the relative residuals are < 0.3% for the hydrostatic delay MF coefficient (a_{{text{h}}}), and < 1% for the wet delay MF coefficient (a_{{text{w}}}). The precision of the new model on the Earth’s surface is evaluated using site-wise VMF1 and VMF3 GNSS (Global Navigation Satellite System) products from Technische Universität Wien. The root mean square error of slant hydrostatic delay and slant wet delay at a 3° elevation angle is approximately 4–5 cm and 2–5 cm, respectively.

An ideal target for geodetic very long baseline interferometry (VLBI) is a strong and point-like radio source. In reality, most celestial sources used in geodetic VLBI have spatial structure. This is as a major source of error in VLBI Global Observing System (VGOS) and also affects legacy S/X observations. Source structure causes a systematic delay, which can affect the geodetic estimates if not modelled or otherwise accounted for. In this work, we aim to mitigate its impact by extending the stochastic model used in the least-squares fitting of the VLBI group delays. We have developed a weighting scheme to re-weight the observations by parameterizing the source structure component in terms of closure delays and jet orientation relative to the observing baseline. It was implemented in the Vienna VLBI Software. To assess the performance of the extended stochastic model, we analysed the CONT17 legacy sessions and generated suitable reference solutions for comparison. The effects of re-weighting were evaluated with respect to the session fit statistics, source-wise residuals, and geodetic parameters. We find that this relatively simple noise model consistently improves the session fit by about 5% with moderate variation from session to session. The geodetic estimates are not affected to a significant level by this new weighting method. Source-wise we see improved post-fit residuals for 63 out of a total of 91 sources observed.

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.