R Heinkelmann

Real-time retrieval of precipitable water vapor from GPS and BeiDou observations

The rapid development of the Chinese BeiDou Navigation Satellite System (BDS) brings a promising prospect for the real-time retrieval of zenith tropospheric delays (ZTD) and precipitable water vapor (PWV), which is of great benefit for supporting the time-critical meteorological applications such as nowcasting or severe weather event monitoring. In this study, we develop a real-time ZTD/PWV processing method based on Global Positioning System (GPS) and BDS observations. The performance of ZTD and PWV derived from BDS observations using real-time precise point positioning (PPP) technique is carefully investigated. The contribution of combining BDS and GPS for ZTD/PWV retrieving is evaluated as well. GPS and BDS observations of a half-year period for 40 globally distributed stations from the International GNSS Service Multi-GNSS Experiment and BeiDou Experiment Tracking Network are processed. The results show that the real-time BDS-only ZTD series agree well with the GPS-only ZTD series in general: the RMS values are about 11–16 mm (about 2–3 mm in PWV). Furthermore, the real-time ZTD derived from GPS-only, BDS-only, and GPS/BDS combined solutions are compared with those derived from the Very Long Baseline Interferometry. The comparisons show that the BDS can contribute to real-time meteorological applications, slightly less accurately than GPS. More accurate and reliable water vapor estimates, about 1.3–1.8 mm in PWV, can be obtained if the BDS observations are combined with the GPS observations in the real-time PPP data processing. The PWV comparisons with radiosondes further confirm the performance of BDS-derived real-time PWV and the benefit of adding BDS to standard GPS processing.

Application of Kalman filtering in VLBI data analysis

In this paper, we demonstrate the advantage of applying a Kalman filter for the parameter estimation in very-long-baseline interferometry (VLBI) data analysis. We present the implementation of a Kalman filter in the VLBI software VieVS@GFZ. The performance is then investigated by looking at the accuracy obtained for various parameters, like baseline lengths, Earth Orientation Parameters, radio source coordinates, and tropospheric delays. The results are compared to those obtained when the classical least squares method (LSM) is applied for the parameter estimation, where clocks and zenith wet delays are estimated with 30-min intervals and gradients with 120-min intervals. We show that the accuracy generally is better for the Kalman filter solution, for example, the baseline length repeatabilities are on average about 10 % better compared to the LSM solution. We also discuss the possibilities to use the Kalman filter to estimate sub-diurnal station position variations and show that the variations caused by solid Earth tides can be retrieved with an accuracy of about 2 cm.

Tropospheric delay determination by Kalman filtering VLBI data

The troposphere is one of the most important error sources for space geodetic techniques relying on radio signals. Since it is not possible to model the wet part of the tropospheric delay with sufficient accuracy, it needs to be estimated from the observational data. In the analysis of very long baseline interferometry (VLBI) data, the parameter estimation is routinely performed using a least squares adjustment. In this paper, we investigate the application of a Kalman filter for parameter estimation, specifically focusing on the tropospheric delays. The main advantages of a Kalman filter are its real-time capability and stochastic approach. We focused on the latter and derived stochastic models for VLBI zenith wet delays, taking into account temporal and location-based differences. Compared to a static noise model, the quality of station coordinates, also estimated in the Kalman filter, increased as a result. In terms of baseline length and station coordinate repeatabilities, this improvement amounted to 2.3 %. Additionally, we compared the Kalman filter and least squares results for VLBI with zenith wet delays derived from GPS (Global Positioning System), water vapor radiometers, and ray tracing in numerical weather models. The agreement of the Kalman filter VLBI solution with respect to water vapor radiometer data was larger than that of the least squares solution by 6–15 %. Our investigations are based on selected VLBI data (CONT campaigns) that are closest to how future VLBI infrastructure is designed to operate. With the aim for continuous and near real-time parameter estimation and the promising results which we have achieved in this study, we expect Kalman filtering to grow in importance in VLBI analysis.

Improving BeiDou real-time precise point positioning with numerical weather models

Precise positioning with the current Chinese BeiDou Navigation Satellite System is proven to be of comparable accuracy to the Global Positioning System, which is at centimeter level for the horizontal components and sub-decimeter level for the vertical component. But the BeiDou precise point positioning (PPP) shows its limitation in requiring a relatively long convergence time. In this study, we develop a numerical weather model (NWM) augmented PPP processing algorithm to improve BeiDou precise positioning. Tropospheric delay parameters, i.e., zenith delays, mapping functions, and horizontal delay gradients, derived from short-range forecasts from the Global Forecast System of the National Centers for Environmental Prediction (NCEP) are applied into BeiDou real-time PPP. Observational data from stations that are capable of tracking the BeiDou constellation from the International GNSS Service (IGS) Multi-GNSS Experiments network are processed, with the introduced NWM-augmented PPP and the standard PPP processing. The accuracy of tropospheric delays derived from NCEP is assessed against with the IGS final tropospheric delay products. The positioning results show that an improvement in convergence time up to 60.0 and 66.7% for the east and vertical components, respectively, can be achieved with the NWM-augmented PPP solution compared to the standard PPP solutions, while only slight improvement in the solution convergence can be found for the north component. A positioning accuracy of 5.7 and 5.9 cm for the east component is achieved with the standard PPP that estimates gradients and the one that estimates no gradients, respectively, in comparison to 3.5 cm of the NWM-augmented PPP, showing an improvement of 38.6 and 40.1%. Compared to the accuracy of 3.7 and 4.1 cm for the north component derived from the two standard PPP solutions, the one of the NWM-augmented PPP solution is improved to 2.0 cm, by about 45.9 and 51.2%. The positioning accuracy for the up component improves from 11.4 and 13.2 cm with the two standard PPP solutions to 8.0 cm with the NWM-augmented PPP solution, an improvement of 29.8 and 39.4%, respectively.

Probing the solar corona with very long baseline interferometry

Understanding and monitoring the solar corona and solar wind is important for many applications like telecommunications or geomagnetic studies. Coronal electron density models have been derived by various techniques over the last 45 years, principally by analysing the effect of the corona on spacecraft tracking. Here we show that recent observational data from very long baseline interferometry (VLBI), a radio technique crucial for astrophysics and geodesy, could be used to develop electron density models of the Sun’s corona. The VLBI results agree well with previous models from spacecraft measurements. They also show that the simple spherical electron density model is violated by regional density variations and that on average the electron density in active regions is about three times that of low-density regions. Unlike spacecraft tracking, a VLBI campaign would be possible on a regular basis and would provide highly resolved spatial–temporal samplings over a complete solar cycle.

GGOS-SIM: Simulation of the Reference Frame for the Global Geodetic Observing System

The accuracy and stability requirements for the International Terrestrial Reference Frame (ITRF) postulated by the Global Geodetic Observing System (GGOS) are not met so far. The GGOS–SIM project builds a software tool that by simulating the space geodetic infrastructure allows to assess the impact of technique upgrades, new sites, new satellites, local ties, and space ties on the ITRF accuracy and stability. As also the procedure for the combination of the techniques plays a fundamental role in the generation of an ITRF, we discuss peculiarities of current day approaches and draw conclusions relevant for this project. As the assessment of the accuracy of an ITRF is needed for checking against the GGOS requirements, we compile actual methods and present here a new measure of stability which is exemplarily applied to recent ITRFs.

GNSS tropospheric gradients with high temporal resolution and their effect on precise positioning

The tropospheric horizontal gradients with high spatiotemporal resolutions provide important information to describe the azimuthally asymmetric delays and significantly increase the ability of ground-based GNSS (Global Navigation Satellite Systems) within the field of meteorological studies, like the nowcasting of severe rainfall events. The recent rapid development of multi-GNSS constellations has potential to provide such high-resolution gradients with a significant degree of accuracy. In this study, we develop a multi-GNSS process for the precise retrieval of high-resolution tropospheric gradients. The tropospheric gradients with different temporal resolutions, retrieved from both single-system and multi-GNSS solutions, are validated using independent numerical weather models (NWM) data and water vapor radiometer (WVR) observations. The benefits of multi-GNSS processing for the retrieval of tropospheric gradients, as well as for the improvement of precise positioning, are demonstrated. The multi-GNSS high-resolution gradients agree well with those derived from the NWM and WVR, especially for the fast-changing peaks, which are mostly associated with synoptic fronts. The multi-GNSS gradients behave in a much more stable manner than the single-system estimates, especially in cases of high temporal resolution, benefiting from the increased number of observed satellites and improved observation geometry. The high-resolution multi-GNSS gradients show higher correlation with the NWM and WVR gradients than the low-resolution gradients. Furthermore, the precision of station positions can also be noticeably improved by multi-GNSS fusion, and enhanced results can be achieved if the high-resolution gradient estimation is performed, instead of the commonly used daily gradient estimation in the multi-GNSS data processing.

A Priori Gradients in the Analysis of Space Geodetic Observations

We introduce a static a priori gradient model (APG) based on a spherical harmonic expansion up to degree and order nine to describe the azimuthal asymmetry of tropospheric delays. APG is determined from climatology data of the European Centre for Medium-Range Weather Forecasts (ECMWF), and the refined model can be used in the analysis of observations from Global Navigation Satellite Systems (GNSS) and Very Long Baseline Interferometry (VLBI). Comparisons reveal that gradients estimated in GNSS analysis are mostly smaller than those provided by APG. This difference is also confirmed by station and source coordinate changes if APG is used in GNSS and VLBI analysis.

Very long baseline interferometry: accuracy limits and relativistic tests

We present a review on relativistic effects and best estimates of the relativistic PPN parameter γ obtained by analysis of data from the International VLBI Service for Geodesy and Astrometry (IVS). Relativistic implications are also considered in view of the upcoming new generation VLBI System: VLBI2010.

Towards the combination of data sets from various observation techniques

Nowadays, heterogeneous data sets are often combined within a parameter estimation process in order to benefit from their individual strengths and favorable features. Frequently, the different data sets are complementary with respect to their measurement principle, the accuracy, the spatial and temporal distribution and resolution, as well as their spectral characteristics. This paper gives first a review on various combination strategies based on the Gauss-Markov model; special attention will be turned on the stochastic modeling of the input data, e.g. the influence of correlations between different sets of input data. Furthermore, the method of variance component estimation is presented to determine the relative weighting between the observation techniques. If the input data sets are sensitive to different parts of the frequency spectrum the multi-scale representation might be applied which basically means the decomposition of a target function into a number of detail signals each related to a specific frequency band. A successive parameter estimation can be applied to determine the detail signals.