06 Fakultät Luft- und Raumfahrttechnik und Geodäsie
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/7
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Item Open Access Stochastic modeling with robust Kalman filter for real-time kinematic GPS single-frequency positioning(2023) Wang, Rui; Becker, Doris; Hobiger, ThomasThe centimeter-level positioning accuracy of real-time kinematic (RTK) depends on correctly resolving integer carrier-phase ambiguities. To improve the success rate of ambiguity resolution and obtain reliable positioning results, an enhanced Kalman filtering procedure has been developed. Based on a posteriori residuals of measurements and state predictions, the measurement noise variance-covariance matrix for double-differenced measurements is adaptively estimated, rather than approximated by an empirical function which uses satellite elevation angle as input. Since, in real-world situations, unexpected outliers and carrier-phase outages can degrade the filter performance, a stochastic model based on robust Kalman filtering is proposed, for which the double-differenced measurement noise variance-covariance matrix is computed empirically with a modified version of the IGG (Institute of Geodesy and Geophysics) III method in order to detect and identify outliers. The performance of the proposed method is assessed by two tests, one with simulated data and one with real data. In addition, the performance of F-ratio and W-ratio tests as proxies for the success of ambiguity fixing is investigated. Experimental results reveal that the proposed method can improve the reliability and robustness of relative kinematic positioning for simulation scenarios as well as in a real urban test.Item Open Access Motivation, structure and goals of the collaborative research centre 1667 : advancing technologies of very low-altitude satellites - ATLAS(2025) Fasoulas, Stefanos; Pagan, Adam S.; Traub, Constantin; Annighöfer, Björn; Barz, Stefanie; Beck, Andrea; Cunis, Torbjørn; Dekorsy, Thomas; Essig, Stephanie; Fichter, Walter; Flemisch, Bernd; Herdrich, Georg; Hobiger, Thomas; Kallfass, Ingmar; Kästner, Johannes; Klinkner, Sabine; Lamanna, Grazia; Loehle, Stefan; Pfeiffer, Marcel; Poser, Rico; Roth, Johannes; Saliba, Michael; Schneider, Martin; Sneeuw, Nico; Wagner, GerdThe Collaborative Research Centre (CRC) 1667 “Advancing Technologies of Very Low Altitude Satellites-ATLAS” was established in April 2024 with the scientific goal of addressing the fundamental challenges of making satellite operations in Very Low Earth Orbits (VLEO) sustainable. These orbits are beneficial for satellite services that have become indispensable to our modern society. Moreover, access to VLEO offers the opportunity to operate satellites without exposure or contribution to the increasing contamination of traditional orbits with space debris. Seventeen highly interlinked research projects have been selected to investigate and advance accurate numerical and experimental methods for gas-surface interactions, novel concepts utilising the residual atmosphere and minimising the satellite sizes, and mission-related challenges of a selected scenario. In addition, support projects cover topics related to public outreach and academic exchange and assist in achieving the strategic goal of positioning the University of Stuttgart as a key contributor to this internationally very important research area. In summary, the CRC ATLAS aims to constitute a research-oriented profile-building measure at the University of Stuttgart with a strong international reputation.Item Open Access INSTINCT : a flow-based open-source PNT framework for satellite navigation and sensor fusion(2025) Topp, Thomas; Maier, Marcel; Hobiger, Thomas; Becker, DorisINS toolkit for integrated navigation concepts and training (INSTINCT) is an open-source positioning, navigation and timing (PNT) framework for global navigation satellite system (GNSS) navigation and sensor fusion written in C++. It uses flow-based programming to encapsulate functionality, enforce clean interfaces and promote reusability. Not only multi-constellation, multi-frequency single point positioning (SPP) and real-time kinematic positioning (RTK) algorithms are available, but also inertial navigation system (INS)/GNSS sensor fusion. Moreover, innovative concepts like multi inertial measurement unit (IMU) arrays and factor graph optimization are featured. Furthermore, most file formats common in the PNT field can be read with the software and converted between them. Also, simulation of trajectories and IMU data with different error models is possible. A graphical user interface allows the user to directly set parameters and analyze results in plots, which enables rapid prototyping and testing. A developer can easily extend the functionality with own algorithms and sensor interfaces building upon the existing modules. In order to evaluate the performance of the algorithms two experiments were performed. Analysis of a static dataset shows that the position accuracy of the RTK algorithm of INSTINCT is comparable to RTKLIB. Additionally, a dynamic dataset was generated using a Spirent GNSS simulator and INSTINCT’s IMU simulation capabilities. In-depth assessment confirms the high accuracy of the results and demonstrates that the INS/GNSS loosely coupled Kalman filter can compensate for GNSS outages.Item Open Access Improving GNSS meteorology by fusing measurements of several colocated receivers on the observation level(2024) Wang, Rui; Marut, Grzegorz; Hadas, Tomasz; Hobiger, ThomasItem Open Access Considering different recent advancements in GNSS on real-time zenith troposphere estimates(2020) Hadas, Tomasz; Hobiger, Thomas; Hordyniec, PawelGlobal navigation satellite system (GNSS) remote sensing of the troposphere, called GNSS meteorology, is already a well-established tool in post-processing applications. Real-time GNSS meteorology has been possible since 2013, when the International GNSS Service (IGS) established its real-time service. The reported accuracy of the real-time zenith total delay (ZTD) has not improved significantly over time and usually remains at the level of 5-18 mm, depending on the station and test period studied. Millimeter-level improvements are noticed due to GPS ambiguity resolution, gradient estimation, or multi-GNSS processing. However, neither are these achievements combined in a single processing strategy, nor is the impact of other processing parameters on ZTD accuracy analyzed. Therefore, we discuss these shortcomings in detail and present a comprehensive analysis of the sensitivity of real-time ZTD on processing parameters. First, we identify a so-called common strategy, which combines processing parameters that are identified to be the most popular among published papers on the topic. We question the popular elevation-dependent weighting function and introduce an alternative one. We investigate the impact of selected processing parameters, i.e., PPP functional model, GNSS selection and combination, inter-system weighting, elevation-dependent weighting function, and gradient estimation. We define an advanced strategy dedicated to real-time GNSS meteorology, which is superior to the common one. The a posteriori error of estimated ZTD is reduced by 41%. The accuracy of ZTD estimates with the proposed strategy is improved by 17% with respect to the IGS final products and varies over stations from 5.4 to 10.1 mm. Finally, we confirm the latitude dependency of ZTD accuracy, but also detect its seasonality.Item Open Access Improving PPP positioning and troposphere estimates using an azimuth-dependent weighting scheme(2024) He, Shengping; Hobiger, Thomas; Becker, DorisAsymmetric troposphere modeling is crucial in Precise Point Positioning (PPP). The functional model of the asymmetric troposphere has been thoroughly studied, while the stochastic model lacks discussion. Currently, there is no suitable stochastic model for asymmetric tropospheric conditions, potentially degrading the positioning accuracy and the reliability of Zenith Total/Wet Delay (ZTD/ZWD) estimates. This paper introduces an Azimuth-Dependent Weighting (ADW) scheme that utilizes information from asymmetric mapping functions to adaptively weight Global Navigation Satellite System (GNSS) observations affected by azimuth-dependent errors. The concept of ADW has been validated using Numerical Weather Prediction data and International GNSS Service data. The results indicate that ADW effectively improves the coordinate repeatability of the PPP solution by approximately 10%in the horizontal and 20%in the vertical direction. Additionally, ADW appears to be capable to improve the ZWD estimates during the PPP convergence period and yields smoother ZWD estimates. Consequently, it is recommended to adopt this new weighting scheme in PPP applications when an asymmetric mapping functions is employed.Item Open Access The B-spline mapping function (BMF) : representing anisotropic troposphere delays by a single self-consistent functional model(2024) He, Shengping; Hobiger, Thomas; Becker, DorisTroposphere’s asymmetry can introduce errors ranging from centimeters to decimeters at low elevation angles, which cannot be ignored in high-precision positioning technology and meteorological research. The traditional two-axis gradient model, which strongly relies on an open-sky environment of the receiver, exhibits misfits at low elevation angles due to their simplistic nature. In response, we propose a directional mapping function based on cyclic B-splines named B-spline mapping function (BMF). This model replaces the conventional approach, which is based on estimating Zenith Wet Delay and gradient parameters, by estimating only four parameters which enable a continuous characterization of the troposphere delay across any directions. A simulation test, based on a numerical weather model, was conducted to validate the superiority of cyclic B-spline functions in representing tropospheric asymmetry. Based on an extensive analysis, the performance of BMF was assessed within precise point positioning using data from 45 International GNSS Service stations across Europe and Africa. It is revealed that BMF improves the coordinate repeatability by approximately 10%horizontally and about 5% vertically. Such improvements are particularly pronounced under heavy rainfall conditions, where the improvement of 3-dimensional root mean square error reaches up to 13%.Item Open Access Physical constraints for zenith wet delay estimation via inequality constrained least squares in real-time PPP(2026) He, Shengping; Brack, Andreas; Hobiger, Thomas; Takamatsu, Naofumi; Wickert, JensIn current conventional precise point positioning (PPP) processing strategies, the tropospheric zenith wet delay (ZWD) is usually dynamically estimated as a stochastic parameter. During the convergence period, ZWD estimates can appear to be negative or unrealistically large due to the low estimation precision, which adversely affects the estimation of other state parameters, especially the Up component of coordinates. To address this issue, we propose a method that incorporates physical constraints on ZWD in PPP processing. This method employs the inequality constrained least squares (ICLS), utilizing Karush-Kuhn-Tucker (KKT) conditions to add boundary conditions on ZWD. The boundary conditions of ZWD are calculated based on the relation between ZWD and relative humidity (RH). The use of physical constraints does not rely on external products or space state representation (SSR) corrections for ZWD during PPP processing and can improve the short-term accuracy of ZWD and coordinate Up component. The efficiency of this approach has been validated using GNSS data and products from GFZ operational networks. For real-time PPP solutions, there is a 30%improvement in short-term accuracy of Up component; for post-processing solutions, the short-term RMSE improvement is about 20%. After convergence, the ZWD upper bound is no longer applied as an ICLS constraint, but is instead used as a diagnostic indicator to identify ZWD anomalies. This indicator demonstrates high sensitivity and reliability under extreme weather conditions, highlighting its potential for application in meteorological hazard early-warning systems.Item Open Access Simultaneous troposphere estimation with precise point positioning(2026) Hadaś, Tomasz; Hobiger, Thomas; Marut, Grzegorz; Wang, Rui; Trzcina, Estera; Kowalczyk, WiktoriaTheoretically, it is possible to reconstruct the 3D distribution of water vapor by means of GNSS tomography using troposphere estimates from a network of GNSS stations, i.e., zenith delays mapped back into satellite directions. However, this technique is still limited by restricted satellite-to-ground observation geometry, a simplified parameterization of troposphere delays in the observation model and mandatory usage of constraints to stabilize the equation system. We propose an alternative approach, called STEPPP, in which a network of ground-based GNSS receivers is used to process GNSS observations, based on the Precise Point Positioning (PPP) technique and, instead of estimating the zenith wet delay and horizontal gradients, the estimation of the whole wet refractivity field in a grid space is performed simultaneously. Contrary to GNSS tomography, STEPPP operates on raw observation data instead of products. Values of wet refractivity at grid nodes are estimated from all stations simultaneously, i.e., they appear as common parameters in PPP. We present the functional and stochastic model of STEPPP, as well as first results of the model performance. We use GPS and Galileo dual-frequency observations generated by the Spirent simulator for 20 evenly distributed stations. The simulated observations are intentionally free of troposphere delays. However, we use a numerical weather model to retrieve reference profiles of wet refractivity and calculate slant wet delays, which are added to the simulated observations. We define a voxel space above the network of stations up to 12 km height and we recover the wet refractivity profiles by means of the STEPPP model. Several numerical experiments are performed using homogenous, inhomogeneous, constant and dynamic wet refractivity profiles. After a convergence time of a few hours, the STEPPP model accurately recovers all model states, including the 3D wet refractivity field and station coordinates.