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 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 Precise orbit determination of agile and non-agile satellites(2024) Gutsche, Kevin; Hobiger, Thomas (Prof. Dr. techn.)Precise orbit determination (POD) is key in fulfilling the scientific objectives of many Earth observation missions. For example, synthetic aperture radars (SARs) onboard low Earth orbit (LEO) satellites provide monitoring capabilities irrespective of lighting and weather conditions but are restricted in their field of view. Agile satellites, which can rapidly rotate around all three spacecraft axes, promise to overcome these limitations. The implications of a satellite’s agility on precise orbit determination have not yet been studied. However, their understanding and handling are crucial for the success of agile SAR missions. This thesis fills this gap by identifying the impact of agility on orbit determination, as well as devising and implementing ways to mitigate these effects. The novel software and its POD concept developed within this thesis are equally applicable to non-agile and agile satellites and are especially suited for extending to other or more numerous measurements in the future. The precise orbits of LEO satellites are most commonly determined from the abundant measurements collected by a global navigation satellite system (GNSS) receiver onboard the satellite. The newly developed C++ software Precise Orbit Determination for Complex and Agile Satellite Technology (PODCAST) pursues the reduced-dynamic orbit determination. This concept processes the GNSS observations combined with rigorous modeling of the satellite’s orbital dynamics. Additional accelerations are estimated to counteract remaining deficiencies in the dynamic models. Based on the measurements and models, the orbits are inferred using a sequential estimator, the extended Kalman filter (EKF). In contrast to common practice, this choice promises lower computational complexity and increased flexibility to incorporate more estimated parameters or measurements. While additional estimated variables can arise from the system’s agility, an increase in the observations is anticipated as the software is extended to new measurement types or multi-frequency multi-GNSS signals. The work offers an in-depth explanation of the employed methods, their rationale, and the new developments required by the EKF approach. A comprehensive study utilizing simulated and in-orbit measurements shows the influence of specific design considerations in POD based on the EKF. Certain shortcomings of this method are entirely circumvented by adhering to specific design criteria. The application to the LEO satellites Sentinel-3A, Sentinel-6A, and GRACE-FO further evidence the viability of using a sequential estimator. The derived orbits are competitive with other solutions derived by the more computationally demanding batch least-squares method. The impact of agility on GNSS-based reduced-dynamic orbit determination is assessed using simulations with realistic mission profiles. The rapid attitude changes of the satellite are shown to lead to a deterioration in the GNSS observables and increase the reliance on the dynamic model. Moreover, an analysis using GRACE-FO as a surrogate agile satellite suggests that the employed POD strategy effectively alleviates these changes, as well as the attitude-related errors in the non-gravitational force models. The results testify to the remarkable resilience of reduced-dynamic POD to measurement gaps caused by attitude maneuvers or jamming. Finally, errors in the lever arm - the vector between the GNSS antenna phase center and satellite center of mass - are shown to cause increased adverse effects for agile spacecraft. Furthermore, established techniques employed for satellites with slowly varying attitudes can only partially compensate for the negative impact on agile satellites. At the same time, using an observability analysis, Monte Carlo simulations, as well as in-orbit data of Sentinel-6A, this work proves the ability to directly estimate the lever arm in the presence of rapid attitude changes. Hence, this property enables dedicated attitude maneuvers to calibrate the lever arm for both agile and non-agile missions, thereby mitigating the negative effects on POD. Ultimately, this work presents an alternative precise orbit determination approach that is effective for both non-agile and agile missions. Compared to existing solutions, the derived orbits for non-agile satellites are consistent by approximately one centimeter. Applying the approach to in-orbit data of future agile satellites, which is not yet available, will enhance its verification and validation. Furthermore, the POD concept is well-suited to cope with upcoming challenges, such as an increasing number of measurements or parameters, and the fusion of various types of observations.Item Open Access Feasibility of using low-cost dual-frequency GNSS receivers for land surveying(2021) Wielgocka, Natalia; Hadas, Tomasz; Kaczmarek, Adrian; Marut, GrzegorzGlobal Navigation Satellite Systems (GNSS) have revolutionized land surveying, by determining position coordinates with centimeter-level accuracy in real-time or up to sub-millimeter accuracy in post-processing solutions. Although low-cost single-frequency receivers do not meet the accuracy requirements of many surveying applications, multi-frequency hardware is expected to overcome the major issues. Therefore, this paper is aimed at investigating the performance of a u-blox ZED-F9P receiver, connected to a u-blox ANN-MB-00-00 antenna, during multiple field experiments. Satisfactory signal acquisition was noticed but it resulted as >7 dB Hz weaker than with a geodetic-grade receiver, especially for low-elevation mask signals. In the static mode, the ambiguity fixing rate reaches 80%, and a horizontal accuracy of few centimeters was achieved during an hour-long session. Similar accuracy was achieved with the Precise Point Positioning (PPP) if a session is extended to at least 2.5 h. Real-Time Kinematic (RTK) and Network RTK measurements achieved a horizontal accuracy better than 5 cm and a sub-decimeter vertical accuracy. If a base station constituted by a low-cost receiver is used, the horizontal accuracy degrades by a factor of two and such a setup may lead to an inaccurate height determination under dynamic surveying conditions, e.g., rotating antenna of the mobile receiver.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 On the asymmetric troposphere modeling in PPP(2025) He, Shengping; Hobiger, Thomas (Prof. Dr. techn.)Tropospheric asymmetry is a crucial error term which needs to be considered for the refinement of tropospheric modeling in Precise Point Positioning (PPP). Wet asymmetry can account for more than one-fifth of the wet delay, causing residuals ranging from centimeters to decimeters at low elevation angles. Tropospheric asymmetry significantly impacts high-precision positioning applications and meteorological research. First models of tropospheric asymmetry are based on the concept of tropospheric horizontal gradient, which has prompted the development of many new models, including the widely used two-axis gradient model. However, the traditional two-axis gradient model is insufficient to represent the complex azimuthal variation of tropospheric delays. To address this issue, a directional mapping function based on cyclic B-spline functions, the so called the B-spline Mapping Function (BMF), is proposed. BMF enables a continuous characterization of tropospheric delay across any azimuth direction. The effectiveness of BMF has been validated using both numerical weather model data and Global Navigation Satellite System (GNSS) data from International GNSS Service (IGS) stations in Europe and Africa. Results reveal that compared to the conventional gradient model, BMF improves coordinate repeatability by approximately 10% horizontally and 5% vertically. The improvement in 3D-RMSE can reach up to 15% under heavy rainfall conditions. While the functional model of the asymmetric troposphere has been extensively studied, the stochastic model of the asymmetric troposphere remains unexplored. The absence of a suitable stochastic model for asymmetric troposphere reduces the accuracy of positioning and Zenith Total/Wet Delay (ZTD/ ZWD) estimates. In this work, an Azimuth-Dependent Weighting (ADW) scheme is introduced with the purpose to adaptively weight GNSS observations affected by azimuth-dependent errors using parameters from asymmetric mapping functions. Validated using NWP and IGS data, ADW improves PPP solution coordinate repeatability by approximately 10% horizontally and 20% vertically. ADW also improves ZWD estimates during the PPP convergence period and yields smoother results. Thus, this new weighting scheme is recommended for PPP applications when the asymmetric mapping functions are used. In the currently used conventional PPP processing strategies, ZWD is usually dynamically estimated as a stochastic parameter. During the convergence period, ZWD could become negative due to the lack of physical constraints. This problem increases the convergence time and reduces short-term accuracy of PPP. To address this issue, a method which incorporates physical constraints on ZWD using Non-negative Least Squares (NNLS) methods and Karush–Kuhn–Tucker (KKT) conditions is proposed. This method reduces ZWD outliers during the PPP convergence period, and effectively improves the short-term accuracy for the Up component of the position up to 20%. Similar to tropospheric delays, there are some other systematic errors that also have azimuth-dependent characteristics, such as multipath error. Consequently, when using an asymmetric troposphere model, the gradient parameters may absorb some of the multipath error, leading to biases in ZWD/ZTD estimates. Due to the site-specific nature of multipath errors, establishing a universal mathematical model is challenging. Therefore, in this thesis, a commercial simulator is employed to simulate multipath signals under different scenarios. The impact of multipath errors on estimated ZTD time series and methods to mitigate this effect by adjusting the process noise of ZWD are studied. This thesis provides an in-depth exploration of asymmetric troposphere modeling in PPP from four perspectives: functional models, stochastic models, constraint conditions, and systematic errors. It investigates methods for refining troposphere modeling and analyzes their effectiveness in PPP and GNSS meteorology.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.