Phase Center Corrections (PCC) are essential for precise GNSS positioning, yet differences between calibration sets ( Δ PCC) are often evaluated at the pattern level, which complicates an assessment of their practical relevance for estimated geodetic parameters. We present PCC-Explorer, an open-source tool written in Python that standardizes the forward propagation of PCC and Δ PCC into the parameter domain without requiring GNSS observation data. The approach combines a linearized observation model in a topocentric frame (North, East, Up, receiver clock error, tropospheric part), an elevation-dependent stochastic model, and a second weighting matrix that reflects the local satellite distribution as a function of geographic location, time span, and sampling rate. A least-squares adjustment yields parameter deviations averaged over user-defined output intervals and supports multi-GNSS single frequencies and ionosphere-free linear combinations (IF-LC). Using Δ PCC between chamber and robot calibrations of a LEIAR25.R4 LEIT antenna, we show that daily parameter deviations are dominated by the Up component and the receiver clock error, while horizontal and tropospheric effects remain within ±1 mm. The impact varies mainly with latitude, reflecting the constellation geometry: for GPS IF-LC the Up component rises from ≈ 1–3.5 mm between ± 55^∘ and ≈ 14 mm near the poles. GLONASS impacts are smaller ( ≈ 0.5–4.5 mm) and show stronger longitudinal variability. Shorter parameter output intervals (e.g., 3 h) yields pronounced variability driven by changing satellite geometry. Over three years, the GPS mean 3D impact is 2.72 mm (range 7.35 mm), with periods consistent with sidereal repeats. Validation with differential PPP results at two EUREF Permanent Network (EPN) sites shows agreement at the sub-millimeter to millimeter level. The results underline that large pattern-level Δ PCC may map into the receiver clock or remain unsensed, motivating parameter-domain assessments. PCC-Explorer enables transparent, comparable studies across sites, intervals, and processing settings, and will be open source for the user community.

This paper describes the discipline of geodesy and geoinformatics with a focus on university studies and career opportunities. It is shown how the discipline contributes to the solutions of major societal challenges such as sustainable development, mobility, and global change. Then, the structure of German universities is shortly reviewed, followed by an overview of where in the country the discipline can be studied. Finally, the example of Leibniz University Hannover, one of the prime centers of excellence in the field, is described in more detail with a focus on the M.Sc. programme. We hope to encourage young talents to consider this exciting field of studies for their future career.

In precise point positioning (PPP) solutions, stochastic modeling of the receiver clock parameter affects solution stability, especially the station up component. This study analyzes GPS + Galileo static and kinematic PPP solutions for 14 GNSS stations equipped with ultra-stable hydrogen masers, utilizing real-time orbit and clock products, such as HAS, IGS, and CNES, as well as final products from CODE. The solution with modeling of the receiver clock parameter enhances stability and precision compared to the reference solution, in which the receiver clocks are estimated independently for each epoch. In static PPP solutions, receiver clock modeling reduces spikes in the clock parameter and improves short-term stability. The most notable improvement of the station up component reaches up to 59, 21, 25, and 38

Abstract The demand for high-precision absolute positioning is rising with the progress in autonomous navigation, yet Global Navigation Satellite System (GNSS)-only solutions often fall short in urban environments due to multipath and non-Line-of-Sight observations. To overcome these challenges, we propose a collaborative multi-agent, multi-sensor Real-Time-Kinematic (RTK) framework that processes multiple rovers simultaneously and augments GNSS with relative Vehicle-to-Vehicle (V2V) observations. The approach is validated with static and kinematic experiments in the urban area of Hannover, Germany. To investigate the theoretical performance, we transform the original GNSS and V2V measurements into bias-free, Gaussian-noise observations and compare the collaborative solution with single-vehicle (SV) RTK positioning under varying GNSS observation qualities, V2V uncertainties, and network geometries. Results show that the achievable improvement is determined by the precision of the V2V information and the number of agents to cooperate. 2D error improvements of up to 60% relative to SV positioning are achieved, driven by improved carrier-phase float-ambiguity estimation. The more precise the SV solution, the higher the required V2V precision to realise significant benefits. Notably, even with absent or low-precision V2V data, the collaborative solution still improves SV positioning by up to 13%, since introduced cross-correlation between the agents already support the ambiguity estimation.

Abstract Achieving frequency transfer by Global Navigation Satellite Systems (GNSSs) links at the $$10^{-16}$$ 1 0 −16 – $$10^{-18}$$ 1 0 −18 stability level requires careful assessment of environmental effects, particularly temperature-induced fluctuations in receivers, antennas, cables, and splitters. We study thermal effects using a common-clock zero-baseline setup with Septentrio PolaRx5TR and JAVAD OMEGA receivers in a controlled temperature chamber. Our Septentrio receivers show significantly higher sensitivity to temperature influences than the JAVAD receivers. Temperature sensitivity is computed for GPS, Galileo and BeiDou systems, and amounts up to approx. 10–40 ps/ $$^{\circ }$$ ∘ C depending on the signal frequency. Signal splitters exhibit varying sensitivity values with a maximum of about $${1.2}\,\mathrm {ps}/^{\circ }\mathrm {C}$$ 1.2 ps ∕ ∘ C depending on the receiver combination. These findings highlight the necessity for thermal noise compensation for high-precision GNSS frequency transfer.

The recent breakthroughs in the distribution of quantum information and high-precision time and frequency (T F) signals over long-haul optical fibre networks have transformative potential for physically secure communications, resilience of timing infrastructure (such as that supporting Global Navigation Satellite Systems (GNSS)) and fundamental physics. To date, these capabilities remain confined to isolated testbeds, with quantum and T F signals accessible, for example in Germany, to only a few institutions. In this white paper we propose the QTF Backbone: a dedicated national fibre-optic infrastructure in Germany for the networked distribution of Quantum and T F signals using dark fibres and specialised hardware. The QTF Backbone is planned as a four-phase deployment over ten years to ensure scalable, sustainable access for research institutions and industry. The concept builds on successful demonstrations of time and frequency distribution at high Technology Readiness Levels (TRLs) across Europe, including PTB–MPQ links in Germany, REFIMEVE in France, and the Italian LIFT network. The QTF Backbone will enable transformative Research and Development (R D), support a nationwide QTF ecosystem, and ensure the transition from innovation to deployment. As a national and European hub, it will position Germany and Europe at the forefront of quantum networking, as well as T F transfer.

The accuracy of global navigation satellite system (GNSS) signal reception is crucial for precise navigation and geodetic positioning. Signal interactions with objects near the receiving antenna can cause multipath errors and distort GNSS antenna group delays, thereby reducing the achievable positioning accuracy. To mitigate these effects, the distortions can be predicted in advance and subsequently reduced through a calibration approach. This approach is possible, for example, for static errors, such as those caused by interactions between the antenna and the installation platform, for instance, on a car. This paper addresses the accurate prediction of distortions caused by the installation of the antenna on a car in automotive scenarios. This work introduces a hybrid calibration approach that combines real-world data and simulations to enhance GNSS antenna performance predictions. This approach allows the simulation to reconstruct the effect of the mounting platform on the data of an individual antenna previously measured in an anechoic chamber, thereby predicting the final error of the installed antenna on the platform. This methodology is then validated and compared with a GNSS-based calibration of the antenna performed directly on a car, i.e., inherently including installation effects. The results show that approximately 48% of the sky plot region exhibits a code phase variation difference within +/- 25 cm, indicating a high level of accuracy and consistency.

Abstract This study investigates vibration effects on GNSS clock performance and their application to receiver fingerprinting in dynamic environments. Through a flight experiment, it was observed that clock stability degrades by roughly one order of magnitude under vibration, and clock behaviors remain observable, exceeding simulated time-difference PLL-based observation noise. A vibration-induced clock behavior model was developed via an integral method. The results of the modeled clock performance show good agreement with the measured kinematic performance for the CSAC Microsemi MAC , while varying levels of discrepancies remain for other oscillator types. Features extracted from vibration-corrected kinematic ADEVs were applied in GNSS receiver fingerprinting, showing improved identification accuracy for short-duration data segments. The findings indicate that accounting for vibration effects not only enables an accurate characterization of clock dynamic stress under motion but also enhances the effectiveness of receiver fingerprinting techniques in dynamic GNSS scenarios.

This work presents an approach to assess the quality requirements for classical inertial measurement units (IMU) used in conjunction with a cold atom interferometer (CAI) for application in a hybrid quantum inertial navigations system (QINS). Based on the steady state formulation of an extended Kalman filter used for the hybridization of CAI and IMU, a model for the sensitivity gain of the QINS over the classical IMU is developed. This sensitivity gain depends on the white noise density of the classical sensor, as well as the scale factor and the signal-to-noise ratio of the CAI. Using the example of a single hybridized accelerometer axis it can be shown that for each CAI setting, an optimal white noise density of the classical accelerometer exists for which the sensitivity gain of the QINS yields a maximum. The findings are applied to evaluate existing experimental assemblies.

The reception of non-line-of-sight (NLOS) signals is a prevalent issue for Global Navigation Satellite System (GNSS) applications in urban environments. Such signals can significantly degrade the positioning and navigation accuracy for pedestrians and vehicles. While various methods, such as dual-polarization antennas and 3D building models, have been proposed to identify NLOS signals, they often require additional equipment or impose computational burdens, which limits their practicality. In this study, we introduce a machine learning (ML)-based classifier designed to detect NLOS signals based solely on quality indicators extracted from raw GNSS observations. We examined several input features, including carrier-to-noise density and elevation, and analyzed their relative importance. The effectiveness of our approach was validated using multi-GNSS data collected statically in the city of Hannover. To establish ground truth (i.e., a target) for training and testing the model, we used ray tracing in combination with a 3D building model of Hannover. The developed ML-based classifier achieved an accuracy of approximately 90% for NLOS signal classification. Furthermore, a vehicle-borne data set was used to test the utility of the ML-based signal classifier for kinematic positioning. The performance of the ML-aided positioning solution was compared against a solution without NLOS classification (raw solution) and with the ray-tracing-based classification results (reference solution). It was found that the ML-based solution demonstrated positioning precisions of 0.47 m, 0.55 m and 1.02 in the east, north and up components, respectively. This represents improvements of 64.6%, 33.4% and 36.6% over the raw solution. Additionally, we examined the performance of the ML-based classifier across various urban environments along the vehicle trajectory to gain deeper insights.

In this contribution, we propose the GNSS Feature Map-aided robust extended Kalman filter, which can provide centimeter-to-decimeter-level GNSS RTK position accuracy in urban environments without the need of additional sensors, city model information or computational intensive ray tracing methods. In this approach, the information on the predicted observation error magnitudes from the generated GNSS Feature Map is combined with the concept of robust estimation. The RTK positioning performance comparison for a dynamic experiment under harsh signal propagation conditions reveals that GNSS Feature Map-aided weighting using the Geman-McClure loss function shows the best overall performance. The RMS of the horizontal position error is improved by 17 % compared to C/N0 weighting, while 3DMA NLOS exclusion even degrades the solution. Furthermore, the combination of Feature Map information with the robust Geman-McClure loss function is effectively enhancing the float solution and reducing the number of falsely fixed ambiguities.

Smartphone-based positioning, navigation, and timing applications have been among the most popular topics within the GNSS community since 2016 when Google announced that raw GNSS observations are publicly available. However, achieving high positioning accuracy with smartphones is troublesome because of their specific limitations, such as the high noise level of observations, low protection against multipath, and discontinuities in carrier phase observations. Due to considerable discontinuities in carrier phase observations, code observations still play a crucial role in smartphone-based positioning applications. Subsequently, a realistic stochastic approach is mandatory to obtain the utmost positioning performance. This is especially true since the stochastic behavior of code observations for geodetic receivers and Android smartphones are quite different i.e., GNSS observations obtained from a smartphone are much noisier. The signal strength of GNSS signals collected from Android smartphones is also not very stable and is significantly lower when compared with geodetic receivers. Unlike observations obtained from geodetic receivers, no significant dependency between observation noise and elevation angle can be observed in smartphone observations. Therefore, conventional stochastic models, mainly based on the satellite elevation angle, are not enough to represent the stochastic behavior of smartphone observations. In this context, this study provides an enhanced stochastic approach for code observations obtained from Android smartphones. The corresponding approach includes a weighting scheme based on carrier-to-noise ratio (C/N0) values representing the signal strength of GNSS code observations. Besides, depending on their observation noises, this approach assigns different model coefficients for each constellation, which means differences between the navigation systems can be considered in adequate observation weighting. This approach also uses a robust Kalman filter method based on the IGG (Institute of Geodesy and Geophysics) III function to compensate for the effects of outliers and incorrectly weighted observations on the filtering performance. In this study, GPS, GLONASS, Galileo, and BeiDou code observations collected from a Xiaomi Mi 8 are processed to evaluate the performance of the proposed stochastic model. Firstly, observation noises are analyzed utilizing code-minus-phase observations, and the results show that GLONASS observations are considerably noisier than observations from other systems. Following, probability distributions of observation noises are evaluated to determine a realistic stochastic model, and the SIGMA- model with different coefficients for each constellation is adopted in this study. The Standard Point Positioning (SPP) method is also used to analyze the positioning performance of the proposed model. The results indicate that the proposed model can provide a 3D positioning accuracy of 1.5 m with the smartphone in static mode, which means the model improves the positioning accuracy by 36.9% compared to the conventional elevation-dependent stochastic approach. From these results, it can be said that the enhanced stochastic approach, based on C/N0 values and computing model coefficients for each constellation differently, can better reflect the stochastic behavior of code observations collected by Android smartphones.

Achieving a high-precision geodetic spatial reference depends on a thorough understanding of the equipment-specific sources of error of phase centre corrections (PCCs) of Global Navigation Satellite System (GNSS) receiver antennas. GNSS station operators and network analysers are constantly challenged regarding consistent PCCs, such as in the latest IGS Repo3 project. The challenges are, on the one hand, that not for all antennas in the network multi-GNSS calibrations are available. On the other hand, not all antennas are individually calibrated, so that type mean combinations with individual PCCs have to be used. Even small differences between PCCs can significantly affect position accuracy, troposphere modelling, and GNSS time and frequency transfer. Such deviations manifest differently depending on used hardware, software, and data processing approach. A generalised and easily accessible benchmark for assessing the quality of PCCs remains difficult to find. There is a lack of easy-to-apply and common quality assessments of PCCs when comparing individual calibrations versus a type mean and results from the various calibration facilities and calibration methods among each other. In response to this challenge, a global initiative involving nine calibration organisations has launched a comprehensive ring calibration campaign. By sharing six constructionally different antenna samples for calibration and presenting the subsequent results, this collaborative effort aims to enhance (1) the consistency of calibration methods and facilities, (2) develop a validation strategy, and (3) provide insights into the stability of receiver antenna calibrations. This contribution provides an overview of the current status of this campaign, initiated one and a half years ago, outlines the calibration and evaluation concept for carrier phase patterns. First initial results from consulting contributors are presented and the roadmap towards a standardised, robust quality assessment framework for PCCs will be covered.

To ensure an accurate and precise position in GNSS applications, phase center corrections (PCC) have to be taken into account. PCC are antenna and frequency dependent correction values. They describe the distance along the line-of-sight direction between the electrical phase center, where the GNSS signal is received, and the antenna reference point. In Melbourne-Wübenna or code-minus-carrier linear combinations, which are often used in highly precise GNSS applications, the codephase of the GNSS signal plays a key role. Similar to the PCC, also correction values for the codephase observation exist, called codephase center corrections (CPC), also known as group delay variations (GDV). The definition of CPC as well as their estimation process with a robot in the field is similar as for PCC. The team at Institut für Erdmessung is optimizing the established absolute antenna calibration approach for estimating CPC and PCC for multi GNSS signals in terms of repeatability, noise reduction and multipath impact. In this calibration process, an antenna under test (AUT) is precisely tilted and rotated around a fixed point in space by using a robot. A nearby reference station allows the calculation of time differenced single differences (dSD), which are used to estimate absolute CPC and PCC with spherical harmonics of degree and order 8. The pattern quality and also the repeatability of this approach depends, among other effects, on the observation noise of the GNSS signals. In this contribution, a detailed study about the influence of observation noise on the estimated patterns is presented. To this end, dSD are simulated based on an existing pattern and the robot positioning. The dSD are modified before the estimation process by polluting them with different kind and magnitude of noise. The estimated patterns are compared using e.g. the root-mean-square or the absolute difference between two runs. Our analysis shows, that 18% of the white noise magnitude is reflected in the repeatability of the pattern estimation in terms of absolute differences between two calibration runs.

Terrestrial laser scanners (TLS) are well-suited for conducting area-based deformation analysis of infrastructures. Unlike common point-based geodetic sensors, TLS can measure millions of points across the environment without requiring pre-defined, signalized measurement locations. However, TLS point clouds are affected by both random variations and residual systematic errors. These uncertainty components are often addressed using only probabilistic approaches, which may inadequately or overly optimistically represent the remaining systematic errors. To overcome these limitations, this study introduces an alternative framework based on interval mathematics to bound uncertainties arising from systematic errors. The proposed methodology includes a sensitivity analysis of TLS observation correction models, examining the variability of key input parameters. Unlike the quadratic approach for variance propagation, the interval-based method enables linear uncertainty propagation, effectively characterizing residual systematic uncertainties and their maximum effects. This paper details the methodology and presents typical interval values validated through simulations and real-data experiments. The findings highlight the potential of interval-based methods to enhance the TLS uncertainty model.

For safety-critical applications like autonomous driving, high trust in the navigation solution is essential, primarily measured by integrity. Multipath and further propagation specific errors in GNSS observations present significant challenges, as they can only be partially corrected. To ensure high integrity in urban navigation, it is crucial to understand the signal propagation mechanisms and potential error sources in these complex environments. Our group has made recent progress in this area, conducting various experiments in urban areas to analyze GNSS positioning performance. Using ray tracing, GNSS channel models, and 3D city models, the signal propagation conditions can be classified and errors quantified. We create GNSS Feature Maps to analyse the spatio-temporal similarity of the geometry-related error features and developed a Feature Map aided robust GNSS RTK algorithm, yielding improved accuracy and fulfilling our newly defined alert limits for German roads. We show how collaborative positioning can further improve this situation.

Cold atom interferometry based quantum accelerometers (Q-ACCs) are very promising for future satellite gravity missions thanks to their strength in providing long-term stable and precise measurements of non-gravitational accelerations. However, their limitations due to the low measurement rate and the existence of ambiguities in the raw sensor measurements call for hybridization of the Q-ACC with a classical one (e.g., electrostatic) with higher bandwidth. While previous hybridization studies have so far considered simple noise models for the Q-ACC and neglected the impact of satellite rotation on the phase shift of the accelerometer, we perform here a more advanced hybridization simulation by implementing a comprehensive noise model for the satellite-based Q-ACCs and considering the full impact of rotation, gravity gradient, and self-gravity on the instrument. We perform simulation studies for scenarios with different assumptions about quantum and classical sensors and satellite missions. The performance benefits of the hybrid solutions, taking the synergy of both classical and Q-ACCs into account, will be quantified. We found that implementing a hybrid accelerometer onboard a future gravity mission improves the gravity solution by one to two orders in lower and higher degrees. In particular, the produced global gravity field maps show a drastic reduction in the instrumental contribution to the striping effect after introducing measurements from the hybrid accelerometers.

Obtaining consistent phase center corrections (PCCs) for GNSS receivers remains a significant challenge, as there is currently a lack of benchmarks to consistently evaluate patterns or comparable values between different calibration institutions and methods (anechoic chamber and field robots). To address this problem, a global collaboration with nine calibration institutions known as the IGS Ring Calibration Campaign (IGS ringCalVal) has been launched. This comprehensive initiative aims to compare results from different calibration methods and create a robust framework for quality assessment. Six antennas from different manufacturers were used for calibration in this campaign.Over the past year, significant progress has been made. We have developed benchmarks and methods that facilitate the comparison of PCC patterns. Our detailed results show that in the pattern domain, the system/frequency consistency per antenna design varies within an uncertainty level of ±1 mm, with an additional elevation-dependent effect. In the positioning domain, system-specific PPP (Precise Point Positioning) results per antenna and GNSS system are presented, which show a deviation of typically less than 2-3 mm for the horizontal coordinate component and less than 5 mm for the vertical component between different systems. But also, special cases will be discussed. Finally, these results are crucial for establishing global standards for PCC calibration and verificationof receiver antennas.

An observability analysis of a Quantum Inertial Navigation System (QINS) is presented for multiple realistic dynamic scenarios. It is performed on an Error State Extended Kalman Filter (ESEKF), which contains loosely coupled position and velocity measurements and 3-axis differential Cold Atom Interferometer (CAI) sensor measurements. The CAI-based measurements are hybridized with conventional IMU measurements, which results, in combination with position and velocity estimates, in a filter structure that contains position, velocity, acceleration and angular-rate based observations of the system at the same time. This in turn results in increased estimability and observability of the system, as well as lower position, velocity and attitude drift. As CAI-based measurements are only available for low measurement frequencies (i.e. 1-10 Hz), and are also only valid for low dynamics, the improvement in estimability has to be evaluated in realistic scenarios.To this end, realistic trajectories (low frequency deterministic movement) and realistic vibrations (high frequency correlated deterministic movements) are generated and combined for this analysis. With this data, a numerical observability analysis is performed for different combinations of GNSS-based and CAI-based measurements. Furthermore, differences in estimability and observability between vehicle types (cars, aircrafts, trains or ships) are shown.The results demonstrate that, as in a conventional GNSS-IMU sensor fusion, dynamics improve the observability of e.g. scale factors, lever arm components, or misalignment terms. The inclusion of misalignments in the ESEKF, orientation difference between the CAI and IMU, and the introduction of larger lever arms between the CAI and IMU leads to increased dependencies between different bias terms of the IMU, but also between components of the lever arm and misalignments at the CAI-IMU level. They are accentuated when larger vehicle-dependent oscillations are introduced in the system, which is demonstrated by an analysis of singular vectors of the Fisher Information Matrix (FIM).The article provides relevant information about tradeoffs between CAI-IMU model complexity and occurring dynamics, and it gives insights which components of the system need to be pre-calibrated, as their on the fly estimation may lead to an insufficiently resolved state, due to increased dependencies.

The navigation performance of autonomous vehicles is highly dependent on using signals from Global Navigation Satellite Systems (GNSS) which can provide very precise positioning solutions through real time kinematic (RTK) technique. However, the received GNSS signals are heavily affected by propagation in urban trenches, impacting significantly the integrity of the navigation solution, that may not fulfill the requirements for automated driving any longer. Thus, in order to design a trajectory planning tool, 3D map aided (3DMA) methods in conjunction with a GNSS channel model will improve our understanding of the signal propagation in this complex environment. Together with satellite positions from almanac and an intended user trajectory, it is the basis for realistic signal availability and error simulations and thus contribute to predict the expected navigation performance. We show that the signal availability in urban trenches and suburban areas is predicted with 90–95