An investigation of interval and set-based uncertainty representation for GNSS navigation

[no abstract available

On the determination of the atmospheric outer scale length of turbulence using GPS phase difference observations : The Seewinkel network

Microwave electromagnetic signals from the Global Navigation Satellite System (GNSS) are affected by their travel through the atmosphere: the troposphere, a non-dispersive medium, has an especial impact on the measurements. The long-term variations of the tropospheric refractive index delay the signals, whereas its random variations correlate with the phase measurements. The correlation structure of residuals from GNSS relative position estimation provides a unique opportunity to study specific properties of the turbulent atmosphere. Prior to such a study, the residuals have to be filtered from unwanted additional effects, such as multipath. In this contribution, we propose to investigate the property of the atmospheric noise by using a new methodology combining the empirical mode decomposition with the Hilbert–Huang transform. The chirurgical “designalling of the noise” aims to filter both the white noise and low-frequency noise to extract only the noise coming from tropospheric turbulence. Further analysis of the power spectrum of phase difference can be performed, including the study of the cut-off frequencies and the two slopes of the power spectrum of phase differences. The obtained values can be compared with theoretical expectations. In this contribution, we use Global Positioning System (GPS) phase observations from the Seewinkel network, specially designed to study the impact of atmospheric turbulence on GPS phase observations. We show that (i) a two-slope power spectrum can be found in the residuals and (ii) that the outer scale length can be taken to a constant value, close to the physically expected one and in relation with the size of the eddies at tropospheric height.[Figure not available: see fulltext.] © 2020, The Author(s)

Improved high-precision GNSS navigation with a passive hydrogen maser

Receiver clock modeling (RCM) based on code observations requires a chip-scale atomic clock to improve the PVT solution. When using carrier phase observations, a more stable oscillator like a passive hydrogen maser (PHM) is necessary. We applied a PHM in an automotive experiment of about 80 minutes in an urban environment recording 10 Hz multi-GNSS data. Modeling the clock process noise in a linearized Kalman filter according to the spectral behavior of the PHM (i.e., RCM), improves position and velocity regarding precision and accuracy by 15% and 57%, respectively, as well as reliability by 30%. In situations with sparse, geometrically unfavorable observations, RCM prevents large position drifts. The convergence time of the carrier phase ambiguities is not affected. Conclusively, precision, accuracy, and reliability in kinematic precise point positioning can be improved by using an oscillator like a PHM. Future advancements in clock technology should make this approach more feasible for ordinary use cases

Integration of atom interferometers and inertial measurement units to improve navigation performance

This paper explores a way of combining conventional inertial sensors with cold atom interferometers (CAI) in order to reduce the drift of the navigation solutions in velocity and orientation. Instead of complementing and improving the CAI with conventional sensors, in this approach the conventional IMU will be used as main sensor for a prediction of the kinematic state. The CAI is then used for the correction of systematic errors and offsets in the framework of an extended Kalman Filter. Monte Carlo simulation studies demonstrate an improvement of the navigation solution precision. In addition, most drifts of velocity and orientation can be eliminated and the uncertainty of the velocity solution can further be reduced by a factor of 30 or more compared to the conventional strapdown. The observability of the error states is discussed

The Atmospheric Scale Lengths of Turbulence and Its Dependencies Derived from GPS Single Difference with a Common Clock

Microwave signals, for example, those from Global Navigation Satellite Systems (GNSS) and very long baseline interferometry, are affected by tropospheric turbulence in such a way that the random fluctuations of the atmospheric index of refraction correlate the phase measurements. These atmospheric correlations are an important error source in space geodetic techniques. For computational reasons, they are neglected in positioning applications, to the detriment of a trustworthy description of the precision, and rigorous test statistics. Fortunately, modelling such correlations is possible by combining concepts from electromagnetic wave propagation in a random medium and the Kolmogorov turbulence theory. In this contribution, we will process single differences GNSS phase observations from a 300 m baseline between two different receivers linked to a common clock. After a preprocessing to filter additional error contributions, such as multipath, we will study the power spectral density of the phase residuals. We will estimate its low and high cutoff frequencies with an adapted unbiased Whittle maximum likelihood estimator. These cutoff frequencies – as predicted by turbulence theory – are related directly to the scale lengths of turbulence, i.e. the size of the eddies that correlate the GNSS observations. The study of their dependencies with the satellite geometry, day of the year, or time of the day provides new insights into the two- and three-dimensional atmospheric turbulence in the atmosphere. In addition, it contributes to improving the stochastic description of random effects impacting GNSS phase observations

Predicting C/N0 as a Key Parameter for Network RTK Integrity Prediction in Urban Environments

Autonomuous transportation systems require navigation performance with a high level of integrity. As Global Navigation Satellite System (GNSS) real-time kinematic (RTK) solutions are needed to ensure lane level accuracy of the whole system, these solutions should be trustworthy, which is often not the case in urban environments. Thus, the prediction of integrity for specific routes or trajectories is of interest. The carrier-to-noise density ratio (C/N0) reported by the GNSS receiver offers important insights into the signal quality, the carrier phase availability and subsequently the RTK solution integrity. The ultimate goal of this research is to investigate the predictability of the GNSS signal strength. Using a ray-tracing algorithm together with known satellite positions and 3D building models, not only the satellite visibility but also the GNSS signal propagation conditions at waypoints along an intended route are computed. Including antenna gain, free-space propagation as well as reflection and diffraction at surfaces and vegetation, the predicted C/N0 is compared to that recorded by an Septentrio Altus receiver during an experiment in an urban environment in Hannover. Although the actual gain pattern of the receiving antenna was unknown, good agreements were found with small offsets between measured and predicted C/N0

Simulation studies to evaluate the impact of receiver clock modelling in flight navigation

GNSS based positioning and navigation always require perfect synchronization between the receiver and satellites clock. Further, due to the limited frequency stability of the GNSS receiver’s internal oscillator, an additional receiver clock error has to be estimated along with the coordinates. Thus, the observation geometry is changed; it results in some disadvantages which are: at least four satellites are required for positioning or navigation, high correlations are generated among the estimated receiver clock, the up-component and tropospheric delay, and the up-component is estimated less precisely than the horizontal coordinates. Research has shown that these drawbacks can be avoided by replacing the receiver internal oscillator with a more stable external clock and modelling its operation in a physically meaningful way over intervals in which the oscillator noise is far less than the observation noise. This method is known as receiver clock modelling (RCM). In this contribution, we will present a simulation study which is done to evaluate the gain in performance by RCM in code-based GNSS flight navigation where the height component is of relevance. Different flight test trajectories are simulated with code observation of a multi-GNSS system. Observations for different test trajectories are evaluated with and without RCM using different types of external clocks. The gain in precision of the coordinates for different trajectories w.r.t different clocks will be presented.Deutsches Zentrum für Luft- und Raumfahrt e.V./DLR Raumfahrtmanagement/FKZ: 50NA1705/E

Performance evaluation of GNSS receiver clock modelling in urban navigation using geodetic and high-sensitivity receivers

In urban areas, the Global Navigation Satellite System (GNSS) can lead to position errors of tens of meters due to signal obstruction and severe multipath effects. In cases of 3D-positioning, the vertical coordinate is estimated less accurately than are the horizontal coordinates. Multisensor systems can enhance navigation performance in terms of accuracy, availability, continuity and integrity. However, the addition of multiple sensors increases the system cost, and thereby the applicability to low-cost applications is limited. By using the concept of receiver clock modelling (RCM), the position estimation can be made more robust; the use of high-sensitivity (HS) GNSS receivers can improve the system availability and continuity. This paper investigates the integration of a low-cost HS GNSS receiver with an external clock in urban conditions; subsequently, the gain in the navigation performance is evaluated. GNSS kinematic data is recorded in an urban environment with multiple geodetic-grade and HS receivers. The external clock stability information is incorporated through the process noise matrix in a Kalman filter when estimating the position, velocity and time states. Results shows that the improvement in the precision of the height component and vertical velocity with both receivers is about 70% with RCM compared with the estimates obtained without applying RCM. Pertaining accuracy, the improvement in height with RCM is found to be about 70% and 50% with geodetic and HS receivers, respectively. In terms of availability, the HS receiver delivers an 100% output compared with a geodetic receiver, which provides an output 99⋅4% of the total experiment duration. Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Institute of Navigation.

Symmetries for Interval Analysis

[no abstract available

Comparison concept and quality metrics for GNSS antenna calibrations: Cause and effect on regional GNSS networks

Precise values for absolute receiver antenna phase centre corrections (PCC) are one prerequisite for high-quality GNSS applications. Currently, antenna calibrations are performed by different institutes using a robot in the field or in an anechoic chamber. The differences between the antenna patterns are significant and require a sound comparison concept and a detailed study to quantify the impact on geodetic parameters, such as station coordinates, zenith wet delays (ZWDs) or receiver clock estimates. Furthermore, a discussion on acceptable pattern uncertainties is needed. Therefore, a comparison strategy for receiver antenna calibration values is presented using a set of individually and absolutely calibrated Leica AR25 antennas from the European Permanent Network (EPN), both from the robot (Geo++ company) and from the chamber approach (University of Bonn). Newly developed scalar metrics and their benefits are highlighted and discussed in relation to further structural analysis. With our metrics, properties of 25 patterns pairs (robot/chamber) could be used to successfully assign seven individual groups. The impact of PCC on the estimated parameters depends on the PCC structure, its sampling by the satellite distribution and the applied processing parameters. A regional sub-network of the EPN is analysed using the double difference (DD) and the precise point positioning (PPP) methods. For DD, depending on the antenna category differences in the estimated parameters between 1 and 12 mm are identified also affecting the ZWDs. For PPP, the consistency of the observables, i.e. potential differences in the reference point of carrier phase and code observations, additionally affects the distribution among the different parameters and residuals