Potentialities of multifrequency ionospheric correction in Global Navigation Satellite Systems

Measurements of propagation time or phase of a signal at two frequencies enable us to eliminate the first ionospheric correction and improve accuracy of the Global Navigation Satellite System (GNSS) from tens of meters to centimetres. This paper explores possibilities of eliminating higher-order ionospheric errors in going to measurements at more frequencies. It is shown that the second-order correction, associated with the geomagnetic field effect on the refractive index, may be taken into account already in dual-frequency measurements. Further improvement of accuracy in the triple-frequency GNSS in view of phase scintillations is complicated by diffraction effects.

Urban environments present major challenges to the global navigation satellite system (GNSS) positioning to estimate the position of a self-driving vehicle. GNSS signals are often obstructed by buildings and other obstacles, leading to reflected and diffracted signals, which cause major positioning errors and known as line-of-sight (LOS) and non-line-of-sight (NLOS) multipath errors. Particularly, real-time kinematic (RTK)-GNSS, which can estimate the position in the centimeter-level accuracy, cannot estimate the precise position when there exist NLOS multipath errors. If we use NLOS GNSS code and carrier phase multipath measurements into the RTK-GNSS algorithm, carrier phase integer ambiguity cannot be solved, or wrong integer ambiguities are estimated. As a result, integer ambiguity resolved to fix solutions cannot be estimated, or wrong fix solutions which have large position error are estimated. That is a major barrier to using RTK-GNSS in autonomous driving. In this paper, we propose a novel NLOS detection and exclusion technique to enhance existing RTK-GNSS positioning in urban areas using only GNSS measurements alone. The key idea behind the proposed technique is that the NLOS pseudorange error will always be a positive value. NLOS pseudorange is longer than the true range, which is the distance between the GNSS antenna and satellite, due to the time delay caused by reflection and diffraction. The distribution of the NLOS error is not along with a Gaussian distribution. We use this phenomenon to detect the NLOS signals. We propose a technique to detect and eliminate the NLOS multipath using double-differenced pseudorange residuals (DD-PR). In the RTK-GNSS, DD GNSS measurement between the rover and base station is typically used. Here, we compute the DD-PR to detect the NLOS signals. In order to compute the DD-PR, the true position of the vehicle must be determined in advance. To solve this contradiction, we use a particle filter. The particle filter generates the position hypotheses, which is called as “particle”. These particles are used as the position candidate for estimating the DD-PR. When the DD-PR can be calculated at each particle position, we detect the large positive errors in DD-PR as NLOS signals. Then we compute the integer ambiguity of only the LOS DD carrier phase to estimate the precise vehicle position. The flow of the proposed technique is as follows: (1) The hypothetical user positions are created as particles, where the state vectors of these particles are 3D positions, x, y, and z. The initial particles are distributed based on the solution of the normal GNSS point positioning and its variance. (2) In the prediction step of the particle filter, the particle state in the next time step is estimated using the velocity of each particle computed from GNSS Doppler measurements. (3) Next, we compute the DD-PR at each particle location. The receiver clock bias, satellite clock bias, ionosphere error, and troposphere error in GNSS pseudorange are canceled through DD computation. As a result, DD geometrical range between receiver and satellite and DD multipath errors remain in the DD measurement. We compute DD-PR using the particle position. As a result, the only multipath error remains if the particle is close to the true position. NLOS multipath error is always positive value; we generate the subset of the LOS measurement hypothesis at each particle using a simple threshold test. (4) Next, we compute the RTK-GNSS position solution using the generated subset of the LOS measurement hypothesis at each particle location. It is expected that the RTK-GNSS fix solution can be calculated if the particle location is close to the true position because the NLOS signal has been eliminated. By contrast, if the particle is far from true position, the integer ambiguity cannot be solved because of using the incorrect subset of LOS measurements. The likelihood of each particle is computed from a distance between the particle location and the RTK-GNSS fix solution. The particle that is closest to the true position has a higher likelihood than the other particles. The probabilistic weight of each particle is then updated based on its likelihood. (5) Finally, all the particles are resampled based on their new weights. Particles that are sufficiently close to the true position survive this resampling step, and the average position of the remaining particles are employed as the final estimated user position. To confirm the effectiveness of the proposed technique, a kinematic positioning test was performed in Shinjuku, Tokyo, Japan. From the several positioning tests, the proposed technique could dramatically improve the availability and accuracy of RTK-GNSS fix solutions in the dense urban canyon where there exist a lot of NLOS multipath signals.

The standard ionospheric correction of bending angles in Global Navigation Satellite System (GNSS) radio occultation (RO) measurements removes most of the influence from the ionosphere, but leaves small systematic residual errors in the corrected data. The main reasons for residual errors at stratospheric and mesospheric altitudes are the neglect of higher‐order terms in the expansion of the ionospheric refractive index, and the fact that the two GNSS signals follow slightly different paths through the ionosphere. Another reason is the neglect of the local electron density at the receiver in orbit. These residual errors depend on the geomagnetic field and the spatial distribution of the ionospheric electron density and its gradients. In this work we derive this dependency to high accuracy for a spherically stratified ionosphere, including the “bi‐local” situation where the ionosphere is different (though still spherically stratified) on the inbound and outbound side of the RO event tangent points. As part of the derivations, we find a small residual error term not previously noted, which can become appreciable for elliptical satellite orbits. The results are verified by ray tracing through simple ionospheric and geomagnetic field models. The accuracy of a higher‐order bi‐local ionospheric residual error correction based on these results would be limited by the uncertainty in knowledge of the electron density and by horizontal electron density gradients along the ray paths.

Wave optics propagators (WOPs) are commonly used to describe the propagation of radio signals through earth's atmosphere. In radio occultation (RO) context, multiple phase screen (MPS) method has been used to model the effects of the atmosphere in Global Navigation Satellite System (GNSS) signals during an occultation event. WOP implementation includes, in addition to MPS, a diffraction integral as the final step to calculate the radio signal measured in the low-earth orbit (LEO) satellite. This approach considers vacuum as the propagation medium at high altitudes, which is not always the case when the ionosphere is taken into account in simulations. An alternative approach is using MPS all the way to LEO in order to sample the GNSS signal in orbit. This approach, named MPS orbit sampling (MPS-OS), is evaluated in this letter. Different scenarios of setting occultation assuming a short segment of the LEO orbit have been simulated using MPS and MPS-OS. Results have been compared to Abel transform references. Furthermore, a long segment scenario has been evaluated as well. A comparison of bending angle (BA) and residual ionospheric error (RIE) shows the equivalence between MPS and MPS-OS results. The main application of MPS-OS should be in occultation events with long segments of orbit and including ionosphere, in which a standard WOP may not be appropriate.

Short-term estimation of GNSS TEC using a neural network model in Brazil

Low Earth Orbit (LEO) constellations have recently gained tremendous attention in the navigational field due to their larger constellation size, faster geometry variations, and higher signal power levels than Global Navigation Satellite Systems (GNSS), making them favourable for Position, Navigation, and Timing (PNT) purposes. Satellite signals are heavily attenuated from the atmospheric layers, especially from the ionosphere. Ionospheric delays are, however, expected to be smaller in signals from LEO satellites than GNSS due to their lower orbital altitudes and higher carrier frequency. Nevertheless, unlike for GNSS, there are currently no standardized models for correcting the ionospheric errors in LEO signals. In this paper, we derive a new model called Interpolated and Averaged Memory Model (IAMM) starting from existing International GNSS Service (IGS) data and based on the observation that ionospheric effects repeat every 11 years. Our IAMM model can be used for ionospheric corrections for signals from any satellite constellation, including LEO. This model is constructed based on averaging multiple ionospheric data and reflecting the electron content inside the ionosphere. The IAMM model’s primary advantage is its ability to be used both online and offline without needing real-time input parameters, thus making it easy to store in a device’s memory. We compare this model with two benchmark models, the Klobuchar and International Reference Ionosphere (IRI) models, by utilizing GNSS measurement data from 24 scenarios acquired in several European countries using both professional GNSS receivers and Android smartphones. The model’s behaviour is also evaluated on LEO signals using simulated data (as measurement data based on LEO signals are still not available in the open-access community; we show a significant reduction in ionospheric delays in LEO signals compared to GNSS. Finally, we highlight the remaining open challenges toward viable ionospheric-delay models in an LEO-PNT context.

The concept of integer ambiguity resolution-enabled Precise Point Positioning (PPP-RTK) relies on appropriate network information for the parameters that are common between the single-receiver user that applies and the network that provides this information. Most of the current methods for PPP-RTK are based on forming the ionosphere-free combination using dual-frequency Global Navigation Satellite System (GNSS) observations. These methods are therefore restrictive in the light of the development of new multi-frequency GNSS constellations, as well as from the point of view that the PPP-RTK user requires ionospheric corrections to obtain integer ambiguity resolution results based on short observation time spans. The method for PPP-RTK that is presented in this article does not have above limitations as it is based on the undifferenced, uncombined GNSS observation equations, thereby keeping all parameters in the model. Working with the undifferenced observation equations implies that the models are rank-deficient; not all parameters are unbiasedly estimable, but only combinations of them. By application of $$\mathcal {S}$$ -system theory the model is made of full rank by constraining a minimum set of parameters, or S-basis. The choice of this S-basis determines the estimability and the interpretation of the parameters that are transmitted to the PPP-RTK users. As this choice is not unique, one has to be very careful when comparing network solutions in different $$\mathcal {S}$$ -systems; in that case the S-transformation, which is provided by the $$\mathcal {S}$$ -system method, should be used to make the comparison. Knowing the estimability and interpretation of the parameters estimated by the network is shown to be crucial for a correct interpretation of the estimable PPP-RTK user parameters, among others the essential ambiguity parameters, which have the integer property which is clearly following from the interpretation of satellite phase biases from the network. The flexibility of the $$\mathcal {S}$$ -system method is furthermore demonstrated by the fact that all models in this article are derived in multi-epoch mode, allowing to incorporate dynamic model constraints on all or subsets of parameters.

Deformation monitoring and dynamic characteristic analysis of bridge structures are the vital and basic requirements for the safe operation of bridges. In recent years, Global Navigation Satellite System (GNSS) has become increasingly widely used in bridge structural health monitoring with the development of the GNSS technology, especially the continuous improvement and development of China's Beidou navigation satellite system (BDS). This article summarizes the application process of GNSS dynamic deformation monitoring and the development of GNSS deformation measurement technology of bridge structural health monitoring, the dynamic characteristic identification method and its application in bridge GNSS monitoring. The positioning solution methods for GNSS monitoring, the high sampling rate GNSS receiver for monitoring, multi-frequency and multi-system GNSS monitoring and the weakening of multipath effect of GNSS monitoring are summarized in detail. Then, the conclusions and prospects are posed for future research and related application.

<p>The PROMICE project runs 27 Automatic Weather Stations (AWSs) in Greenland. Most of these are located in the ablation zone of the Greenland ice sheet. From March to September 2020 a multi-frequency Global Navigation Satellite System (GNSS) antenna was installed on the AWS NUK-K at a small local glacier outside Nuuk with the purpose of testing the setup for high precision positioning. Due to the remote location, power supply is limited and the GNSS setup is constructed to minimize the power consumption. Therefore, data collection is limited to three hours each day, the antenna is passive and the data is stored on a local drive and not transmitted.<br><br>This study tests if the setup is feasible for GNSS Interferometric Reflectometry (GNSS-IR) measurements of snow depth. The method estimates the average snow depth over an area on the order 10-20 • 10<sup>3</sup> m<sup>2</sup>. GNSS-IR analysis shows good reflections during most of the covered time period. A sonic ranger is mounted on the PROMICE AWSs and used for measurement of snow depth. The GNSS reflector heights are compared to measurements from the sonic ranger. Though some differences are present, the GNSS-IR estimates capture the snow melt, as measured by the sonic ranger, well. The quality of the reflections decreases towards the end of the data series when the snow is melted. We expect that this is due to a rougher ice surface. However, useful reflections are still obtained but the uncertainty on the daily estimates increase significantly. The transition from snow to ice surface is confirmed by an albedo estimate based on measurements of shortwave radiation at the AWS.</p>

Implementing the International GNSS Service 2021+ Strategic Plan: Vision and Use Cases

Variation of ionospheric range errors for L1 frequency GPS users during the 23rd solar cycle over BAHR IGS station

Global Navigation Satellite System (GNSS) plays an increasingly important role in all walks of life. In order to meet the demands of different users, it is crucial to establish corresponding correct mathematical models, especially in the field of precise positioning and navigation. However, due to the spatiotemporal complexity of and limited knowledge on GNSS errors, some residual errors would inevitably remain even after being corrected with differencing and linear combination, empirical model correction, and traditional parameterization. These residual observation errors are referred to as unmodeled errors. In fact, the unmodeled errors have adverse impacts on high-precision GNSS positioning. However, most existing studies mainly focus on handling the part of systematic errors that can be adequately modeled and then simply ignore the part of unmodeled errors that may actually exist. To make a breakthrough in the precision and reliability of GNSS applications currently, this study focuses on the theory and method for processing the GNSS unmodeled errors based on the mathematical model compensation, including resilient functional model adjustment and resilient stochastic model optimization. Specifically, according to the significance and properties of unmodeled errors, the unmodeled-error-ignored model, unmodeled-error-corrected model, unmodeled-error-fixed model, unmodeled-error-float model, and unmodeled-error-weighted model are proposed, where the approaches of significance testing, geometry-free/based/fixed models, hemispherical/hierarchy maps, composite stochastic model, multi-epoch partial parameterization, and inequality and equality constraints are adopted. Ultimately, an unmodeled error processing flow that can adaptively adjust as the external conditions change is proposed, then one can obtain high-precision GNSS positioning solutions.

Currently Global Navigation Satellite Systems (GNSS) are the primary source for the determination of absolute position, velocity and time (PVT) for merchant vessel navigation. On a ship bridge a number of systems like Electronic Chart and Information Systems (ECDIS), automatic track control systems and the Automatic Identification System (AIS) are relying on that PVT provision. Nevertheless it is well known that GNSS performance can strongly degrade due to space weather events, jamming and spoofing. Especially the availability and usage of low cost jammers, so called personal privacy devices (PPD), lead to the question on how a continuous onboard provision of PVT data can be realized in the presence of such a PPD jammer. Generally three possible solutions for that challenge are contemplated: i) the usage of a terrestrial backup system, ii) a jamming resistant GNSS receiver or iii) the integration of GNSS with other onboard self-contained navigation sensors like, e.g. speed log, gyrocompass and inertial sensors (Inertial Measurement Unit - IMU). The paper will focus on option (iii) and addresses the question whether it is possible to bridge real maritime GNSS Jamming attacks by a Kalman Filter (KF) using GNSS, inertial and Doppler velocity log (DVL). The main challenge for the KF here is, that a free inertial integration needs to be performed after a time period with already degraded GNSS signal reception. As KF are known to be optimum estimators only under the assumption of known statistics of the measurements, the question arises, whether the pseudoranges under the influence of jamming still follow a certain statistics. In order answer this question an additional lab experiment was performed and analyzed. Concretely the sensor fusion was realized by using both loosely and tightly coupled architectures which have been implemented using an Unscented Kalman Filter (UKF). The fusion algorithm is formulated in ECEF coordinate frame with quaternion attitude parameterization, where the heading observability is addressed by fusing the baseline measurements from the GNSS compass. In order to evaluate the performance of the proposed sensor fusion scheme under the influence of a real maritime jamming attack we performed an experiment in our civilian maritime jamming testbed in the Baltic, which has been established together with the German Federal Network Agency approximately 6 nmi north of the peninsula Dars. Here a PPD jammer was mounted on the monkey deck of an anchored vessel. A test vessel was maneuvering around the jammer. As a test vessel the multipurpose research and diving vessel Baltic Diver II (length 29 m, beam 6.7 m and draught 2.8 m) was used, which was equipped with three dual frequency GNSS receivers, a fiber-optic gyroscope IMU and a Doppler velocity log. The obtained results confirm that real maritime jamming attacks using PPD Jammers can be bridged by the proposed tightly coupled GNSS-IMU-DVL integration scheme resulting in horizontal position errors of less than 10m only.

In Global Navigation Satellite Systems (GNSS) using L-band frequencies, the ionosphere causes signal delays that correspond with link related range errors of up to 100 m. In a first order approximation the range error is proportional to the total electron content (TEC) of the ionosphere. Whereas this first order range error can be corrected in dual-frequency measurements by a linear combination of carrier phase- or code-ranges of both frequencies, single-frequency users need additional information to mitigate the ionospheric error. This information can be provided by TEC maps deduced from corresponding GNSS measurements or by ionospheric models. In this paper we discuss and compare different ionospheric correction methods for single-frequency users. The focus is on the comparison of the positioning quality using dual-frequency measurements, the Klobuchar model, the NeQuick model, the IGS TEC maps, the Neustrelitz TEC Model (NTCM-GL) and the reconstructed NTCM-GL TEC maps both provided via the ionosphere data service SWACI (http://swaciweb.dlr.de) in near real-time. For that purpose, data from different locations covering several days in 2011 and 2012 are investigated, including periods of quiet and disturbed ionospheric conditions. In applying the NTCM-GL based corrections instead of the Klobuchar model, positioning accuracy improvements up to several meters have been found for the European region in dependence on the ionospheric conditions. Further in mid- and low-latitudes the NTCM-GL model provides results comparable to NeQuick during the considered time periods. Moreover, in regions with a dense GNSS ground station network the reconstructed NTCM-GL TEC maps are partly at the same level as the final IGS TEC maps.

The current cycle slip detection methods of Global Navigation Satellite System (GNSS) were mostly proposed on the basis of assuming the ionospheric delay varying smoothly over time. However, these methods can be invalid during active ionospheric periods, e.g., high Kp index value and scintillations, due to the significant increase of the ionospheric delay. In order to detect cycle slips during high ionospheric activities successfully, this paper proposes a method based on two modified Hatch–Melbourne–Wübbena combinations. The measurement noise in the Hatch–Melbourne–Wübbena combination is minimized by employing the optimally selected combined signals, while the ionospheric delay is detrended using a smoothing technique. The difference between the time-differenced ambiguity of the combined signal and this estimated ionospheric trend is adopted as the detection value, which can be free from ionospheric effect and hold the high precision of the combined signal. Five threshold determination methods are proposed and compared to decide the cycle slip from the magnitude aspect. This proposed method is tested with triple-frequency Global Navigation Satellite System observations collected under high ionospheric activities. Results show that the proposed method can correctly detect and fix cycle slips under disturbed ionosphere.