GNSS unmodeled error processing based on the resilient mathematical model compensation in high-precision GNSS positioning

In complex environments, signals are inevitably subject to phenomena such as reflection, refraction, diffraction, and obstruction, which result in significant unmodeled errors like colored noise, residual systematic errors, and other special outliers. Consequently, the achievement of high-precise and high-reliable global navigation satellite systems (GNSS) precise point positioning (PPP) is not a readily solvable problem in complex environments, especially in varying terrain topography. This paper proposed the resilient inequality constrained GNSS kinematic PPP method considering the terrain topography to improve the abnormal positioning results caused by unmodeled errors. Specifically, the proposed method is composed of the adaptive inequality constraint with dynamic penalty function and the timing-varying inequality considering the terrain topography. Two representative experiments including one set of designed data and three sets of daily measured data were conducted. The results show that the proposed method can improve the positioning results resulting from the unmodeled errors while preserving the trend of the original data. Typically, the proposed method decreases the standard deviations by 2.47, 0.25, and 1.46 cm in the U direction of the three real datasets, respectively. Consequently, the proposed method exhibits prospects in precision and reliability for complex environments.

Cycle slip detection and repair based on the unmodeled-error-constrained geometry-free combining geometry-based models for a single-frequency receiver

This paper presents one of the solutions to the problem of multipath propagation and effects on Global Navigation Satellite Systems (GNSS) signals in urban canyons. GNSS signals may reach a receiver not only through Line-of-Sight (LOS) paths, but they are often blocked, reflected or diffracted from tall buildings, leading to unmodelled GNSS errors in position estimation. Therefore in order to detect and mitigate the impact of multipath, a new ray-tracing model for simulation of GNSS signals reception in urban canyons is proposed - based on digital 3D maps information, known positions of GNSS satellites and an assumed position of a receiver. The model is established and validated using experimental, as well as real data. It is specially designed for complex environments and situations where positioning with highest accuracy is required - a typical example is navigation for blind people.

Comparison and analysis of unmodelled errors in GPS and BeiDou signals

Global navigation satellite systems (GNSS) products are integral to a wide array of scientific and commercial applications such as pecise orbit determination of low Earth orbit satellites, earthquake monitoring, GNSS reflectomrety, tropospheric and ionospheric research, surveying and much more. These products consisting of GNSS orbit, clock, phase biases and more are generated by the analysis centres of the International GNSS Service (IGS) by processing observations from a global network of ground stations to one or more GNSS constellations. The processing consists of a combined station position and GNSS satellite orbit determination through a least squares approach donated as global multi-GNSS processing.Within global multi-GNSS processing it is assumed that the observation noise is elevation-dependent and any spatial and temporal correlations are disregarded. Within numerous studies it has been shown that this assumption is incorrect while several studies additional pointed out that a sophisticated stochastic modelling has a positiv impact on GNSS processing and resulting products. In past reseach we have shown to exploit the post-fit residuals to derive temporal correlations for a sophisticated stochastic modeling. However, there have not been any large-scale investigations regarding the impact of stochastic modelling of observation noise on global GNSS processing products. Furthermore, to guarantee the quality of the GNSS products global multi-GNSS processing requires a sophisticated cycle slip detection and repairing algorithm. Cycle slips are discontinuities in the phase observations and if not corrected can lead to degrading quality of GNSS products.   We present our advancements in global multi-GNSS processing by exploiting post-fit residuals for stochastic modeling and cycle slip detection. We used several years of observations and a selected IGS network of ground stations to generate GNSS products. Based on this data we analysed the impact our newly integrated approaches have on GNSS products such as orbits, clocks, phase biases and station coordinate time series.  

Global Navigation Satellite Systems (GNSSs) have both internal and independent methods to maintain integrity. This chapter discusses two different methods– GNSS‐ receiver autonomous integrity monitoring and use of ground monitoring stations to monitor the health of the satellites, as is done via space‐based augmentation system (SBAS) and the ground‐based augmentation system. SBAS integrity is based on the premise that errors not detected or corrected in the operational environment can become threats to integrity and, if not mitigated, can become hazards to the user. The user must be protected from residual errors that can become threats to the integrity data that could result in hazardously misleading information being transmitted to the user. The SBAS system must compute estimates of the reference receiver clocks and GNSS/geostationary Earth orbit satellite clock errors. The chapter also describes some approaches that may be used to eliminate and minimize data errors, mitigate integrity threats, and satisfy the safety integrity requirements.

Accurate localization with high availability is a key requirement for autonomous vehicles. It remains a major challenge when using automotive sensors such as single‐frequency Global Navigation Satellite System (GNSS) receivers, a lane detection camera, and proprioceptive sensors. This paper describes a method that enables the estimation of stand‐alone single‐frequency GNSS errors by integrating the measurements from a forward‐looking camera matched with lane markings stored in a digital map. It includes a parameter identification method for a shaping model, which is evaluated using experimental data. An algebraic observability study is then conducted to prove that the proposed state vector is fully observable in a road‐oriented frame. This observability property is the basis to develop a road‐centered Extended Kalman filter (EKF) that can maintain the observability of every component of the state vector on any road, whatever its orientation. To accomplish this, the filter needs to handle road changes, which it does using bijective transformations. The filter was implemented and tested intensely on an experimental vehicle for driverless valet parking services. Field results have shown that the performance of the estimation process is better than solutions based on EKF implemented in a fixed working frame. The proposed filter guarantees that the drift along the road direction remains bounded. This is very important when the vehicle navigates autonomously. Furthermore, the road‐centered modeling improves the accuracy, consistency, and robustness of the localization solver.

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.

We studied geoid validation using ship-borne global navigation satellite systems (GNSS) on the Baltic Sea. We obtained geoid heights by combining GNSS–inertial measurement unit observations, tide gauge data, and a physical sea model. We used two different geoid models available for the area. The ship route was divided into lines and the lines were processed separately. The GNSS results were reduced to the sea surface using attitude and draft parameters available from the vessel during the campaign. For these lines, the residual errors between ellipsoidal height versus geoid height and absolute dynamic topography varied between 0 and 15 cm, grand mean being 2 cm. The mean standard deviations of the original time series were approximately 11 cm and reduced to below 5 cm for the time series filtered with 10 min moving average. We showed that it is possible to recover geoid heights from the GNSS observations at sea and validate existing geoid models in a well-controlled area.

The first-order ionospheric error is reduced in the dual-frequency Global Navigation Satellite Systems (GNSS). In this paper, the possibility of eliminating ionospheric higher-order errors in the multifrequency GNSS is explored. Since the second-order error associated with the geomagnetic field effect on the refractive index can be eliminated in dual-frequency measurements, we explore the possibility of eliminating third-order errors in triple-frequency GNSS in view of phase scintillations. A connection between the possibility of improving the multifrequency GNSS accuracy and diffraction effects in radio signal propagation through the randomly inhomogeneous ionosphere is shown. The numerical simulation has revealed that the systematic, residual ionospheric error is considerably reduced when we pass on from dual-frequency to triple-frequency measurements. The change in the residual error variance during such a transition depends however on the relationship between the inner scale of the turbulent spectrum of ionospheric irregularities and the Fresnel radius. Given the inner scale larger than the Fresnel radius, not only the systematic error, but also the standard deviation reduces when we pass on from dual-frequency to triple-frequency measurements. Otherwise, when the Fresnel radius exceeds the inner scale, the variance increases with increasing number of frequencies in use.

For global navigation satellite system (GNSS), ionospheric disturbances caused by the geomagnetic storm can reduce the accuracy and reliability of precision point positioning (PPP). At present, common stochastic models in GNSS PPP, such as the elevation angle stochastic (EAS) model or carrier‐to‐noise power‐density ratio () based SIGMA‐ model, do not properly consider storm effects on GNSS measurements. To mitigate severe storm effects on GNSS PPP, this study further implements the rate of total electron content index (ROTI) parameter into the EAS model referred to as the EAS‐ROTI model. This model contains two operations. The first one is to adjust variance of GNSS measurements using ROTI observations on EAS model. The second one is to determine the ratio of the priori variance factor between pseudorange and carrier phase measurements during severe storm conditions. The performance of EAS‐ROTI model is verified by using a large number of international GNSS service stations datasets on 17 March and 23 June in 2015. Experimental results indicate that on a global scale, the EAS‐ROTI model improves the PPP accuracy in 3D direction by approximately 12.9%–14.7% compared with the EAS model, and by about 24.8%–45.9% compared with the SIGMA‐ model.

Vibration displacement extraction based on an auto-tuning Kalman smoother from GNSS

Safety as the key quality property among RAMS (reliability, availability, maintainability, and safety) demonstrates the most stringent performance in correspondence with the safety requirements and performance standards like EN 50126. Meanwhile, GNSS (Global Navigation Satellite Systems) are penetrating the railway now widely in non-safety related applications as passenger information, fleet management, etc. GNSS also have great potential for safety-related applications in railway such as the train location determination function, which the safety performance needs to be assured through hazard analysis and risk assessment process. The train location determination by satellite-based localization system is elevating the train control to the next level. The European Train Control System (ETCS) has being trying to implementing Level 3, the Chinese Train Control System (CTCS) has been implementing CTCS Level 3 low cost especially for secondary lines, and the U.S. is implementing train control systems under Positive Train Control (PTC) requirements. The train control system needs GNSS to provide more accurate location information of trains, more flexible and condensed trains on tracks with the consistency of still keeping the current safety level or even improve safety. Some researchers are trying to understand the performance of GNSS (GPS / EGNOS / Beidou) for railway applications from the fundamental accuracy level. A satellite-based train localization unit (SaLuT) as the entity to perform the train location determination function is to bring the GNSS accuracy evaluation up to safety integrity according to the safety requirements and standards for risk assessment. One of the key consequential result derived from the train location is the adequate safety margin. The safety margin, which can also be called as “safe braking distance”, is a margin indicated to rail traffic that would allow the train to stop with the application of normal service braking. The safety margin estimation quality and the risk of the safety margin shows the hazard rate for the safety margin estimation function performed by the designed localization unit SaLuT. This paper discusses the safety margin estimation method considering both GNSS accuracy and integrity assessment aspects of SaLuT, in accordance of the settled safety requirements of location determination function. To analyze the hazard of the safety margin estimation, a formal method is applied to model the SaLuT behavior and functions. The formal method based on stochastic Petri net enables the modeling process to include the GNSS receiver collected real data on the test track into it. The safety margin estimation method together with the risk assessment method using the real data can generate quantitative indicators to represent the localization function and safety margin estimation quality. The data used for the analysis is collected in the Qinghai-Tibet railway line from Golmud station to Ganlong station by SaLuT installed on a locomotive along the track. With the stochastic Petri net model and the systematic equation using the real collected data to estimate the safety margin based on the GNSS technologies, the SaLuT can be validated and verified for its hazard rates, which provides information for the safety cases in order to meet the industrial normative requirements.

Map-aided adaptive GNSS/IMU sensor fusion scheme for robust urban navigation

Within the European Space Agency's (ESA) Space Weather Service Network, the development of performance indicators for the Global Navigation Satellite System (GNSS) has been identified as essential to meet the growing needs of end users for Space Weather information in the field of navigation. This requires a targeted analysis of Space Weather-related disturbances of technical systems and services in the field of satellite-based navigation, considering the growing requirements of all the different users in this domain. The goal of the Space Weather Impact on GNSS Performance: Application Development (SWIGPAD) project is to develop GNSS performance indicators (GPI) based on Space Weather data provided by European research institutes through the ESA Space Weather Service Portal (available at https://swe.ssa.esa.int) with the aim to fulfill representative use cases derived from dedicated meeting with industry and government experts. The application that serves the GPI will provide the user with information about current and expected effects of Space Weather on positioning at their respective location. Additionally, end users in the various GNSS application domains shall be assisted with an overall numerical and graphical estimate of the positioning uncertainty resulting from ionospheric conditions and its evolution over time. The intent of this article is to present the results of the project and the capabilities of the GPI application.