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Towards Integrity for GNSS-based urban navigation - challenges and lessons learned
Abstract
For safety critical applications like autonomous driving, high trust in the reported navigation solution is mandatory. This trust can be expressed by the navigation performance parameters, especially integrity. Multipath errors are the most challenging error source in GNSS since only partial correction is possible. In order to ensure high integrity of GNSS-based urban navigation, signal propagation mechanisms and the potential error sources induced by the complex measurement environment should be sufficiently understood. In this contribution , we report on recent progress on this topic in our group. We conducted various experiments in urban areas and investigated the behavior and magnitude of GNSS signal propagation errors. To this end, ray tracing algorithms combined with 3D city models are implemented to identify propagation obstructions and quantify propagation errors. A Fresnel zone-based criterion is exploited to determine the occurrence and magnitude of diffraction. GNSS Feature Maps are proposed to visualize the analyses and to predict situations with potential loss of integrity. To measure the integrity of urban navigation, we developed alternative set-based approaches in addition to the classical stochastic approach. Based on interval mathematics and geometrical constraints, they are sufficient to bound remaining systematic uncertainty and feasible for integrity applications.
... However, locationspecific errors remain, which are not common between receivers nor between satellites, namely multipath or non-line-of-sight (NLOS) signal reception [9]. These kinds of errors are more severe in urban environments where GNSS signals are interacting with different obstacles such as buildings, bridges, trees, utility poles, etc. [10,11]. For mitigating NLOS and multipath effects, different approaches have been used, namely antenna and receiver design, signal processing techniques, navigation-based techniques, postprocessing and 3DMA (three-dimensional-mapping-aided) techniques [12], which include ranging based and shadow matching, i.e., comparing the C/N 0 to nominal values to determine blockages. ...
... Commercial product "Sim3D" by Spirent [25] simulates the C/N 0 considering multipath and NLOS situations by incorporating different 3D objects as desired by the user, e.g., building, tree, car, etc. The 3DMA technique has been used in the "PosNav" research group of the Institut für Erdmessung at Leibniz University Hannover to investigate the NLOS and multipath effect in urban environments [11,[26][27][28]. Current work basically takes advantage of [26], in which the multipath effects are modelled specifically for the carrier phase by developing compact expressions. ...
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.
... However, GNSS signals suffer from the harsh reception conditions in urban areas. NLOS (Non-line of Sight) and multipath signals caused by surrounding buildings, trees, or other interfering factors lead to ranging errors that can exceed 50 meters (Hsu, 2017;Kubo et al., 2020;Schön et al., 2022;Schaper et al., 2022), and assistance data might not be available for every type of navigation module. The presence of cellular transmitters, especially in such harsh environments, highlights an interest in the emitted signals to improve GNSS localization. ...
The standardization of fifth-generation (5G) New Radio (NR) cellular networks offers possibilities to provide low latency
and high data rate communication in higher frequency bands. The increasing communication demand, both in public and
private spaces, makes the deployment of denser networks especially interesting for urban areas. As a by-product, the emerging
signal source can be used for positioning without the need for dedicated positioning infrastructures. Global navigation satellite
systems (GNSS) are the workhorse for absolute outdoor localization, with few meters uncertainties; or even centimeter level in
urban areas when complemented by dedicated base stations, such as Real Time Kinematic (RTK) positioning and additional
information. However, GNSS signals suffer from the harsh reception conditions in urban areas. NLOS (Non-line of Sight) and
multipath signals caused by surrounding buildings, trees, or other interfering factors lead to ranging errors. The presence of a
signal transmission infrastructure in an environment that is susceptible to GNSS positioning errors is an incentive to analyze
these signals to enhance GNSS localization.
This paper evaluates the ranging capabilities of current state-of-the-art 5G NR signals in dense urban environments. Publicly
available signal synchronization blocks (SSBs) are analyzed in simulations to evaluate the augmentation capabilities of urban
GNSS positioning by additional NR range measurements. The analysis on the SSB Cramér-Rao lower bound (CRLB) shows, that
the addition of SSB ranges can improve GNSS-Single Point Positioning (GNSS-SPP) in severe GNSS conditions. Consequently,
real SSBs broadcasted by commercial cellular networks in the vicinity of Leibniz University, Hannover are captured and processed
to evaluate the ranging quality of the SSBs in dense urban environment.
... urban canyons, tunnels or underground car parks). Non-Line-of-Sight and multipath signals caused by surrounding buildings, trees or other interfering factors lead to ranging errors that can exceed 50 meters (Hsu, 2017;Kubo et al., 2020;Schaper et al., 2022;Schön et al., 2022). A one-metre error perpendicular to the direction of travel can have fatal consequences in road traffic. ...
In recent years, the demand for accurate and reliable positioning has increased. Especially with regard to autonomous driving, highly accurate positioning information is needed. While conventional Global Navigation Satellite System (GNSS) positioning solutions provide reliable results in open areas such as highways, this is quite different in urban environments (e.g. urban canyons, tunnels or underground car parks). For these areas, GNSS positioning must be supported by other information in order to guarantee accurate and reliable positioning. For this contribution, sensor fusion is applied to a multi-vehicle network in order to make statements about the opportunities and limitations of collaborative navigation on the accuracy and robustness of position determination. The focus is on collaboration itself and not on communication. We use a Real-Time Kinematic (RTK) algorithm supported by inter-vehicle observations from stereo imagery to aid the position estimation. For this paper, we consider real data collected in a GNSS challenging environment in Hannover, Germany. The original inter-vehicle and GNSS observations are modified into bias-free observations with Gaussian noise. As Vehicle-to-Vehicle observations, we simulate a total of 18 coordinate differences with different precisions. The estimated position results are verified with a reference solution. This approach is then used to understand the potential and limitations of collaborative positioning. We demonstrate that the improvement of the C-RTK solution as well as its magnitude are determined by the precision of the V2V observations, the amount of available GNSS observations, and the performance of the aiding agents in the network. We show that the use of a collaborative RTK leads to a max. improvement of the 3D RMSE of up to 51% compared to the single-vehicle (SV) RTK solution. The collaborative solution has a particularly positive effect on the determination of the height component. In contrast, a careful selection of collaboration partners is required, since imprecise and inaccurate aiding agents might lead to a significant deterioration compared to the SV solution.
... reception of both direct and reflected signals introduces the multipath effect, whereas the sole reception of the reflected signal introduces non-line-of-sight (NLOS) reception [6], [7], [8]. These receptions frequently occur in dense urban areas, leading to significant extra delays in the GNSS ranging measurements [9]. ...
Accurate positioning from the global navigation satellite system (GNSS) is critical for various civil applications, like location-based services and intelligent transportation systems. GNSS Doppler frequency can provide reliable velocity estimation to improve positioning performance. Unfortunately, the quality of Doppler frequency measurements can be significantly degraded in urban canyons. This is due to the non-line-of-sight (NLOS) receptions altering the incoming signal direction and its dynamic characteristic. Thus, correcting the NLOS error on Doppler frequency is essential for the velocity as well as position estimation in urban canyons. The 3D mapping aided (3DMA) GNSS is a promising technique for NLOS error correction. Its effectiveness on pseudorange measurements has been well proven. However, its feasibility on Doppler frequency correction has not been investigated yet. Therefore, this paper first verifies the feasibility of ray-tracing in modelling Doppler frequency. Then, an urban Doppler frequency assessment is conducted. Finally, the effectiveness of ray-tracing in correcting velocity estimation accuracy is evaluated. The assessment and evaluation assessment are conducted via experiments in both open-sky and urban areas. Results demonstrate ray-tracing has an excellent capability in modelling the NLOS Doppler frequency, which reduces the corresponding measurement error by 62.8% in average and the root-mean-square of velocity estimation error by 51.92%.
... Besides reflection delay, ray-tracing simulation can also calculate the GNSS signal strength based on the multipath propagation model [31,32]. A research study was conducted on the use of the ray-tracing technique to identify propagation obstructions and quantity propagation errors [33]. The study proposed measuring the position integrity as a set-based approach to bound the remaining systematic uncertainty. ...
Smart health applications have received significant attention in recent years. Novel applications hold significant promise to overcome many of the inconveniences faced by persons with disabilities throughout daily living. For people with blindness and low vision (BLV), environmental perception is compromised, creating myriad difficulties. Precise localization is still a gap in the field and is critical to safe navigation. Conventional GNSS positioning cannot provide satisfactory performance in urban canyons. 3D mapping-aided (3DMA) GNSS may serve as an urban GNSS solution, since the availability of 3D city models has widely increased. As a result, this study developed a real-time 3DMA GNSS-positioning system based on state-of-the-art 3DMA GNSS algorithms. Shadow matching was integrated with likelihood-based ranging 3DMA GNSS, generating positioning hypothesis candidates. To increase robustness, the 3DMA GNSS solution was then optimized with Doppler measurements using factor graph optimization (FGO) in a loosely-coupled fashion. This study also evaluated positioning performance using an advanced wearable system’s recorded data in New York City. The real-time forward-processed FGO can provide a root-mean-square error (RMSE) of about 21 m. The RMSE drops to 16 m when the data is post-processed with FGO in a combined direction. Overall results show that the proposed loosely-coupled 3DMA FGO algorithm can provide a better and more robust positioning performance for the multi-sensor integration approach used by this wearable for persons with BLV.
As the digital twins for the urban area, 3D building models have been applied in many areas and their reliability has become more and more vital. In a fast-developing city, the scale of construction renewal is usually tremendous with a high frequency, which makes the existing 3D building models easy to be out-of-date and introduces errors. In this paper, we proposed a monitoring algorithm for building updates based on satellite signals. We use satellite measurements to estimate the sky visibility from building blockages. By comparing it to the sky visibility from the existing dataset, we can obtain the direction of the building being updated. Finally, the building update directions detected from multiple agents are collaborated in a crowd-sourcing manner to estimate the overall update probability of buildings. A simulation and a real experiment are conducted to evaluate the performance of the proposed algorithm. The proposed monitoring algorithm is robust to sky visibility estimation accuracy, number of agents, and agent positioning error from the simulation analysis. In the real experiment, the building with updates can be accurately detected by the satellite measurements collected from a short pedestrian trajectory around this area.
With many applications requiring individuals to share spaces with autonomous systems, not only do accurate positioning solutions become crucial, but also understanding of the uncertainty associated with these systems. For applications like public transportation or logistics, position tracking algorithms need to be evaluated on accuracy and consistency. The selection of the appropriate algorithms heavily relies on the specific requirements of the applications, thus demanding novel algorithms for these new use cases.This paper introduces a novel error state Kalman filter with implicit measurement equations, presenting a solution for new applications. The filter facilitates the fusion of inertial measurement unit (IMU) sensor data with other sensors using arbitrary measurement models. To showcase its effectiveness, the filter is demonstrated by fusing simulated IMU and LiDAR observations for position tracking (complete code on Github). Specifically, the LiDAR points are employed in the update step by minimizing the distances to known planes. Furthermore, the performance of the filter is enhanced by motion compensation through pose interpolation, utilizing the available timestamps. The results are thoroughly discussed in terms of accuracy and consistency, revealing significant improvements by employing pose interpolation. However, the consistency analysis indicates slightly pessimistic results, suggesting the need for further optimizations.
GNSS integrity monitoring requires proper bounding to characterize all ranging error sources. Unlike classical approaches based on probabilistic assumptions, the alternative interval-based integrity approach depends on deterministic interval bounds as inputs [1]. Different from a quadratic variance propagation, the interval approach has intrinsically a linear uncertainty propagation which is adequate to describe remaining systematic uncertainty [2].
As one of the primary error sources, the tropospheric error is corrected in practice widely by the well-developed empirical troposphere models. In order to quantify and bound the residual tropospheric error for those models, we will make a proposal on how to derive the required interval bounds based on interval analysis.
Multipath in urban environments still represents a great challenge for
Global Navigation Satellite System (GNSS) positioning as it is a
degrading factor which limits the attainable accuracy, precision and
integrity. In an urban trench, the dense building structures in the vicinity
of the antenna cause reflections of the satellite rays resulting in multipath
errors. Various work has been presented for simulating reflections for
stations under laboratory conditions, yet the simulative analysis of
multipath propagation in urban environments is still missing.In this
contribution, we enhanced an existing ray-tracing algorithm which
identifies potentially multipath affected satellite signals. So far, it
calculates reflection points on a plane ground and estimates the resulting
multipath error. We extended it for the urban area case by introducing a
3D city building model with possible reflections on all surfaces of the
buildings. Based on the geometry between the antenna position, satellite
position and the reflection surface, the extra path delays, the
characteristics of the propagation channel and the signal amplitudes are
calculated. The resulting multipath errors are then estimated from the
discriminator function using state of the art correlator parameters and
antenna models.In a second step, the simulation results are validated.
We conducted real world GNSS measurements using parked cars in
dense urban areas. Different approaches of combining observations
(multipath linear combination, code-minus-carrier combination, double
difference processing) for determining the multipath error are
compared.Finally, the empirically derived multipath errors are evaluated
with the multipath errors from our simulation tool.
The GNSS performance is significantly degraded in urban canyons because of the signal interferences caused by buildings. Besides the multipath and non‐line‐of‐sight (NLOS) receptions, the diffraction effect frequently occurs in urban canyons, which will severely attenuate the signal strength when the satellite line‐of‐sight (LOS) transmitting path is close to the building edge. It is essential to evaluate the performance of current diffraction models for GNSS before applying mitigation. The detailed steps of applying the knife‐edge model and the uniform geometrical theory of diffraction (UTD) model on GNSS are given, including the and pseudorange simulation of the diffracted signal. The performances of both models are assessed using real data from two typical urban scenarios. The result shows the UTD can adequately model the GNSS diffraction effect even in a complicated urban area. Compared with the knife‐edge model, the UTD achieves better modeling accuracy, whereas requiring higher computational loads.
Accurate localization of road agents (GNSS receivers) is the basis of intelligent transportation systems, which is still difficult to achieve for GNSS positioning in urban areas due to the signal interferences from buildings. Various collaborative positioning techniques were recently developed to improve the positioning performance by the aid from neighboring agents. However, it is still challenging to study their performances comprehensively. The GNSS measurement error behavior is complicated in urban areas and unable to be represented by naive models. On the other hand, real experiments requiring numbers of devices are difficult to conduct, especially for a large-scale test. Therefore, a GNSS realistic urban measurement simulator is developed to provide measurements for collaborative positioning studies. The proposed simulator employs a ray-tracing technique searching for all possible interferences in the urban area. Then, it categorizes them into direct, reflected, diffracted, and multipath signal to simulate the pseudorange, , and Doppler shift measurements correspondingly. The performance of the proposed simulator is validated through real experimental comparisons with different scenarios based on commercial-grade receivers. The proposed simulator is also applied with different positioning algorithms, which verifies it is sophisticated enough for the collaborative positioning studies in the urban area.
GNSS (Global Navigation Satellite Systems) multipath has been subject to scientific research for decades and although numerous methods and techniques have already been developed to mitigate this effect, it is still one of the accuracy-limiting factors in many GNSS applications. Since multipath is highly dependent on the individual antenna environment, there is still a need for new methods and further investigations to increase the understanding of this systematic effect. In this paper, the concept of Fresnel zones is applied to two different aspects of multipath. First, Fresnel zones are determined for the line-of-sight transmission between satellite and receiver. By comparing the boundary of the Fresnel zones to an obstruction adaptive elevation mask, potentially diffracted signals can be identified and excluded from the position estimation process. Both the percentage of epochs with fixed ambiguities and the positioning accuracy can be increased by the proposed method. Second, Fresnel zones are used to analyze the multipath induced by a horizontal and spatially-limited reflector. The comparison of simulated and real signal-to-noise (SNR) observations reveals a relationship between the percentage of the overlap of the Fresnel zone and reflector and the occurrence of multipath. It is found that an overlap of 50% is sufficient to induce multipath effects. This is of special interest, since this does not confirm theoretical assumptions of the multipath theory.
The paper presents an innovative GNSS fault detection and exclusion approach for the adoption of satellite localization in the rail sector. Current global integrity monitoring systems cannot guarantee the safety level needed for such applications as train control where Tolerable Hazard Rate in the order of 10
is required. A new method, named 2-tiers, enabling to integrate local augmentation systems and global augmentation infrastructures, is presented. It is based on the comparison of single differences residuals among satellites for detecting signal in space faults and double difference residuals among local augmentation stations and SBAS RIMS for detecting reference stations faults. GPS SIS faults described in literature and real GNSS raw data recorded on a train are taken into account. The present work reports the performance analysis for the 2-tiers approach carried out during relevant European projects. A Test-Bed architecture has been developed through the implementation of the algorithm in real-time on a local augmentation operational centre. Relevant performances have been tested on a rail track for validating the algorithm in real operative conditions. Significant results of the analysis are reported for SIS integrity assessment only.
Global Navigation Satellite Systems (GNSS) deliver absolute position and velocity, as well as time information (P, V, T). However, in urban areas, the GNSS navigation performance is restricted due to signal obstructions and multipath. This is especially true for applications dealing with highly automatic or even autonomous driving. Subsequently, multi-sensor platforms including laser scanners and cameras, as well as map data are used to enhance the navigation performance, namely in accuracy, integrity, continuity and availability. Although well-established procedures for integrity monitoring exist for aircraft navigation, for sensors and fusion algorithms used in automotive navigation, these concepts are still lacking. The research training group i.c.sens, integrity and collaboration in dynamic sensor networks, aims to fill this gap and to contribute to relevant topics. This includes the definition of alternative integrity concepts for space and time based on set theory and interval mathematics, establishing new types of maps that report on the trustworthiness of the represented information, as well as taking advantage of collaboration by improved filters incorporating person and object tracking. In this paper, we describe our approach and summarize the preliminary results.
Integrity is one criteria to evaluate GNSS performance, which was first introduced in the aviation field. It is a measure of trust which can be placed in the correctness of the information supplied by the total system. In recent years, many GNSS-based applications emerge in the urban environment including liability critical ones, so the concept of integrity attracts more and more attention from urban GNSS users. However, the algorithms developed for the aerospace domain cannot be introduced directly to the GNSS land applications. This is because a high data redundancy exists in the aviation domain and the hypothesis that only one failure occurs at a time is made, which is not the case for the urban users. The main objective of this paper is to provide an overview of the past and current literature discussing the GNSS integrity for urban transport applications so as to point out possible challenges faced by GNSS receivers in such scenario. Key differences between integrity monitoring scheme in aviation domain and urban transport field are addressed. And this paper also points out several open research issues in this field.
Commercial GNSS devices tend to perform poorly in urban canyon environments. The dense and tall buildings block the signals from many of the satellites. In this work, we present a particle filter algorithm for a Shadow Matching framework to face this problem. Given a 3D city map and given the satellites' signal properties, the algorithm calculates in real-time invalid regions inside the Region Of Interest (ROI). This approach reduces the ROI to a fraction of its original size. We present a general framework for a Shadow Matching positioning algorithm based on a modified particle filter. Using simulation experiments we have shown that the suggested method can improve the accuracy of existing GNSS devices in urban regions. Moreover, the proposed algorithm can be efficiently extended to 3D positioning in high sampling rate, inherently applicable for UAVs and Drones.
Reliable GPS positioning in city environment is a key issue: actually, signals are prone to multipath, with poor satellite geometry in many streets. Using a 3D urban model to forecast satellite visibility in urban contexts in order to improve GPS localization is the main topic of the present article. A virtual image processing that detects and eliminates possible faulty measurements is the core of this method. This image is generated using the position estimated a priori by the navigation process itself, under road constraints. This position is then updated by measurements to line-of-sight satellites only. This closed-loop real-time processing has shown very first promising full-scale test results.
Positioning in the urban environment using GNSS is hampered by poor satellite availability due to signal obstruction created by both man-made and natural features of the urban environment. In addition, range measurement to satellites for positioning and for navigation is severely degraded by the multipath effect. The arrival and continuous enhancement of computerised geometric city models makes it possible to tackle these problems through modelling. In this paper description is given of a method for determining the local multipath environment, defined by the surfaces within a city model that will cause disruptive signal reflections to be presented to a receiver. An example simulation is performed, and graphical and numerical results are produced.
The Global Positioning System (GPS) is unreliable in dense urban areas, known as urban canyons, which have tall buildings or narrow streets. This is because the buildings block the signals from many of the satellites. Combining GPS with other Global Navigation Satellite Systems (GNSS) significantly increases the availability of direct line-of-sight signals. Modelling is used to demonstrate that, although this will enable accurate positioning along the direction of the street, the positioning accuracy in the cross-street direction will be poor because the unobstructed satellite signals travel along the street, rather than across it. A novel solution to this problem is to use 3D building models to improve cross-track positioning accuracy in urban canyons by predicting which satellites are visible from different locations and comparing this with the measured satellite visibility to determine position. Modelling is used to show that this shadow matching technique has the potential to achieve metre-order cross-street positioning in urban canyons. The issues to be addressed in developing a robust and practical shadow matching positioning system are then discussed and solutions proposed.
Multipath is one of the most important error sources in Global Navigation Satellite System (GNSS) carrier-phase-based precise
relative positioning. Its theoretical maximum is a quarter of the carrier wavelength (about 4.8cm for the Global Positioning
System (GPS) L1 carrier) and, although it rarely reaches this size, it must clearly be mitigated if millimetre-accuracy positioning
is to be achieved. In most static applications, this may be accomplished by averaging over a sufficiently long period of observation,
but in kinematic applications, a modelling approach must be used. This paper is concerned with one such approach: the use
of ray-tracing to reconstruct the error and therefore remove it. In order to apply such an approach, it is necessary to have
a detailed understanding of the signal transmitted from the satellite, the reflection process, the antenna characteristics
and the way that the reflected and direct signal are processed within the receiver. This paper reviews all of these and introduces
a formal ray-tracing method for multipath estimation based on precise knowledge of the satellite–reflector–antenna geometry
and of the reflector material and antenna characteristics. It is validated experimentally using GPS signals reflected from
metal, water and a brick building, and is shown to be able to model most of the main multipath characteristics. The method
will have important practical applications for correcting for multipath in well-constrained environments (such as at base
stations for local area GPS networks, at International GNSS Service (IGS) reference stations, and on spacecraft), and it can
be used to simulate realistic multipath errors for various performance analyses in high-precision positioning.
Robust Set Inversion via Interval Analysis methods in a bounded error frame are used in this paper to compute three-dimensional location zones in real time, at a given confidence level. This approach differs significantly from the usual Gaussian error model paradigm since the satellite positions and the pseudo-ranges measurements are represented by intervals enclosing the true value with a particular confidence. The method computes a location zone recursively, using contraction and bisections of an arbitrarily big initial location box. Such an approach also enables to consider the presence of an arbitrary number of erroneous measurements using a -relaxed solver, and allows integration of geographic and cartographic information such as digital elevation models or 3-dimensional maps. With enough data redundancy, inconsistent measurements can be detected and even rejected.The integrity risk of the location zone is only brought by the measurement bounds settings, since the solver is guaranteed. A way to set these bounds for a particular location zone confidence is proposed. An experimental validation using real L1 code measurements and a digital elevation model is also reported to illustrate the performance on the method with real data.
Although originally developed for the military, the Global
Positioning System (GPS) has proven invaluable for a multitude of
civilian applications. Each application demands specific performance
from the GPS receiver and the associated requirements often vary widely.
This paper describes the architectures and functions of civilian GPS
receivers and then focuses on performance considerations. The
fundamental receiver measurements are described and the quality of these
measurements are related to the aforementioned receiver architectures
Uncertainty modeling and bounding are of vital importance for high-integrity GNSS applications. Classical approaches are mostly developed in a stochastic manner with probabilistic assumptions. However, the exact error distribution is often unknown, and remaining systematics may persist, so that a purely stochastic modeling of all error sources will not be adequate, and alternative uncertainty bounding and propagation should be studied. This paper introduces two deterministic approaches for GNSS uncertainty bounding and compares them with the conventional least-squares method theoretically and experimentally with simulated and real measurements. Both methods use deterministic intervals to denote observation uncertainty, subsequently following a linear uncertainty propagation instead of quadratic one. The interval extension of least-squares transfers the uncertainty into the position domain in the form of zonotope and further bound the stochasticity by the extended point confidence domain. As a comparison, the other method takes advantage of geometrical constraints and convex optimization, leading to a polytopic solution set and zonotopic confidence region. We show their theoretical similarities and highlight different interpretations in practice. Nevertheless, both are sufficient to account for both random and systematic components of uncertainty.
Urban environments are challenging for GNSS (Global Navigation Satellite System) signal propagation. Surrounding buildings cause signal reflection and blockage resulting in numerous non-line-of-sight (NLOS) and multipath (LOS plus reflection) signal receptions. In a kinematic application, like e.g., pedestrian navigation and autonomous driving, the main error sources in urban areas (NLOS biases, multipath) have a complex spatiotemporal behaviour, i.e. their occurrence and magnitude depend on the satellite ray direction, the user antenna location and properties as well as on the buildings in the surrounding area. In this study, we present a new method for mapping GNSS signal propagation-related features, which depend on both the varying user antenna location and satellite position, into one common GNSS Feature Map. Our proposed approach improves the understanding of GNSS signal propagation in challenging environments, especially for kinematic trajectories in urban trenches. Based on this map, users can identify environmental structures and critical trajectory sections for both the user locations and satellite positions and thus exploit the map for trajectory planning. Furthermore, we show how the GNSS Feature Map can contribute to the correction of NLOS biases. Ray tracing can be performed offline at given positions in the 3D model which provides the predicted errors to users that will pass at that location simultaneously minimizing the computation load at the rover. Our proposed approach of NLOS bias correction reduces the observed DD biases due to NLOS reception by 50% for the 68%-quantile. Thereby the distance to the reference way point of the map is not important if we assume a search space of 5 m around the ground truth to make sure we are comparing positions in the same street.
In urban environments, non-line-of-sight (NLOS) signal conditions are a major error contributor for GNSS positioning, the signal delay can reach up to more than one hundred meters due to reflection in urban canyons such as Hong Kong. Collaborative positioning between traffic participants can help to eliminate common errors, but comprehensive analyses on how to find common errors in cities and how to quantify them are required. In this study, we present a new method for finding locations in urban areas with similar extra path delays on the basis of ray-tracing with 3D building models, exemplarily for an urban canyon in Hong Kong. Using the 2D Pearson correlation coefficient, we calculate the spatial correlation of reflection extra paths at two locations to generate a similarity measure. With this measure, we quantify the amount of similar errors at two locations. In realistic simulations, we show that two locations with highly correlated extra path delays show better results concerning single-difference error correction and relative positioning errors. The single differences show that for the selected area in Hong Kong, the higher the spatial correlation, the higher the amount of common extra path delays. Furthermore, we are able to show that the mean relative positioning error can be reduced from 42.4 m for a low correlation pair of agents to 12.7 m for a high spatial correlation pair.
Integrity monitoring is of great importance for Global Navigation Satellite Systems (GNSS) applications. Unlike classical approaches based on probabilistic assumptions, the alternative interval-based integrity approach depends on deterministic interval bounds as inputs. Different from a quadratic variance propagation, the interval approach has intrinsically a linear uncertainty propagation which is adequate to describe remaining systematic uncertainty. In order to properly characterize all ranging error sources and determine the improved observation interval bounds, a processing scheme is proposed in this contribution. We validated for a first time how the sensitivity analysis is feasible to determine uncertainty intervals for residual ionospheric errors and residual tropospheric errors, taking advantage of long-term statistics against reference data. Transforming the navigation problem into a convex optimization problem, the interval bounds are propagated from the range domain to the position domain. We implemented this strategy for multi-GNSS positioning in an experiment with static data from International GNSS Service (IGS) station Potsdam (POTS) and an experiment with kinematic data from a measurement campaign conducted in the urban area of Hannover, Germany, on August 26, 2020.
This chapter describes the concept of integrity for global navigation satellite system (GNSS) applications. It defines integrity in the context of other navigation system parameters and explains the trade‐off between integrity on one hand and continuity and availability on the other. The chapter also explains the key variables used to quantify integrity and discusses the context in which integrity risk probabilities are estimated. It explores how and why integrity is evaluated by users in real time by computing protection levels for the position, velocity, and time outputs that matter to particular applications. The chapter examines the building blocks of protection level calculations: rare‐event bounds under nominal conditions and bounds under faulted conditions. It shows how these principles are applied to the design and analysis of receiver autonomous integrity monitoring, which is a monitoring technique that exploits redundancy in user measurements and is applied by both stand‐alone and augmented GNSS users.
Positioning integrity is crucial for Intelligent Transport Systems (ITS) applications. In this article, a method is presented for prediction of GNSS positioning integrity for ITS journey planning. This information, in addition to other route information, such as distance and time, can be utilized to choose the safest and economical route. We propose to combine the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) technique, tailored for ITS, with 3D city models. Positioning is performed by GNSS Real-Time Kinematic (RTK) method, which can provide the accuracy required for ITS. A new threat model employed for computation of the protection levels (PLs) for RTK positioning is discussed. Demonstration of the proposed approach is performed through a kinematic test in an urban area in Tokyo. The comparison between the prediction method and the actual observations show that the two estimate close satellite geometry and PLs. The method produced PLs that bounds the actual position errors all the time and they were less than the preset alert limit.
The articles in this special section focus on recent advancements on the use of the global navigation satellite system (GNSS)-based positioning for intelligent transport systems. The civil applications of geopositioning are undergoing exponential development. The latest market analysis for global navigation satellite systems (GNSSs) shows two major fields of application which share the majority of the market: intelligent transport systems (ITS), mainly in the road ITS domain, and location-based services, accessible on smartphones and tablets. The modernization of GPS and Russia’s GLONASS system and the development of Galileo and Bei- Dou are proceeding at a fast pace, introducing improved potential capabilities and higher performance levels for satellite-based positioning, and leading to new architectures for positioning and new strategies for positioning by means of other sensors. GNSSs are considered the superior system to provide accurate and global position, velocity, and time.
Reliable confidence domains for Global Navigation Satellite System (GNSS) positioning and inconsistency measures of the observations are of great importance for any navigation system, especially for safety critical applications. In this work, deterministic error bounds are introduced in form of intervals to assess remaining observation errors. The intervals can be computed based on expert knowledge or based on a sensitivity analysis of the measurement correction process. Using convex optimization, bounding zones are computed for GPS positioning using the geometrical constraints imposed by the observation intervals. The bounding zone is a convex polytope, where exploiting only the navigation geometry, confidence domain is computed in form of zonotope. We show that the relative volume between the polytopes and the zonotope is an inconsistency measures. Small polytope volume indicates bad consistency of the observations. In extreme cases empty sets are obtained which indicates large outliers. We determine the observation intervals via sensitivity analysis of the Klobuchar ionospheric model and Saastamoinen tropospheric model. The remaining errors are treated as white noise. We explain how the shape and the volume of the polytope are related to the positioning geometry. We show that this assignment has to be interpreted with care. Furthermore, we propose a new concept of Minimum Detectable Biases (MDB). Taking GPS data from simulations and real experiments, a comparison analysis between the proposed deterministic bounding method and the classical least-squares adjustment has been conduct in terms of accuracy and reliability. This helps validating that our proposed deterministic bound methods shows high internal and external reliability compared to the probabilistic approaches and that it provides rigorous inconsistency measures.
In this contribution a new integrity monitoring system for the Trimble CenterPoint RTX Fast positioning service is introduced, that will allow RTX correction data to be used in safety-critical applications. The system monitors the integrity of the RTX correction data by computing carrier phase observation residuals for 20-25 independent monitoring station per RTX Fast service area, currently Europe and North America. Based on these residuals integrity checks are performed both on all newly generated corrections before broadcasting as well as on already broadcast corrections received by the monitoring stations. In case out-of-tolerance corrections are detected, the corrections are flagged as not usable. In addition when the outof-tolerance correction is detected with already broadcast correction data a corresponding alarm flag is sent to the user within seconds. In addition to describing the overall integrity concept and the new integrity monitoring modules, the accuracy of the RTX Fast corrections is assessed and examples of real-life integrity events are discussed.
This chapter describes the virtual balise concept and summarizes the benefits associated with its use in the evolution of the ERTMS system. A possible-enhanced ERTMS functional architecture suitable for implementing the virtual balise concept is also presented along with the detailed description of the main new functional blocks. This chapter also introduces the proposed extensions of the key ERTMS concepts for estimating the train position based on virtual balises, and consequently, an innovative railway integrity concept is described based on the peculiarities of the railway operational rules and the signalling principles for guaranteeing safe train movements. Finally, a preliminary apportionment of the ETCS Core Hazard tolerable hazard rate based on the use of not only physical balises but also virtual balises is presented.
Multipath
is the phenomenon whereby the signal from a satellite arrives at the receiver via multiple paths due to reflection and diffraction. These nondirect-path signals distort the received signal and cause errors in code and phase measurements. Differential techniques do not eliminate multipath and thus multipath is an important error source in high precision applications. The physical surroundings around the receiver’s antenna dictate the multipath environment and thus cause significant differences for land, marine, airborne, and spaceborne users.
This chapter describes the multipath environment and presents models describing the impact of multipath on code and phase measurements. The influence of the type and rate of the broadcast code as well as the receiver architecture will be highlighted. Mitigation techniques based on receiver design will also be described along with the impact of receiver dynamics. Finally, a technique to measure multipath is described and its usage in evaluating static environments is discussed.
The goal of this chapter is to provide the reader with the tools to assess the impact of multipath on both the code and phase and to understand the performance improvements and limitations associated with various multipath mitigation techniques.
This paper provides new integrity and continuity risk evaluation methods for fault detection and exclusion (FDE) using receiver autonomous integrity monitoring (RAIM). These methods are developed for both solution separation (SS) and Chi-squared RAIM: they capture the fact that exclusion enables continuity risk reduction in exchange for a higher integrity risk. The two approaches are implemented in an example advanced RAIM (ARAIM) application for worldwide vertical guidance of aircraft using multiconstellation Global Navigation Satellite Systems (GNSS).
In this study, we propose a novel global navigation satellite system (GNSS) positioning technique that can be used in urban canyon environments where GNSS positioning is almost useless. Multipath signals, which are reflected or diffracted by objects such as buildings, are recognized as the most important causes of major positioning errors in urban environments. This problem has been investigated for many years. Various practical and popular signal correlator techniques can also help to mitigate multipath errors. However, if an antenna cannot receive a direct signal (line of sight signal), these techniques do not produce satisfactory results because they assume that the antenna mainly receives direct and multipath signals. Thus, we propose a novel GNSS positioning technique that can be used in multipath environments, which is based on a multipath error simulation using a 3D surface model of a building. To calculate a user's position based on multipath simulation, it is necessary to predetermine their position accurately because the multipath effect is highly dependent on the surrounding obstructions. Thus, a particle filter, which hypothesizes a number of user positions, is used to solve this problem, thereby allowing the multipath simulation to estimate the position. The proposed technique attempts to estimate a user's position by comparing the distance between the particle position and the point positioning solution using pseudoranges to correct the multipath error, which is estimated from the multipath simulation. The multipath error in the observed pseudorange depends on a signal correlator design, which is implemented using GNSS receivers. The consumer's GNSS receivers cannot be used to estimate multipath errors because the correlator is a black box. Therefore, we use a GNSS software receiver to implement the proposed techniques. A positioning test was performed in a real-world urban canyon environment, which confirmed the effectiveness of the proposed technique. The proposed technique is effective and it provides increased positioning accuracy in urban canyon environments that suffer from large reflection and diffraction multipath errors in GNSS signals.
This paper focuses on the pedestrian navigation in highly urbanized area, where a current smartphone and a commercial global navigation satellite system (GNSS) receiver perform poorly because of the reflection and blockage of GNSS signal by buildings and foliage. A 3-D map-aided pedestrian positioning method is previously developed to mitigate and correct the multipath GNSS signal. However, it still suffers from the low availability due to the insufficient number of satellites. We develop a smartphone-based pedestrian dead reckoning (PDR) algorithm, which is carried in the pedestrian's trousers. This PDR is capable of not only providing continues solutions but also indicating the pedestrian motions. A closed-loop Kalman filter with adaptive tuning is proposed to integrate the 3-D map-aided GNSS method with the smartphone-based PDR system. According to the experiment results, the proposed integration system can achieve ∼ 1.5-and 5.5-m of positioning errors in a middle-class and deep urban canyon, respectively.
GNSS signals may arrive at the receiving antenna not only through the direct path, i.e. the line-of-sight (LOS) path, but also on multiple indirect paths, due to different electromagnetic effects as signal reflection or diffraction. These signal components arrive with a certain delay, phase, and amplitude difference relative to the LOS component. We will call these signal components multipath components (MPCs) and the phenomena multipath propagation.
Multipath propagation degrades the positioning accuracy. Moreover, in precise applications, multipath errors dominate the total error budget. Despite the different approaches developed, several aspects of multipath propagation are still not fully understood. The generally unknown number of MPCs and their path geometry, the signal characteristics, the diffraction and reflection effects as well as their changing nature together with a complex antenna and receiver design make multipath mitigation very challenging. Furthermore, the site-dependent characteristics of multipath decorrelate the errors caused by multipath propagation at different antenna locations and thus, differential techniques, like e.g. double differences (DD), cannot mitigate it.
The superposition of the MPCs and the LOS signals yields a compound signal at the receiving antenna. Depending on the relative phase between the MPCs and the LOS signal, constructive or destructive interference appears. As a result, during signal tracking the correlation output between the received signal and the local pseudorandom noise (PRN) code replica generated by the receiver is deformed. Since MPCs arrive generally at the receiving antenna with small extra paths, up to 20 m, relative to the LOS signal, the correlation output is biased and the receiver is not able to discriminate between MPC and the LOS signals. This correlation output is the fundamental input for the next iteration of the code and phase tracking loops of the receiver as well as for C/N0 estimation algorithms. As a result, the three GNSS observables code-phase, carrier-phase, and C/N0 are biased by multipath propagation. In this text, errors in code-phase and carrier-phase observations caused by multipath propagation are referred to as code multipath and carrier-phase multipath, respectively, and in general as multipath errors.
In the observation domain, multipath errors are not constant in time. They show a sinusoidal behavior which can be noticed in carrier-phase residuals from Precise Point Positioning (PPP), double differences (DD) or C/N0 time series. This behavior is due to the change of the relative phase between the direct and indirect signals as the satellite vehicle moves above the local horizon of the antenna. The magnitude of these oscillations depends on the relative amplitude of the MPC which varies as geometry changes. The C/N0 observable is the only GNSS observation type in which multipath propagation effects are directly visible without any sophisticated data pre-processing. In contrast, in the phase or code domain, residuals should be analyzed or differences should be formed in order to eliminate all other errors sources. This is one of the main reasons why signal strength measures have attracted much attention in GNSS multipath studies. Since the relative signal amplitude between the LOS and MPC signals plays a key role for the understanding of multipath propagation and also for the magnitude of the multipath error in the GNSS observables, the following contribution focuses on an extended description and proposes an analytical model for modeling GNSS signal amplitudes.
This chapter is structured as follows. A compact overview on different approaches for multipath mitigation or characterization will be presented next. The approaches are categorized into techniques in the observation domain, receiver-internal as well as antenna-related techniques and further methods. Cornerstone methods of each category will be highlighted. In the third section, the multipath phenomenon and its impact on GNSS code, carrier phase and C/N0 will be summarized. Special emphasize is given to the reflection process including signal polarization. An analytical model for GNSS signal amplitude is proposed. The equations for phase and code errors due to multipath propagation are extended so that the signal amplitude can be analytically calculated for each epoch. Finally, results from a dedicated experiment are shown in order to highlight the key features of multipath propagation.
Advanced RAIM (ARAIM) for vertical guidance has attracted considerable attention both from integrity providers and receiver manufacturers, due to its potential to achieve worldwide coverage of vertical guidance with a reduced investment on the ground segment compared to Space-based Augmentation Systems. Several user algorithms have been published, mostly variants of solution separation and possible optimizations. These descriptions have mostly focused on the definition of the Vertical Protection Level (VPL), because that is what was needed to simulate ARAIM availability as a function of different parameters and constellation configurations. However, an ARAIM user algorithm has many more elements that need to be defined. The purpose of this work is to describe an Advanced RAIM user algorithm step-by-step including: the Integrity Support Message (ISM) processing, the fault detection and exclusion, and the Protection Level calculation ? including the Horizontal Protection Level. In this description, we attempt to clarify areas that have remained undefined. We give the contents of the ISM contents, and a clarification of the interpretation of its parameters. These parameters describe both the nominal error behavior and the probability of fault of one or more satellites. The nominal error is characterized by two sets of standard deviation and maximum bias, the first one for integrity purposes and the second one, less conservative, for accuracy and continuity evaluation purposes. We show how to compute the nominal error model as a function of the ISM content, and how to determine which faults must be monitored ? including which subset solutions must be computed and compared against the all-in-view solution. In this paper, we make explicit under which conditions a fault must be declared. In addition to the solution separation statistics, we show why it is prudent to include a chi-square test on the residuals as well. We also describe the actions that follow the detection of a fault or faults, and under which conditions fault exclusion can be performed. Although this is not expected to be fundamentally different than the current approaches in horizontal RAIM, there are differences that arise. As mentioned above, the Vertical Protection Level has been defined in several publications (each with small variations). In this paper we address the implementation details in both the VPL and the HPL. First, in case a large number of fault modes need to be monitored, a large number of subset solutions must be computed. We show how to efficiently compute the subset solutions. Second, the PLs that provide good availability typically require an iterative halving algorithm. We describe a method to compute a tight upper bound with very few steps. In addition, we provide the formulas for the Effective Monitor Threshold, the fault free 10-7 error bound, and the 95% bound on the accuracy. A concrete numerical example is given to facilitate the verification of the provided formulas and algorithms.
Accurate and reliable positioning is an important prerequisite for numerous vehicular applications. Localization techniques based on satellite navigation systems are nowadays standard and deployed in most commercial vehicles. When such a standalone positioning is used in challenging environments like dense urban areas, the localization performance often dramatically degrades due to blocked and reflected satellites signals. In this paper, a general and lightweight probabilistic positioning algorithm with integrated multipath detection through 3D environmental building models is presented. It will be shown that the proposed system outperforms—in terms of accuracy and integrity—existing methods without introducing additional hardware sensors. Furthermore, a benefit analysis of the suggested D model for tightly and loosely coupled GPS/INS sensor integration schemas is provided. Finally, the algorithm will be evaluated with real-world data collected during an urban measurement campaign.
A realistic assessment of the total uncertainty budget of Global Positioning System (GPS) observations and its adequate mathematical treatment is a basic requirement for all analysis and interpretation of GPS-derived point positions, in particular GPS heights, and their respective changes. This implies not only the random variability but also the remaining systematic errors. At present in geodesy, the main focus is on stochastic approaches in which errors are modeled by means of random variables. Here, an alternative approach based on interval mathematics is presented. It allows us to model and to quantify the impact of remaining systematic errors in GPS carrier-phase observations on the final results using deterministic error bands. In this paper, emphasis is given to the derivation of the observation intervals based on influence parameters and to the study of the complex linear transfer of this type of uncertainty to estimated point positions yielding zonotopes. From the presented simulation studies of GPS baselines, it turns out that the uncertainty due to remaining systematic effects dominates the total uncertainty budget for baselines longer than 200km.
In this work, a methodology of statistical channel modeling for 60 GHz WLAN systems is proposed and a channel model for the office conference room environment is developed. The proposed methodology takes into account the most important properties of the indoor 60 GHz propagation channel such as large propagation loss and necessity to use steerable directional antennas by the WLAN stations, quasi-optical propagation nature, clustering of the channel, and significant impact of the polarization characteristics. A general mathematical structure of the channel model that supports all the above 60 GHz propagation channel properties is presented. The application of the proposed methodology is demonstrated by development of a channel model for the conference room environment. Inter cluster, intra cluster, and polarization modeling characteristics are defined in accordance with the proposed methodology and using results of experiments and ray-tracing simulations.
Position, Navigation, and Timing Technologies in the 21st Century: Integrated Satellite Navigation, Sensor Systems, and Civil Applications
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Fig. 10. Experimental positioning results using classical and alternative set-based approach (a) before FDE, left (b) after FDE, right.
Hannover3d - virtual city map
- Landeshauptstadt Hannover
- Und Fb Planen
- Bereich Stadtentwicklung
- Geoinformation
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map," 2020. [Online]. Available: https://stadtmodell-test.hannoverstadt.de/HostingMap-extern/#/
On the prediction of network RTK integrity performance in urban environments
- A Karimidoona
- L Icking
- F Ruwisch
- S Schön
A. Karimidoona, L. Icking, F. Ruwisch, and S. Schön, "On the prediction of network RTK integrity performance in urban environments,"
in 2022 10th ESA Workshop on Satellite Navigation Technologies
and European Workshop on GNSS Signals and Signal Processing
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On the prediction of network RTK integrity performance in urban environments
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