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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

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.

Reliable GPS positioning in city environment is a key issue: actually, signals are prone to multipath, and satellite geometry, despite its improvement with GNSS interoperability, remains poor in many streets. Non-Line-Of-Sight (NLOS) satellites cause important receiver-satellite range measuring errors, because the direct signal is blocked and only the reflected signal is tracked. Contrary to multipath where direct and reflected signals interfere, errors with NLOS satellites grow unboundedly. The geometrical properties of the local environment of the antenna can explain deterministically the phenomena that occur, which makes 3D city models of great interest in this tricky problem.

First, let us mention, even if there is no use of 3D models, the image processing approach like, e.g., that of the LocoPROL project (Low cost satellite based train location system for signalling and train PROtection for Low density railway lines) [

Concerning 3D models, in 2007, Bradbury

Well-founded results were shown with these first contributions, but more recently, a full-scale experiment of this concept applied to localization in a 3D modelled urban center has been proposed in CityVIP [

Similar approaches are proposed by [

This article is divided into three main sections. We first explain the methodology and mention the results obtained in the feasibility study based on a kinematic GPS INS solution. In the second part, a map-aided positioning filter is presented that takes advantage of the information given by the 3D model in terms of road constraints. The third and last part analyzes the experimental results obtained by the LOS/NLOS separation algorithm based on the previous constrained solution. The efficiency of the road constraints in this process will be demonstrated. Finally, we will discuss the impact of the separation algorithm and its interest with respect to the localization problem, before and after a final map-aiding, and we will compare this algorithm to a more usual satellite selection based on signal-to-noise ratio (SNR). These comparisons are done from data registered in a real experiment in the center of Paris (France). The duration of this experiment is about 10 minutes and the total length of the circuit is about 2 km in an archetypal European urban center.

The core of the method consists in checking whether a satellite that generates a signal received by the GNSS receiver can be directly viewed (LOS) or not (NLOS) by the receiver antenna. With this aim in mind, one needs the predicted position of the receiver, the predicted positions of the satellites, and the map of the environment in the same reference frame. A 3D city model of the environment is available in a Geographical Information System (GIS) embedded software from BeNomad company [

The method starts with the computation of a virtual image of each satellite, with a virtual camera located at the antenna center, oriented with the azimuth of the considered satellite, with tilt angles (roll and pitch) set to zero (

Basic image processing functions provided by BeNomad make it possible to compute the front building elevation. These functions are twofold:
_{c}

The comparison of the satellite elevation

A more straightforward method consists in computing the virtual image with the camera tilted according to the elevation of the satellite, and, like ray tracing, check whether or not a pixel is detected along the optical axis (if not, Get_depth (pixel) returns −1 and the satellite is in LOS). The standard focal distance is always suitable. Note that the critical elevation is no more available that way, but actually not essential.

In practice, azimuth and elevation of satellites are delivered by standard NMEA (National Marine Electronics Association) GSV (Satellites in view) messages. Note that the correction of the azimuthal deviation (up to a few degrees) between the true north and the north of the map (the one using the Lambert 93 plane projection) must be done.

The position of the user is in fact the most critical point in the process. In a first step of this research [

Here, the position of the antenna will come from a City VIP positioning sub-system that combines data from dead-reckoning sensors and GNSS, under the 3D map constraints.

The method consists in computing a 3D localization of a wheeled vehicle based on a 3D kinematic model and improved by map-aiding on the road layer of the 3D city map. This functionality was a task of the CityVIP project [

A state space formulation of the problem is used in order to use state estimation techniques such as variants of Kalman filtering. As it is usual in Robotics, the configuration is taken as a state vector. The kinematic model then gives the progression part of the state equation.

The world reference frame being the one where the travel is specified (_{0}, _{0}, _{0}) as this world reference frame and
_{3}, _{3}, _{3}) as the vehicle reference frame (

In other words, the configuration may be defined as the transformation from W to

The rationale of the model is based upon the motion of the wheels that roll without slipping on a plane surface. Here the plane is inclined and its inclination is assumed to evolve slower than the other variables (in particular, slope and cross slope angles have slower variations than the one of the yaw angle). Note that such a model is coherent with the 3D map composed of planar patches that is further used.

Moreover, like in the usual 2D kinematic models, the longitudinal speed (

For a vehicle with two motorized wheels where:

_{r}_{l}

_{r}_{l}

From the non-holonomic constraints linked to the rolling without slipping rotations of the wheels on the plane surface, the vector speed of _{3} of the vehicle (_{3} to the road and its norm is

Expressing those relations in the world reference frame (

A discrete time version (5) is deduced from

In this expression, _{k}_{k}_{k}_{+1} − _{k}_{k}_{k}_{k}_{+1} − _{k}_{k}_{k}_{+1}.

In the CityVIP project, a localization task has been introduced in order to continuously update an estimation of the configuration of the vehicle in a 3D world together with an accuracy statement. This estimation is iteratively computed by combining 3 data sources (

GPS localization is obtained by a positioning algorithm at the update rate of the receiver (4 Hz). A complete localization may be scarce in environments with poor satellite visibility

odometric data are generated by the wheel speed sensors of the ABS (Anti-Blocking System). When some data become available, the configuration is updated by using

geographic data, 3D polylines modelling the road network, are given upon request but require a map-matching procedure prior to using them for localization.

In this research, an Extended Kalman Filtering (EKF) is used in the odometric/GPS fusion process. Geographic data are used to constrain the localization with an ellipsoidal set-membership method [_{k}_{k}_{k}

Note that the symmetric positive matrix _{k}

Each time odometric measurements are available (

This gives an updated estimation _{k}_{k}

The use of the geographical data is based on the assumption that the vehicle moves on a road with a known geometric specification stored in the GIS. It is a sequence of two steps:

Map-matching, i.e., the selection of the road segment on which the vehicle is supposed to be. The segment should minimize a criterion calculated from (1) the 3D distance between the current estimation of the localization and the segment and (2) the angular error between the velocity vector of the state and direction of the segment.

Exploitation of the geometric attributes of the road segment selected as constraints of the configuration (2). Constraints are defined from the 3D polylines by taking into account the width of the way and the uncertainty on the altitude. The ellipsoidal set-membership method computes the minimum volume ellipsoid resulting from the intersection of the current ellipsoidal domain and constraints. The final map-aided solution is obtained [

For validation purpose, we use data that have been recorded in an experiment carried out for the final demonstration of the cityVIP project in September 2011 in Paris. The data were collected on 13 September 2011, and two circuits, both with two laps, were performed at respectively 11:48 AM and 12:08 PM (local time). The first lap was used by the CityVIP partners in charge of several image processing localization tasks for their machine learning; afterwards, the second and next laps could be used for evaluation purpose.

The distance travelled per lap is around 1 kilometer. The urban environment in the vicinity of the 12^{th}

The experimental vehicle of IFSTTAR/MACS (Monitoring, Assessment, Computational Sciences) is shown in

a CAN (Controller Area Network) bus connection (for the odometry),

a low-cost automotive GPS receiver LEA-6T from U-blox (for raw data and NMEA GGA [

the MRT (Reference Trajectory Measurement) dedicated specific equipment, LANDINS of the IXSEA society, from which the reference trajectory of the present experiment is issued. Its accuracy is about 10 centimeters,

a Marlin video camera (not used here).

Data were logged in real-time using the Aroccam multithread software architecture [

Typical errors of standard GPS solutions are so large (several tens of meters) that creating a virtual image would be nonsense. As a consequence, the image extraction is based on the output of the map-aided positioning process where road constraints have been applied. To do so, the “Map-Aided Fusion” task of the state chart (

Afterwards, two different subsequent processes are possible:

The LOS satellites are only fed to the GPS Positioning Algorithm and fused with the odometry. It yields non-map-aided or “free” solutions. In this case, we collect the updated position and covariance of the “GPS Fusion” task.

The LOS satellites are only fed to the GPS Positioning Algorithm, fused with the odometry, and constrained again by the road map. It yields map-aided or constrained solutions and we collect the updated position and covariance of the “Map-Aided Fusion” task. This very last implementation can run in closed-loop, since its solution can be returned to the image extractor, which makes the duplication of the “Map-Aided Fusion” task not necessary.

The purpose of this final section is to evaluate whether or not the LOS/NLOS separation leads to positions at least as accurate as a simple SNR-based selection would do.

The comparison has been made on one lap,

Four replications (in Aroccam replay mode) have successively been executed:

1 - SNR-based satellite selection, no final map-aiding,

2 - LOS-based satellite selection, no final map-aiding,

3 - SNR-based satellite selection, and final map-aiding,

4 - LOS-based satellite selection, and final map-aiding.

Note that the last replication (item 4) has been operated in closed-loop, whereas the second (item 2) used GGA map-aided solutions.

The main tuning to do is the SNR threshold applicable to the GPS Positioning Algorithm. We have adjusted its value (40 dB-Hz) so that the average number of satellites actually used by both processes (SNR and LOS) are similar.

Statistics have been computed on the whole dataset,

Absolute errors, in 2D and 3D, with respect to the reference trajectory have been computed and sorted in a cumulative distribution function in

The reference trajectory (provided by the LANDINS system) is the fusion result of an INS (Inertial Navigation System) based on a high-grade fiber optic gyroscope (FOG), a distance measurement instrument and a PPK (Post Processed Kinematic) trajectory from a high-performance GNSS receiver.

Considering the errors of the “free” solutions (

For map-aided solutions (

An overview of the trajectories is visible in

Since

On

On

This paper has shown that using NLOS detection and exclusion prior to incorporating data from a GNSS receiver was efficient for the localization in dense urban areas. Such a test needs (1) 3D maps of the urban environment, which are more and more easily available and (2) an a priori estimation of the position and orientation of the vehicle.

The results have shown the prior importance of the 3D maps of the urban environment. First, it constrains the position and orientation estimations in coherence with the streets network, thus enhancing the accuracy of the localization. Moreover, it makes it possible to check the direct visibility of a given satellite from the estimated pose of the vehicle. The results shown in the paper lead to conclude that the NLOS test gives an equivalent accuracy to the SNR test when the estimated pose is not constrained by the map-aiding procedure after being updated by GNSS data (slightly worse when the vertical dimension is considered). In contrast, when the map-aiding procedure is applied after having used the GNSS data with the NLOS (or SNR) test, the NLOS test gives slightly better accuracy than the SNR test. It thus confirms the feasibility study previously exposed in [

NLOS detection and exclusion based on virtual image processing and a 3D map seems to be promising. This alternative to a simple SNR test on the satellites tracked by a standard automotive receiver has yielded better positioning.

Given that this dataset corresponds to a relatively short experimentation (5 min, 1 km in Paris), other tests will be realized to confirm our first conclusions.

The GPS Positioning Algorithm was also very simple: no fault detection or exclusion of satellites (FDE strategy) based on the predicted position (and consequently predicted pseudo-ranges) was done in addition to the SNR or LOS tests. A future version of our algorithm will improve this Positioning Algorithm, including FDE through a ^{2} test. Doppler measurements, which are not employed in the current study, will also be used.

This work has been financed by the French National Agency for Research (ANR) within the general framework of the CityVip project (project ANR-07-TSFA-013-01). The authors would particularly like to thank the MATIS lab from the French National Geographic Institute (IGN) for having supplied the geographical data used in this paper.

Since we consider the kinematic configuration of a slow vehicle induced by the road and not its dynamic state, we prefer to use heading in place of yaw, slope in place of pitch and cross slope in place of roll.

The positive definite matrix _{k}_{k}_{0} probability.

NMEA GGA: Latitude, Longitude and Altitude computed by the receiver from raw data with its own algorithm.

Details on the Aroccam multithread software architecture. Available online:

Illustration of the computation of the critical elevation using a virtual image.

Cumulative distribution function of the horizontal position error (HPE).

3D vehicle configuration for a fixed rear axle model, with the world and mobile reference frames as

Data fusion state chart.

The experimental vehicle of IFSTTAR/MACS.

Satellite visibility using GGA map-aided solutions.

Satellite visibility in closed-loop.

Cumulative distribution function of the absolute error in 2D for “free” solutions (without map-aiding).

Cumulative distribution function of the absolute error in 3D for “free” solutions (without map-aiding).

Cumulative distribution function of the absolute error in 2D for map-aided solutions.

Cumulative distribution function of the absolute error in 3D for map-aided solutions.

2D overview of “free” solutions (without map-aiding) for both strategies.

2D overview of map-aided solutions for both strategies.

2D overview of “free” solutions (without map-aiding) for both strategies. Simplified representation.

2D overview of map-aided solutions for both strategies. Simplified representation.