# About Non-Line-Of-Sight Satellite Detection and Exclusion in a 3D Map-Aided Localization Algorithm

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## Abstract

**:**

## 1. Introduction

## 2. Presentation of the NLOS Detection Method

`Get_depth (pixel)`, which returns the depth of the closest point corresponding to the input pixel in the 3D model of the environment,

`Get_distance (pixel_1, pixel_2)`, which returns the Euclidian distance between the closest points of the 3D model that corresponds to pixel_1 and pixel_2. The geometrical computation of the critical elevation β

_{c}(1) by using the output of these functions applied onto the central and critical pixels respectively is illustrated on Figure 1.

## 3. Presentation of the Positioning Method with Road Constraints

#### 3.1. Definition of the Vehicle Configuration (Figure 3)

_{0}, j⃗

_{0}, k⃗

_{0}) as this world reference frame and : (M, i⃗

_{3}, j⃗

_{3}, k⃗

_{3}) as the vehicle reference frame (Figure 3). By definition, the vehicle configuration states the pose of the vehicle reference frame with respect to the world frame. In the 3D Euclidian world, it may be defined by:

#### 3.2. Kinematic Model Processing

- ○
- E denotes the track, e.g., the distance between the centers of the left and right wheels,
- ○
- ω
_{r}(resp. ω_{l}) is the measured rotation speed of the right (resp. left) wheel, - ○
- R
_{r}(resp. R_{l}) is the radius of the right (resp. left) wheel, assumed to be known.

_{3}of the vehicle (Figure 3) and its norm is υ given by Equation (3). In the same way, the axis of the yaw rotation is the local normal k⃗

_{3}to the road and its norm is ω given by Equation (3).

_{k}= υ

_{k}* (t

_{k}

_{+1}− t

_{k}) (resp. dψ

_{k}= ω

_{k}* (t

_{k}

_{+1}− t

_{k})) is the elementary travelled distance (resp. elementary yaw rotation in ) between the successive time samples t

_{k}and t

_{k}

_{+1}.

#### 3.3. Localization Method

- 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 Equation (5),
- geographic data, 3D polylines modelling the road network, are given upon request but require a map-matching procedure prior to using them for localization.

_{k}where some information becomes available, the algorithm updates an estimate q̂

_{k}together with a symmetric positive matrix P

_{k}, defining thus an ellipsoidal confidence domain [20]:

_{k}quantifies the magnitude of the ellipsoidal domain. The square-roots of its eigenvalues are the measures of its principal axes.

#### Odometric and GPS Data Fusion

_{k}and an updated matrix P

_{k}resulting from both odometric and GPS measurements, when available.

#### Map-Aided Fusion

- 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 [22].

## 4. Improving the NLOS Detection Method and Experimental Results

#### 4.1. Experimental Set-Up and Test Data

^{th}district city hall is very dense, with high Haussmann style buildings.

- 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 [23], Global Positioning System Fix Data, and GSV, Satellites in view, sequences at 4 Hz) and its patch antenna,
- 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).

#### 4.2. NLOS Detection Based on Map-Aided Solutions

- 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.

#### 4.3. Comparison with the SNR-Based Selection

- ○
- 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.

## 5. Conclusions and Future Works

#### 5.1. Conclusions

#### 5.2. Future Work

^{2}test. Doppler measurements, which are not employed in the current study, will also be used.

## Acknowledgments

## References and Notes

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

**Figure 8.**Cumulative distribution function of the absolute error in 2D for “free” solutions (without map-aiding).

**Figure 9.**Cumulative distribution function of the absolute error in 3D for “free” solutions (without map-aiding).

**Figure 14.**2D overview of “free” solutions (without map-aiding) for both strategies. Simplified representation.

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**MDPI and ACS Style**

Peyraud, S.; Bétaille, D.; Renault, S.; Ortiz, M.; Mougel, F.; Meizel, D.; Peyret, F.
About Non-Line-Of-Sight Satellite Detection and Exclusion in a 3D Map-Aided Localization Algorithm. *Sensors* **2013**, *13*, 829-847.
https://doi.org/10.3390/s130100829

**AMA Style**

Peyraud S, Bétaille D, Renault S, Ortiz M, Mougel F, Meizel D, Peyret F.
About Non-Line-Of-Sight Satellite Detection and Exclusion in a 3D Map-Aided Localization Algorithm. *Sensors*. 2013; 13(1):829-847.
https://doi.org/10.3390/s130100829

**Chicago/Turabian Style**

Peyraud, Sébastien, David Bétaille, Stéphane Renault, Miguel Ortiz, Florian Mougel, Dominique Meizel, and François Peyret.
2013. "About Non-Line-Of-Sight Satellite Detection and Exclusion in a 3D Map-Aided Localization Algorithm" *Sensors* 13, no. 1: 829-847.
https://doi.org/10.3390/s130100829