# A Redundant Configuration of Four Low-Cost GNSS-RTK Receivers for Reliable Estimation of Vehicular Position and Posture

^{*}

## Abstract

**:**

## 1. Introduction

- The best geometrical configuration for three and four antennas to minimize position and posture uncertainty of a vehicle is deduced.
- A redundant setup with four antennas is analyzed, so when the precision of one receiver degrades, reliable 3D coordinates can be still calculated in real-time.
- A decentralized node architecture using the Robot Operating System (ROS) that integrates all the available measurements from the receivers is presented.

## 2. Spatial Configurations for the Antennas of the GNSS-RTK Receivers

- The mean errors of the receivers along time are null, i.e., $E[\Delta {v}_{i}\left(t\right)]=0\phantom{\rule{0.166667em}{0ex}}\forall i$.
- The errors of different receivers are independent, i.e., $E[\Delta {v}_{i}\left(t\right)\Delta {v}_{j}^{T}\left(t\right)]=0$ for $i\ne j$.
- All the receivers share the same covariance matrix, i.e., $C={C}_{1}={C}_{2}={C}_{3}={C}_{4}$.

#### 2.1. Three Receivers Optimal Configuration

- The distances ${d}_{a}$ and ${d}_{b}$ of the second and third antenna with respect to the first antenna, respectively, are constant values determined without uncertainty.
- The angle $\theta $ between the directions given by ${d}_{a}$ and ${d}_{b}$ is also known certainly on the plane that contains the three antennas.

#### 2.2. Four Receivers Optimal Layout

#### 2.3. Four Receivers Redundant Configuration

## 3. Sensor System

#### ROS Programming

`ntrip_ros`(https://github.com/ros-agriculture/ntrip_ros, accessed on 28 July 2021) node connects to a nearby CORS to get RTCM streams through internet and to publish them into the topic

`RTCM`. Each receiver i has associated a driver node (https://github.com/KumarRobotics/ublox, accessed on 28 July 2021) named

`gnss_i`that is subscribed to this topic to receive differential corrections via callbacks. These nodes publish NED coordinates on its own topic

`NED_i`along with a time stamp and three accuracy estimates (each one $\ge 10\mathrm{m}\mathrm{m}$).

`reliable_estimator`node receives all the messages from the four

`NED_i`topics and computes the six 3D coordinates with three or four synchronized measurements. Finally, it publishes the current pose into the

`3D_POSE`topic, making this data available for any navigation node on the ROS system.

## 4. Experiments with the Rover Argo XTR

^{−1}and zero turning radius. The robotic rover can be controlled via a follow-me system with a 2D laser scanner or via remote teleoperation with a joystick and a line-of-sight wireless link.

#### 4.1. Calibration Test

#### 4.2. Reliability Test

#### 4.3. Dynamic Test

^{−1}.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

3D | Three-Dimensional |

CORS | Continuously Operating Reference Station |

ECEF | Earth-Centered, Earth-Fixed |

GPS | Global Positioning System |

GNSS | Global Navigation Satellite System |

IMU | Inertial Measurement Unit |

MEMS | Micro Electro Mechanical Systems |

NTRIP | Networked Transport of RTCM via Internet Protocol |

ROS | Robot Operating System |

RTCM | Radio Technical Commission for Maritime Services |

SBAS | Satellite Based Augmentation Systems |

USB | Universal Serial Bus |

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**Figure 5.**Hardware components of the sensor system: a GNSS-RTK board (

**a**), an antenna (

**b**), a ground plate (

**c**) and the mini computer (

**d**).

**Figure 7.**The rover Argo XTR with the sensor system mounted on the rear deck. GNSS antennas are numbered from 1 to 5.

**Figure 12.**Comparison between the position coordinates obtained by the fifth receiver and the proposed sensor.

a (m) | b (m) | c (m) | |
---|---|---|---|

${v}_{1}^{*}$ | −0.672 | −0.675 | −0.004 |

${v}_{2}^{*}$ | 0.673 | −0.676 | −0.004 |

${v}_{3}^{*}$ | −0.672 | 0.672 | −0.004 |

${v}_{4}^{*}$ | 0.671 | 0.678 | 0.011 |

${v}_{5}^{*}$ | −0.004 | 0.005 | 0.166 |

${v}_{0}^{*}$ (21) | 0 | 0 | 0 |

${v}_{0}^{*}$ (28) | 0.001 | −0.002 | −0.004 |

${v}_{0}^{*}$ (29) | 0 | 0.002 | 0.004 |

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**MDPI and ACS Style**

Morales, J.; Martínez, J.L.; García-Cerezo, A.J.
A Redundant Configuration of Four Low-Cost GNSS-RTK Receivers for Reliable Estimation of Vehicular Position and Posture. *Sensors* **2021**, *21*, 5853.
https://doi.org/10.3390/s21175853

**AMA Style**

Morales J, Martínez JL, García-Cerezo AJ.
A Redundant Configuration of Four Low-Cost GNSS-RTK Receivers for Reliable Estimation of Vehicular Position and Posture. *Sensors*. 2021; 21(17):5853.
https://doi.org/10.3390/s21175853

**Chicago/Turabian Style**

Morales, Jesús, Jorge L. Martínez, and Alfonso J. García-Cerezo.
2021. "A Redundant Configuration of Four Low-Cost GNSS-RTK Receivers for Reliable Estimation of Vehicular Position and Posture" *Sensors* 21, no. 17: 5853.
https://doi.org/10.3390/s21175853