# Vehicular Localization Enhancement via Consensus

^{*}

## Abstract

**:**

## 1. Introduction

- An uncomplicated strategy to enhance localization performance in vehicular networks is constructed. The strategy involves the exchange of local data and the exploitation of a superior anchor vehicle within the vehicular network. Using local estimates of different qualities, the proposed strategy enhances the overall accuracy of all vehicles’ localization to that of the anchor. The execution of the protocol does not involve a central manager, thus greatly improving the adaptability of the protocol to networks of different scales.
- Mathematical formulations for the analyses of the different stages of the proposed strategy are made. Despite the computational simplicity, the analytically found optimal estimator efficiency is ultimately achieved in terms of CRLB.
- Visual representations of the experiments based on 3GPP TR 37.885 urban scenario specifications are provided and discussed. The effects of the execution of the proposed strategy are observed under diverse scenarios. Comparisons to centralized localization are also made in order to show the effectiveness of the distributed protocol for the intended environments.

## 2. System Model

## 3. Proposed Strategy

#### 3.1. Consensus-Based Update

#### 3.2. Compensation

#### 3.3. Practical Implementation

Algorithm 1 Strategy of improvement of localization of ${v}_{i}$ |

1: At time $t=0$ initialization |

2: Measure ${\mathbf{p}}_{{v}_{i}}^{(t)}$ |

3: while (11) does not hold do |

4: $t\Leftarrow t+1$ |

5: Receive ${\mathbf{p}}_{v}^{(t-1)}$ and measure ${\mathbf{d}}_{{v}_{i},v}$ from $v\in \mathcal{N}({v}_{i})$ |

6: Calculate ${\mathbf{p}}_{{v}_{i}}$ by (1) |

7: if broadcast from anchor received then |

8: ${\mathbf{p}}_{{v}_{i}}^{(t)}\Leftarrow {\mathbf{p}}_{{v}_{i}}+{\mathbf{p}}_{{v}_{*}}^{(t-1)}-{\mathbf{p}}_{{v}_{*}}^{(t)}$ |

9: else |

10: ${\mathbf{p}}_{{v}_{i}}\Leftarrow {\mathbf{p}}_{{v}_{i}}^{(t)}$ |

11: end if |

12: end while |

## 4. Experiment

## 5. Evaluation

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Campolo, C.; Molinaro, A.; Iera, A.; Menichella, F. 5G network slicing for vehicle-to-everything services. IEEE Wirel. Commun.
**2017**, 24, 38–45. [Google Scholar] [CrossRef] - Misra, P.; Enge, P. Global Positioning System: Signals Measurements and Performance; Ganga-Jamuna: Lincoln, MA, USA, 2006; pp. 42–43. ISBN 0-9709544-1-7. [Google Scholar]
- Patwari, N.; Ash, J.N.; Kyperountas, S.; Hero, A.O.; Moses, R.L.; Correal, N.S. Locating the nodes: Cooperative localization in wireless sensor networks. IEEE Signal Proc. Mag.
**2005**, 22, 54–69. [Google Scholar] [CrossRef] - Shen, Y.; Win, M.Z. Fundamental limits of wideband localization—Part I: A general framework. IEEE Trans. Inf. Theory
**2010**, 56, 4956–4980. [Google Scholar] [CrossRef] - Yuan, W.; Wu, N.; Etzlinger, B.; Wang, H.; Kuang, J. Cooperative joint localization and clock synchronization based on Gaussian message passing in asynchronous wireless networks. IEEE Trans. Veh. Technol.
**2016**, 65, 7258–7273. [Google Scholar] [CrossRef] [Green Version] - Leng, M.; Wu, Y.C. Distributed clock synchronization for wireless sensor networks using belief propagation. IEEE Trans. Signal Process.
**2011**, 59, 5404–5414. [Google Scholar] [CrossRef] [Green Version] - Kim, H.; Choi, S.W.; Kim, S. Connectivity Information-Aided Belief Propagation for Cooperative Localization. IEEE Wirel. Commun.
**2018**, 7, 1010–1013. [Google Scholar] [CrossRef] - Ihler, A.T.; Fisher, J.W.; Moses, R.L.; Willsky, A.S. Nonparametric belief propagation for self-localization of sensor networks. IEEE J. Sel. Area Commun.
**2005**, 23, 809–819. [Google Scholar] [CrossRef] [Green Version] - Thrun, S.; Fox, D.; Burgard, D.; Dellaert, F. Robust Monte Carlo localization for mobile robots. Artif. Intell.
**2001**, 128, 99–141. [Google Scholar] [CrossRef] [Green Version] - Howard, A.; Matark, M.J.; Sukhatme, G.S. Localization for mobile robot teams using maximum likelihood estimation. IEEE/RSJ Int. Conf. Intell. Robot. Syst.
**2002**, 1, 434–439. [Google Scholar] [CrossRef] [Green Version] - Chausse, F.; Laneurit, J.; Chapuis, R. Vehicle localization on a digital map using particles filtering. IEEE Proc. Intell. Veh Symp.
**2005**, 21, 243–248. [Google Scholar] [CrossRef] - Karam, N.; Chausse, F.; Aufrere, R.; Chapuis, R. Cooperative multi-vehicle localization. In Proceedings of the 2006 IEEE Intelligent Vehicles Symposium, Tokyo, Japan, 13–15 June 2006; pp. 564–570. [Google Scholar] [CrossRef]
- Roumeliotis, S.I.; Rekleitis, I.M. Propagation of uncertainty in cooperative multirobot localization: Analysis and experimental results. Auton. Robot.
**2004**, 17, 41–54. [Google Scholar] [CrossRef] [Green Version] - Wymeersch, H.; Lien, J.; Win, M.Z. Cooperative localization in wireless networks. Proc. IEEE
**2009**, 97, 427–450. [Google Scholar] [CrossRef] - Loeliger, H.A. An introduction to factor graphs. IEEE Signal Proc. Mag.
**2004**, 21, 28–41. [Google Scholar] [CrossRef] [Green Version] - Han, Y.; Wei, C.; Lu, T.; Wang, R. A Multi-platform Cooperative Localization Method Based on Dead Reckoning and Particle Filtering. In Proceedings of the 2019 Chinese Control Conference (CCC), Guangzhou, China, 27–30 July 2019. [Google Scholar] [CrossRef]
- Putra, H.A.; Nazaruddin, Y.Y.; Juliastuti, E. Application of Sensor Fusion for Determining Position and Velocity of Automated People Mover System at Soekarno-Hatta Airport with Extended Kalman Filter. In Proceedings of the 2019 6th International Conference on Instrumentation, Control, and Automation (ICA), Bandung, Indonesia, 31 July–2 August 2019. [Google Scholar] [CrossRef]
- Kim, H.; Granström, K.; Gao, L.; Battistelli, G.; Kim, S.; Wymeersch, H. 5G mmWave Cooperative Positioning and Mapping Using Multi-Model PHD Filter and Map Fusion. IEEE Trans. Wirel. Commun.
**2020**, 19, 3782–3795. [Google Scholar] [CrossRef] [Green Version] - Kim, H.; Lee, S.H.; Kim, S. Cooperative localization with distributed ADMM over 5G-based VANETs. In Proceedings of the 2018 IEEE Wireless Communications and Networking Conference (WCNC), Barcelona, Spain, 15–18 April 2018; Volume 24, pp. 1–5. [Google Scholar] [CrossRef]
- Rao, C.R. Information and Accuracy Attainable in the Estimation of Statistical Parameters. Bull. Calcutta Math Soc.
**1945**, 37, 81–89. [Google Scholar] [CrossRef] - Molina-Masegosa, R.; Gozalvez, J. LTE-V for Sidelink 5G V2X Vehicular Communications: A New 5G Technology for Short-Range Vehicle-to-Everything Communications. IEEE Veh. Technol. Mag.
**2017**, 12, 30–39. [Google Scholar] [CrossRef] - Xie, T.; Dai, L.; Ng, D.W.K.; Chae, C.B. On the power leakage problem in millimeter-wave massive MIMO with lens antenna arrays. IEEE Trans. Signal Process.
**2019**, 67, 4730–4744. [Google Scholar] [CrossRef] - Cho, Y.J.; Suk, G.Y.; Kim, B.; Kim, D.K.; Chae, C.B. RF lens-embedded antenna array for mmWave MIMO: Design and performance. IEEE Commun. Mag.
**2018**, 56, 42–48. [Google Scholar] [CrossRef] [Green Version] - Ma, S.; Wen, F.; Zhao, X.; Wang, Z.; Yang, D. An Efficient V2X Based Vehicle Localization Using Single RSU and Single Receiver. IEEE Access
**2019**, 7, 46114–46121. [Google Scholar] [CrossRef]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kim, H.K.; Kim, M.; Lee, S.H.
Vehicular Localization Enhancement via Consensus. *Sensors* **2020**, *20*, 6506.
https://doi.org/10.3390/s20226506

**AMA Style**

Kim HK, Kim M, Lee SH.
Vehicular Localization Enhancement via Consensus. *Sensors*. 2020; 20(22):6506.
https://doi.org/10.3390/s20226506

**Chicago/Turabian Style**

Kim, Hong Ki, Minji Kim, and Sang Hyun Lee.
2020. "Vehicular Localization Enhancement via Consensus" *Sensors* 20, no. 22: 6506.
https://doi.org/10.3390/s20226506