# AOA-Based Three-Dimensional Positioning and Tracking Using the Factor Graph Technique

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- An integrated FG structure is formulated to realize 3D location detection and tracking with AOA measurements.
- It has been proven that the information from the elevation angle can help to improve the detection of 2D space, from both theoretical and simulation analyses.
- The proposed technique has exhibited robust performances even with an unstable sensing environment.
- By utilizing the ACRB as side information (SI) to the detector, the proposed system can greatly reduce the impacts of burst sensing errors.

## 2. System Model

## 3. Location Detector

## 4. FG-EKF

#### 4.1. Prediction of the State

#### 4.2. State Refinement

## 5. ACRB Derivation

## 6. Results

#### 6.1. Accuracy Evaluation

#### 6.2. Convergence

#### 6.3. Robustness Analysis

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Holfeld, B.; Wieruch, D.; Wirth, T.; Thiele, L.; Ashraf, S.A.; Huschke, J.; Aktas, I.; Ansari, J. Wireless Communication for Factory Automation: An opportunity for LTE and 5G systems. IEEE Commun. Mag.
**2016**, 54, 36–43. [Google Scholar] [CrossRef] - Vo, N.; Duong, T.Q.; Guizani, M.; Kortun, A. 5G Optimized Caching and Downlink Resource Sharing for Smart Cities. IEEE Access
**2018**, 6, 31457–31468. [Google Scholar] [CrossRef] - Shah, S.A.A.; Ahmed, E.; Imran, M.; Zeadally, S. 5G for Vehicular Communications. IEEE Commun. Mag.
**2018**, 56, 111–117. [Google Scholar] [CrossRef] - Li, R.; Zhao, Z.; Zhou, X.; Ding, G.; Chen, Y.; Wang, Z.; Zhang, H. Intelligent 5G: When Cellular Networks Meet Artificial Intelligence. IEEE Wirel. Commun.
**2017**, 24, 175–183. [Google Scholar] [CrossRef] - Zanetti, R. Recursive Update Filtering for Nonlinear Estimation. IEEE Trans. Autom. Control
**2012**, 57, 1481–1490. [Google Scholar] [CrossRef] - Saha, M.; Ghosh, R.; Goswami, B. Robustness and Sensitivity Metrics for Tuning the Extended Kalman Filter. IEEE Trans. Instrum. Meas.
**2014**, 63, 964–971. [Google Scholar] [CrossRef] - Vermaak, J.; Godsill, S.J.; Perez, P. Monte Carlo Filtering for Multi-Target Tracking and Data Association. IEEE Trans. Aerosp. Electron. Syst.
**2005**, 41, 309–332. [Google Scholar] [CrossRef] - Ikoma, N.; Ichimura, N.; Higuchi, T.; Maeda, H. Particle Filter Based Method for Maneuvering Target Tracking. In Proceedings of the IEEE International Workshop on Intelligent Signal Processing, Budapest, Hungary, 24–25 May 2001; pp. 3–8. [Google Scholar]
- Grisetti, G.; Kümmerle, R.; Stachniss, C.; Burgard, W. A Tutorial on Graph-Based SLAM. IEEE Intell. Transp. Syst. Mag.
**2010**, 2, 31–43. [Google Scholar] [CrossRef] - Laoudias, C.; Moreira, A.; Kim, S.; Lee, S.; Wirola, L.; Fischione, C. A Survey of Enabling Technologies for Network Localization, Tracking, and Navigation. IEEE Commun. Surv. Tutor.
**2018**, 20, 3607–3644. [Google Scholar] [CrossRef] [Green Version] - Yang, C.; Huang, Y.; Zhu, X. Hybrid TDOA/AOA method for indoor positioning systems. In Proceedings of the The Institution of Engineering and Technology Seminar on Location Technologies, London, UK, 6 December 2007; pp. 1–5. [Google Scholar]
- Chen, J.C.; Maa, C.S.; Chen, J.T. Factor graphs for mobile position location. In Proceedings of the 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, Hong Kong, China, 6–10 April 2003; Volume 2, pp. 393–396. [Google Scholar]
- Loeliger, H.; Dauwels, J.; Hu, J.; Korl, S.; Ping, L.; Kschischang, F.R. The Factor Graph Approach to Model-Based Signal Processing. Proc. IEEE
**2007**, 95, 1295–1322. [Google Scholar] [CrossRef] [Green Version] - Huang, C.; Wu, C.; Lee, Y.; Chen, J. A novel indoor RSS-based position location algorithm using factor graphs. IEEE Trans. Wirel. Commun.
**2009**, 8, 3050–3058. [Google Scholar] [CrossRef] - Mensing, C.; Plass, S. TDOA Positioning Based on Factor Graphs. In Proceedings of the 2006 IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications, Helsinki, Finland, 11–14 September 2006; pp. 1–5. [Google Scholar]
- Aziz, M.R.K.; Anwar, K.; Matsumoto, T. A new DOA-based factor graph geolocation technique for detection of unknown radio wave emitter position using the first-order Taylor series approximation. EURASIP J. Wirel. Commun. Netw.
**2016**, 2016, 189. [Google Scholar] [CrossRef] - Jhi, H.; Chen, J.; Lin, C.; Huang, C. A Factor-Graph-Based TOA Location Estimator. IEEE Trans. Wirel. Commun.
**2012**, 11, 1764–1773. [Google Scholar] [CrossRef] - Cheng, M.; Aziz, M.R.K.; Matsumoto, T. A DOA-Based Factor Graph Technique for 3D Multi-Target Geolocation. IEEE Access
**2019**, 7, 94630–94641. [Google Scholar] [CrossRef] - Cheng, M.; Aziz, M.R.K.; Matsumoto, T. Integrated Factor Graph Algorithm for DOA-Based Geolocation and Tracking. IEEE Access
**2020**, 8, 49989–49998. [Google Scholar] [CrossRef] - Chen, J.; Guan, S.; Tong, Y.; Yan, L. Two-Dimensional Direction of Arrival Estimation for Improved Archimedean Spiral Array with MUSIC Algorithm. IEEE Access
**2018**, 6, 49740–49745. [Google Scholar] [CrossRef] - Bencheikh, M.L.; Wang, Y. Joint DOD-DOA estimation using combined ESPRIT-MUSIC approach in MIMO radar. Electron. Lett.
**2010**, 46, 1081–1083. [Google Scholar] [CrossRef]

Approximated Mean | Approximated Variance | |
---|---|---|

$tan\left(\alpha \right)$ | $tan\left({m}_{\alpha}\right)$ | ${sec}^{4}\left({m}_{\alpha}\right)\xb7{\sigma}_{\alpha}^{2}$ |

$cot\left(\alpha \right)$ | $cot\left({m}_{\alpha}\right)$ | ${csc}^{4}\left({m}_{\alpha}\right)\xb7{\sigma}_{\alpha}^{2}$ |

$sin\left(\alpha \right)$ | $sin\left({m}_{\alpha}\right)$ | ${cos}^{2}\left({m}_{\alpha}\right)\xb7{\sigma}_{\alpha}^{2}$ |

$cos\left(\alpha \right)$ | $cos\left({m}_{\alpha}\right)$ | ${sin}^{2}\left({m}_{\alpha}\right)\xb7{\sigma}_{\alpha}^{2}$ |

$sec\left(\alpha \right)$ | $sec\left({m}_{\alpha}\right)$ | ${sec}^{2}\left({m}_{\alpha}\right)\xb7{tan}^{2}\left({m}_{\alpha}\right)\xb7{\sigma}_{\alpha}^{2}$ |

$csc\left(\alpha \right)$ | $csc\left({m}_{\alpha}\right)$ | ${csc}^{2}\left({m}_{\alpha}\right)\xb7{cot}^{2}\left({m}_{\alpha}\right)\xb7{\sigma}_{\alpha}^{2}$ |

© 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**

Zhang, H.; Zhang, Z.
AOA-Based Three-Dimensional Positioning and Tracking Using the Factor Graph Technique. *Symmetry* **2020**, *12*, 1400.
https://doi.org/10.3390/sym12091400

**AMA Style**

Zhang H, Zhang Z.
AOA-Based Three-Dimensional Positioning and Tracking Using the Factor Graph Technique. *Symmetry*. 2020; 12(9):1400.
https://doi.org/10.3390/sym12091400

**Chicago/Turabian Style**

Zhang, Haiyang, and Zhiwei Zhang.
2020. "AOA-Based Three-Dimensional Positioning and Tracking Using the Factor Graph Technique" *Symmetry* 12, no. 9: 1400.
https://doi.org/10.3390/sym12091400