# A Fusion Localization Method based on a Robust Extended Kalman Filter and Track-Quality for Wireless Sensor Networks

^{*}

## Abstract

**:**

## 1. Introduction

- 1)
- The proposed algorithm fully combines the advantageous features of the two filters to obtain precise localization result. It achieves both efficiency and robustness and even outperforms the EKF in LOS case and REKF in NLOS environment.
- 2)
- It only assumes that the measurement noise variance in LOS and the process noise covariance are known in this paper. The prior knowledge of the NLOS errors is not required. Therefore, the proposed algorithm has better latent capacity to reduce localization error.
- 3)
- The fusion algorithm heavily exploits the data about the state estimate at previous time, which makes it more immediate and dynamic.
- 4)
- An experiment is conducted under indoor environment. The result shows the proposed algorithm performs better than the standard techniques, which indicates the feasibility of the algorithm in the practical environment.

## 2. Related Works

## 3. Problem Statement

#### 3.1. Signal Model

#### 3.2. Introduction of REKF

#### 3.3. Introduction of Fusion Algorithm Based on the Track Quality

## 4. Proposed Algorithm

#### 4.1. General Concept

#### 4.2. Extended Kalman Filter (EKF)

#### 4.3. Robust Extended Kalman Filter (REKF)

#### 4.4. Kalman Filter with New Measurement Equation

#### 4.5. Combination Based on Track Quality

## 5. Simulation and Experimental Results

#### 5.1. Simulation Results

#### 5.1.1. The Effect of Historical Weight Factor

#### 5.1.2. The NLOS Errors Obey Gaussian Distribution

#### 5.1.3. The NLOS Errors Obey Exponential Distribution

#### 5.1.4. The NLOS Errors Obey Uniform Distribution

#### 5.2. Experimental Results

#### 5.2.1. Localization Results Analysis

#### 5.2.2. Computation Time

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Wann, C.-D.; Yeh, Y.-J.; Hsueh, C.-S. Hybrid TDOA/AOA Indoor Positioning and Tracking Using Extended Kalman Filters. In Proceedings of the 2006 IEEE 63rd Vehicular Technology Conference, Melbourne, Australia, 7–10 May 2006; Volumes 1–6, pp. 1058–1062. [Google Scholar]
- Julier, S.J.; Uhlmann, J.K. Unscented filtering and nonlinear estimation. Proc. IEEE
**2004**, 92, 401–422. [Google Scholar] [CrossRef] - Ou, X.H.; Wu, X.Q.; He, X.X.; Chen, Z.T.; Yu, Q.-A. An Improved Node Localization Based on Adaptive Iterated Unscented Kalman Filter for WSN. In Proceedings of the 2015 10th IEEE Conference on Industrial Electronics and Applications, Auckland, New Zealand, 15–17 June 2015; pp. 393–398. [Google Scholar]
- Gustafsson, F.; Gunnarsson, F.; Bergman, N.; Forssell, U.; Jansson, J.; Karlsson, R.; Nordlund, P.-J. Particle filters for positioning, navigation, and tracking. IEEE Trans. Signal Process.
**2002**, 50, 425–437. [Google Scholar] [CrossRef] - Bardenet, R. Monte Carlo methods. In SOS 2012—IN2P3 School of Statistics; Delemontex, T., Lucotte, A., Eds.; EDP Sciences: Les Ulis, France, 2013; Volume 55. [Google Scholar]
- Del Moral, P.; Doucet, A.; Jasra, A. An adaptive sequential Monte Carlo method for approximate Bayesian computation. Stat. Comput.
**2012**, 22, 1009–1020. [Google Scholar] [CrossRef] - Mihaylova, L.; Carmi, A.Y.; Septier, F.; Gning, A.; Pang, S.K.; Godsill, S. Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking. Digit. Signal Prog.
**2014**, 25, 1–16. [Google Scholar] [CrossRef] - Chen, P.-C. A non-line-of-sight error mitigation algorithm in location estimation. In Proceedings of the WCNC. 1999 IEEE Wireless Communications and Networking Conference (Cat. No.99TH8466), New Orleans, LA, USA, 21–24 September 1999; Volume 311, pp. 316–320. [Google Scholar]
- Chen, P.C. A cellular based mobile location tracking system. In Proceedings of the 1999 IEEE 49th Vehicular Technology Conference (Cat. No.99CH36363), Houston, TX, USA, 16–20 May 1999; Volumes 1–3, pp. 1979–1983. [Google Scholar]
- Grosicki, E.; Abed-Meraim, K. A new trilateration method to mitigate the impact of some non-line-of-sight errors in TOA measurements for mobile localization. In Proceedings of the 2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, PA, USA, 23 March 2005; pp. 1045–1048. [Google Scholar]
- Hammes, U.; Zoubir, A.M. Robust Mobile Terminal Tracking in NLOS Environments Based on Data Association. IEEE Trans. Signal Process.
**2010**, 58, 5872–5882. [Google Scholar] [CrossRef] - Tomic, S.; Beko, M. A bisection-based approach for exact target localization in NLOS environments. Signal Process.
**2018**, 143, 328–335. [Google Scholar] [CrossRef][Green Version] - Su, Z.Q.; Shao, G.F.; Liu, H.P. Semidefinite Programming for NLOS Error Mitigation in TDOA Localization. IEEE Commun. Lett.
**2018**, 22, 1430–1433. [Google Scholar] [CrossRef] - Yang, X.F. NLOS Mitigation for UWB Localization Based on Sparse Pseudo-Input Gaussian Process. IEEE Sens. J.
**2018**, 18, 4311–4316. [Google Scholar] [CrossRef] - Ma, Y.T.; Wang, B.B.; Pei, S.Y.; Zhang, Y.L.; Zhang, S.; Yu, J.X. An Indoor Localization Method Based on AOA and PDOA Using Virtual Stations in Multipath and NLOS Environments for Passive UHF RFID. IEEE Access
**2018**, 6, 31772–31782. [Google Scholar] [CrossRef] - Yang, K.H.; Wang, G.; Luo, Z.Q. Efficient Convex Relaxation Methods for Robust Target Localization by a Sensor Network Using Time Differences of Arrivals. IEEE Trans. Signal Process.
**2009**, 57, 2775–2784. [Google Scholar] [CrossRef] - Wang, G.; So, A.M.C.; Li, Y.M. Robust Convex Approximation Methods for TDOA-Based Localization Under NLOS Conditions. IEEE Trans. Signal Process.
**2016**, 64, 3281–3296. [Google Scholar] [CrossRef] - Lee, K.; Oh, J.; You, K. TDOA/AOA Based Geolocation Using Newton Method under NLOS Environment; IEEE: New York, NY, USA, 2016; pp. 373–377. [Google Scholar]
- Liao, J.F.; Chen, B.S. Robust mobile location estimator with NLOS mitigation using interacting multiple model algorithm. IEEE Trans. Wirel. Commun.
**2006**, 5, 3002–3006. [Google Scholar] [CrossRef] - Jo, K.; Chu, K.; Sunwoo, M. Interacting Multiple Model Filter-Based Sensor Fusion of GPS with In-Vehicle Sensors for Real-Time Vehicle Positioning. IEEE Trans. Intell. Transp. Syst.
**2012**, 13, 329–343. [Google Scholar] [CrossRef] - Chen, B.S.; Yang, C.Y.; Liao, F.K.; Liao, J.F. Mobile Location Estimator in a Rough Wireless Environment Using Extended Kalman-Based IMM and Data Fusion. IEEE Trans. Veh. Technol.
**2009**, 58, 1157–1169. [Google Scholar] [CrossRef] - Johnston, L.A.; Krishnamurthy, V. An improvement to the interacting multiple model (IMM) algorithm. IEEE Trans. Signal Process.
**2001**, 49, 2909–2923. [Google Scholar] [CrossRef] - Yang, N.; Tian, W.F.; Jin, Z.H. An interacting multiple model particle filter for manoeuvring target location. Meas. Sci. Technol.
**2006**, 17, 1307–1311. [Google Scholar] [CrossRef] - Boers, Y.; Driessen, J.N. Interacting multiple model particle filter. IEE Proc. Radar Sonar Navig.
**2003**, 150, 344–349. [Google Scholar] [CrossRef] - Gustafsson, F.; Gunnarsson, F. Mobile positioning using wireless networks. IEEE Signal Process. Mag.
**2005**, 22, 41–53. [Google Scholar] [CrossRef] - Kai, X.; Wei, C.L.; Liu, L.D. Robust Extended Kalman Filtering for Nonlinear Systems with Stochastic Uncertainties. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum.
**2010**, 40, 399–405. [Google Scholar] [CrossRef] - Einicke, G.A.; White, L.B. Robust extended Kalman filtering. IEEE Trans. Signal Process.
**1999**, 47, 2596–2599. [Google Scholar] [CrossRef] - Donatelli, M.; Garoni, C.; Manni, C.; Serra-Capizzano, S.; Speleers, H. Robust and optimal multi-iterative techniques for IgA Galerkin linear systems. Comput. Meth. Appl. Mech. Eng.
**2015**, 284, 230–264. [Google Scholar] [CrossRef] - Rousseeuw, P.J.; Hubert, M. Robust statistics for outlier detection. Wiley Interdiscip. Rev. Data Min. Knowl. Discov.
**2011**, 1, 73–79. [Google Scholar] [CrossRef] - Iwase, T.; Suzuki, N.; Watanabe, Y. Estimation and exclusion of multipath range error for robust positioning. GPS Solut.
**2013**, 17, 53–62. [Google Scholar] [CrossRef] - Hammes, U.; Wolsztynski, E.; Zoubir, A.M. Robust Tracking and Geolocation for Wireless Networks in NLOS Environments. IEEE J. Sel. Top. Signal Process.
**2009**, 3, 889–901. [Google Scholar] [CrossRef] - Chang, G.B.; Liu, M. M-estimator-based robust Kalman filter for systems with process modeling errors and rank deficient measurement models. Nonlinear Dyn.
**2015**, 80, 1431–1449. [Google Scholar] [CrossRef] - Huber, P.; Ronchetti, E.M. Robust Statistics, 2nd ed.; Wiley: New York, NY, USA, 2009. [Google Scholar]
- Collins, J.R. Robust Estimation of a Location Parameter in the Presence of Asymmetry. Ann. Stat.
**1976**, 4, 68–85. [Google Scholar] [CrossRef] - Jennison, C. Robust Statistics: The Approach Based on Influence Functions. Wiley Online Libr.
**1987**, 150, 281–282. [Google Scholar] [CrossRef]

Parameter | Symbol | Default Values |
---|---|---|

The number of beacon nodes | N | 7 |

The probability of LOS propagation | $\epsilon $ | 0.7 |

The standard deviation of measurement noise | ${\sigma}_{LOS}$ | 1 |

The NLOS errors | $N\left({\mu}_{NLOS},{\sigma}_{NLOS}^{2}\right)$ | $N\left(3,{4}^{2}\right)$ |

The number of sample points | K | 100 |

The number of Monte Carlo runs | ${T}_{n}$ | 1000 |

Parameter | Symbol | Default Values |
---|---|---|

The number of beacon nodes | N | 7 |

The probability of LOS propagation | $\epsilon $ | 0.7 |

The standard deviation of measurement noise | ${\sigma}_{LOS}$ | 1 |

The NLOS errors | $E(\lambda )$ | $E(4)$ |

The number of sample points | K | 100 |

The number of Monte Carlo runs | ${T}_{n}$ | 1000 |

Parameter | Symbol | Default Values |
---|---|---|

The number of beacon nodes | N | 7 |

The probability of LOS propagation | $\epsilon $ | 0.7 |

The standard deviation of measurement noise | ${\sigma}_{LOS}$ | 1 |

The NLOS errors | $U({U}_{\mathrm{min}},{U}_{\mathrm{max}})$ | $U(0,7)$ |

The number of sample points | K | 100 |

The number of Monte Carlo runs | ${T}_{n}$ | 1000 |

**Table 4.**The mean value of error, standard deviation of error, root mean squared error (in m) of estimators for Gaussian, exponential and uniform NLOS Distributions.

Mean Value of Error | Standard Deviation of Error | Root Mean Squared Error | |
---|---|---|---|

Gaussian Distribution $({\mu}_{NLOS},{\sigma}_{NLOS}^{2})=(3,{4}^{2})$ | |||

R-IMM | 1.396 | 0.179 | 1.887 |

REKF | 1.457 | 0.184 | 1.948 |

EKF | 1.988 | 0.158 | 2.406 |

REKF-TQ | 1.338 | 0.143 | 1.701 |

Exponential Distribution $\lambda =4$ | |||

R-IMM | 1.359 | 0.180 | 1.845 |

REKF | 1.436 | 0.181 | 1.921 |

EKF | 2.187 | 0.193 | 2.760 |

REKF-TQ | 1.348 | 0.139 | 1.731 |

Uniform Distribution $({U}_{\mathrm{min}},{U}_{\mathrm{max}})=(0,7)$ | |||

R-IMM | 1.459 | 0.158 | 1.885 |

REKF | 1.526 | 0.162 | 1.954 |

EKF | 1.790 | 0.116 | 2.086 |

REKF-TQ | 1.389 | 0.112 | 1.685 |

Method Used | Running Time/s |
---|---|

R-IMM | 0.77 |

REKF | 0.64 |

EKF | 0.02 |

REKF-TQ | 0.79 |

© 2019 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**

Wang, Y.; Jie, H.; Cheng, L.
A Fusion Localization Method based on a Robust Extended Kalman Filter and Track-Quality for Wireless Sensor Networks. *Sensors* **2019**, *19*, 3638.
https://doi.org/10.3390/s19173638

**AMA Style**

Wang Y, Jie H, Cheng L.
A Fusion Localization Method based on a Robust Extended Kalman Filter and Track-Quality for Wireless Sensor Networks. *Sensors*. 2019; 19(17):3638.
https://doi.org/10.3390/s19173638

**Chicago/Turabian Style**

Wang, Yan, Huihui Jie, and Long Cheng.
2019. "A Fusion Localization Method based on a Robust Extended Kalman Filter and Track-Quality for Wireless Sensor Networks" *Sensors* 19, no. 17: 3638.
https://doi.org/10.3390/s19173638