# NLOS Identification and Positioning Algorithm Based on Localization Residual in Wireless Sensor Networks

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model

_{1}and AN

_{2}, are presented. In Figure 1, the line $\overline{AF}$ denotes the intersection line of two circles centered at $A{N}_{1}$ and $A{N}_{2}$, where the circle radiuses equal to measured distances between ANs and TN. Then the measured AOA line of $A{N}_{1}$ ($\overline{AD}$) intersects $\overline{AF}$ at the position A, which can be treated as an intermediate position estimate of TN. Similarly, the position B represents the intermediate position estimate for the measured AOA line of $A{N}_{2}$. In addition, the circle intersecting point C can be treated as another intermediate position estimation of TN. Obviously, due to the measurement noise and NLOS errors, positions {A, B, C} do not coincide.

## 3. The Proposed NLOS-AN Identification and Localization

#### 3.1. System Error Analysis

#### 3.2. Threshold Determination and NLOS-AN Identification

- (1)
- Find the coordinates of points A and B using (8), and then solve the circle intersections C and F.
- (2)
- Calculate the lengths of AC and AF separately, then find the nearest point ${C}^{{}^{\prime}}$ of point A from $\phantom{\rule{4.pt}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\{\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{-0.166667em}{0ex}}\phantom{\rule{4.pt}{0ex}}C,F\}$.
- (3)
- Treat {A, B, C’} as three intermediate position estimates.
- (4)
- Use ${C}^{{}^{\prime}}$ to calculate $\Delta AC$ as well as $\Delta BC$, and finally compute $\Delta AB$.
- (5)
- Identify the NLOS-AN by the detector (22).
- (6)
- Estimate the TN position by using LOS-ANs only.

## 4. Simulation and Analysis

#### 4.1. Threshold Determination

#### 4.2. Analysis for the Positioning Performance

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 6.**The cumulative distributed function (CDF) of tested algorithms: $SDR$ = 2 m, $SDA=1{}^{\circ}$.

Algorithm | Description |
---|---|

RWGH | Residual weighting algorithm [25] |

CLS | Constrained Least Squares Algorithm [26] |

NI-LS | Using the least squares algorithm after NLOS-AN identification |

Ideal-NI-LS | Using the least squares algorithm with known LOS-AN |

CRLB | Cramer-Rao lower bound (CRLB) with known LOS-AN [24] |

SDP | Convex semidefinite programming algorithm [4] |

opt-LLOP | Linear optimization algorithm [27] |

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**MDPI and ACS Style**

Hua, J.; Yin, Y.; Lu, W.; Zhang, Y.; Li, F. NLOS Identification and Positioning Algorithm Based on Localization Residual in Wireless Sensor Networks. *Sensors* **2018**, *18*, 2991.
https://doi.org/10.3390/s18092991

**AMA Style**

Hua J, Yin Y, Lu W, Zhang Y, Li F. NLOS Identification and Positioning Algorithm Based on Localization Residual in Wireless Sensor Networks. *Sensors*. 2018; 18(9):2991.
https://doi.org/10.3390/s18092991

**Chicago/Turabian Style**

Hua, Jingyu, Yejia Yin, Weidang Lu, Yu Zhang, and Feng Li. 2018. "NLOS Identification and Positioning Algorithm Based on Localization Residual in Wireless Sensor Networks" *Sensors* 18, no. 9: 2991.
https://doi.org/10.3390/s18092991