Wi-Fi RTT/RSS混合定位CRLB推导与最优节点布局设计

doi:10.11947/j.AGCS.2024.20230220.

测绘学报 ›› 2024, Vol. 53 ›› Issue (10): 1993-2006.doi: 10.11947/j.AGCS.2024.20230220.

• 大地测量学与导航 • 上一篇

Wi-Fi RTT/RSS混合定位CRLB推导与最优节点布局设计

孙猛¹^,²^,(), 汪云甲¹^,²(), 王潜心¹^,², 陈国良¹^,², 李增科¹^,²

^1.中国矿业大学环境与测绘学院，江苏　徐州　221116
^2.中国矿业大学自然资源部国土环境与灾害监测重点实验室，江苏　徐州　221116

收稿日期:2023-06-20 发布日期:2024-11-26
通讯作者: 汪云甲 E-mail:msun@cumt.edu.cn;wyjc411@163.com
作者简介:孙猛（1995—），男，博士，讲师，主要研究方向为室内定位与导航。E-mail：msun@cumt.edu.cn
基金资助:
国家自然科学基金(42304047);国家重点研发计划(2020YFA0713502);江苏省重点研发计划(BE2022716)

Wi-Fi RTT/RSS fusion localization CRLB derivation and optimal access points layout design

Meng SUN¹^,²^,(), Yunjia WANG¹^,²(), Qianxin WANG¹^,², Guoliang CHEN¹^,², Zengke LI¹^,²

^1.School of Environment and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China
^2.Key Laboratory of Land Environment and Disaster Monitoring, MNR, China University of Mining and Technology, Xuzhou 221116, China

Received:2023-06-20 Published:2024-11-26
Contact: Yunjia WANG E-mail:msun@cumt.edu.cn;wyjc411@163.com
About author:SUN Meng (1995—), male, PhD, lecturer, majors in indoor positioning and navigation. E-mail: msun@cumt.edu.cn
Supported by:
The National Natural Science Foundation of China(42304047);The National Key Research and Development Program of China(2020YFA0713502);Jiangsu Key Research and Development Program(BE2022716)

摘要/Abstract

摘要：

基于精细时间测量协议（FTM）的Wi-Fi RTT定位是目前领域内的研究热点，但其定位算法性能的评估手段较为单一且缺乏理论基础，Wi-Fi接入点（AP）布局对于定位精度的影响也尚未深入研究。本文以智能手机Wi-Fi FTM为研究对象，推导了基于Wi-Fi RTT/RSS混合定位方法的克拉美罗下界（CRLB），阐明了单一定位与混合定位方法CRLB的理论关系，为算法性能评估确立了理论依据；研究了Wi-Fi AP布局对RTT/RSS混合定位精度的影响，以增强遗传算法（EGA）和CRLB为基础，设计了Wi-Fi RTT/RSS混合定位的最优节点布局方案。研究表明，Wi-Fi RSS/RTT混合定位可作为高效的FTM定位方法，提出的基于EGA和CRLB的最优节点布局方法能快速给出定位区域内的最优AP布局方案。试验结果表明，在最优节点布局下（7个Wi-Fi节点），Wi-Fi RSS、RTT和RSS/RTT混合定位在本文试验环境的理论精度分别为0.92、1.07和0.61 m。研究结果可为Wi-Fi FTM定位算法性能评估提供理论支持，也能为合理布设Wi-Fi节点、减少定位成本投入提供可行方案。

关键词: 室内定位与导航, Wi-Fi精细时间测量, 智能手机定位, Wi-Fi节点布局, 克拉美罗界, 增强遗传算法

Abstract:

The fine time measurement (FTM) protocol-based Wi-Fi RTT positioning is currently a research spotlight in the community. However, the performance evaluation methods of localization algorithms are relatively simplistic and lack theoretical basis. Furthermore, the impact of Wi-Fi access points (AP) layout on positioning accuracy has not been thoroughly studied. This paper focuses on smartphone-based Wi-Fi FTM as the research object. It derives the Cramer-Rao lower bound (CRLB) of the Wi-Fi RTT/RSS hybrid positioning method and clarifies the theoretical CRLB relationships of the single and hybrid positioning methods, which establishes a theoretical foundation for algorithm performance evaluation. The influence of Wi-Fi AP deployments on the localization accuracy of the RTT/RSS fusion positioning is studied, and an optimal access point layout approach for Wi-Fi RTT/RSS hybrid positioning is designed based on the enhanced genetic algorithm (EGA) and CRLB. Research shows that Wi-Fi RSS/RTT fusion localization is also an efficient FTM positioning method. The proposed EGA and CRLB-based optimal layout approach for Wi-Fi APs can quickly produce the optimal access point deployment strategy for the positioning area. The experimental results reveal that under the optimal layout of 7 Wi-Fi APs, the theoretical accuracy of Wi-Fi RSS, RTT, and RSS/RTT fusion positioning in the testing site of this manuscript is 0.92, 1.07 and 0.61 m, respectively. The research work provides theoretical support for evaluating the performance of Wi-Fi FTM positioning and offers practical strategies for deploying Wi-Fi APs effectively, thereby reducing positioning investment.

Key words: indoor positioning and navigation, Wi-Fi fine time measurement, smartphone-based positioning, Wi-Fi AP layout, Cramer-Rao lower bound, enhanced genetic algorithm

中图分类号:

P228

孙猛, 汪云甲, 王潜心, 陈国良, 李增科. Wi-Fi RTT/RSS混合定位CRLB推导与最优节点布局设计[J]. 测绘学报, 2024, 53(10): 1993-2006.

Meng SUN, Yunjia WANG, Qianxin WANG, Guoliang CHEN, Zengke LI. Wi-Fi RTT/RSS fusion localization CRLB derivation and optimal access points layout design[J]. Acta Geodaetica et Cartographica Sinica, 2024, 53(10): 1993-2006.

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定位方法	NLoS/LoS识别	测距补偿	测试场景	定位精度
Wi-Fi FTM+地图^[6-7]	否	无	试验室办公环境(>1000 m²)	<2 m (90%)
Wi-Fi FTM+GPS+里程计^[10]	否	有/多径补偿	市区街道/住宅区/郊区环境	1.3 m/2.1 m/0.8 m
Wi-Fi FTM+RSS测距^[15]	否	有/钟差补偿	室内房间(16.7 m×12.14 m)	1.44 m
Wi-Fi FTM+RSS测距+PDR^[16]	否	有/RSS测距	建筑楼/办公室	0.58 m(50%)
Wi-Fi RSS测距+FTM+PDR^[17]	否	有/RSS测距	2层试验室环境(33 m×9 m)	<1.1 m(67.5%)
Wi-Fi RSS测距+FTM+PDR^[18]	无	有/RSS测距	室内办公环境(约126 m²)	0.39 m
时空约束的Wi-Fi FTM定位^[19]	无	无	办公室环境	<1 m (80%)
基于高斯模型的Wi-Fi FTM定位^[22]	是	无	试验室办公环境(20 m×8 m)	<1 m
基于高斯过程回归的Wi-Fi FTM定位^[23]	是	有/NLOS误差补偿	试验室办公环境(20 m×8 m)	<1 m
Wi-Fi FTM+PDR^[24]	是	有/测距误差补偿	试验室办公环境(20 m×8 m)	0.98 m
Wi-Fi FTM+Encoder+INS^[25]	否	无	LoS/NLoS环境	0.54 m/0.77 m
Wi-Fi FTM+地图+MEMS^[26]	是	无	2层试验室环境	<1 m (94%)

定位方法	最小值	最大值	平均值	75 th	90 th
RSS	0.16	3.42	1.16	1.56	2.06
RTT	0.47	3.08	1.35	1.76	2.11
RSS/RTT	0.10	2.12	0.74	0.93	1.20

AP数量	统计量	RSS/m	RTT/m	RSS/RTT/m
3	均值	2.05	2.32	1.20
	75 th	2.52	2.87	1.37
	90 th	3.61	3.78	2.03
4	均值	1.88	2.13	1.09
	75 th	2.42	2.80	1.25
	90 th	3.51	3.71	1.94
5	均值	1.78	1.97	1.00
	75 th	2.35	2.62	1.19
	90 th	3.46	3.55	1.78

定位方法	最小值	最大值	平均值	75 th	90 th
RSS	0.41	1.72	0.92	1.05	1.18
RTT	0.75	1.89	1.07	1.13	1.35
RSS/RTT	0.17	1.23	0.61	0.68	0.77

Wi-Fi RTT/RSS混合定位CRLB推导与最优节点布局设计

Wi-Fi RTT/RSS fusion localization CRLB derivation and optimal access points layout design

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