室内圆柱引导的激光雷达全局定位与回环检测

史鹏程, 李加元, 刘欣怡, 张永军

史鹏程, 李加元, 刘欣怡, 张永军. 室内圆柱引导的激光雷达全局定位与回环检测[J]. 武汉大学学报 ( 信息科学版), 2024, 49(7): 1088-1099. DOI: 10.13203/j.whugis20220761
引用本文: 史鹏程, 李加元, 刘欣怡, 张永军. 室内圆柱引导的激光雷达全局定位与回环检测[J]. 武汉大学学报 ( 信息科学版), 2024, 49(7): 1088-1099. DOI: 10.13203/j.whugis20220761
SHI Pengcheng, LI Jiayuan, LIU Xinyi, ZHANG Yongjun. Indoor Cylinders Guided LiDAR Global Localization and Loop Closure Detection[J]. Geomatics and Information Science of Wuhan University, 2024, 49(7): 1088-1099. DOI: 10.13203/j.whugis20220761
Citation: SHI Pengcheng, LI Jiayuan, LIU Xinyi, ZHANG Yongjun. Indoor Cylinders Guided LiDAR Global Localization and Loop Closure Detection[J]. Geomatics and Information Science of Wuhan University, 2024, 49(7): 1088-1099. DOI: 10.13203/j.whugis20220761

室内圆柱引导的激光雷达全局定位与回环检测

基金项目: 

国家自然科学基金 42271444

国家自然科学基金 42201474

武大-华为空间信息技术创新实验室开放基金 TC20210901025-2023-06

详细信息
    作者简介:

    史鹏程,博士生,研究方向为地图定位与位置识别。shipc_2021@whu.edu.cn

    通讯作者:

    张永军,博士,教授。zhangyj@whu.edu.cn

Indoor Cylinders Guided LiDAR Global Localization and Loop Closure Detection

  • 摘要:

    针对移动机器人在大范围室内环境的定位难题,提出了一种基于圆柱特征的全局定位方法。首先,设计一种参数化地图,采用随机采样一致性算法和几何模型分割出地图中的圆柱点云,利用栅格地图描述环境中稳定人工构筑物的分布。其次,采用轻量级二进制文件记录圆柱和地物分布。然后,基于圆柱独特的几何特性(离群性、对称性和显著性),提出一种实时LiDAR点云圆柱分割方法。最后,设计两种位姿求解策略:第一种是启发式搜索,在地图与实时数据中搜索出最佳匹配圆柱,进而分别解算平移量和旋转量;第二种是优化求解,利用圆柱之间的拓扑关系构建约束条件并计算最优位姿。为验证所提方法的可行性,采用16线激光雷达在大厅、走廊及混合场景3种典型室内环境进行全局定位和回环检测实验。实验结果表明,该方法可有效实现典型空旷室内环境中机器人的全局定位,可达到90%的定位成功率以及0.073 m定位误差,部分数据可达到毫米级定位精度,最快速度在100 ms内,位置识别性能达到主流方法水平。该方法基本满足实际应用中自动驾驶对全局定位的精度和效率要求。

    Abstract:
    Objectives 

    Localization is an important module of the light detection and ranging (LiDAR) simultaneous localization and mapping (SLAM) system, which provides basic information for perception, control, and planning, further assisting robots to accomplish higher-level tasks. However, LiDAR localization methods still face some problems: The localization accuracy and efficiency cannot meet the requirements of the robot products. In some textureless or large open environments, the lack of features easily leads to dangerous robot kidnappings. Consequently, aiming at the localization problems of mobile robots in large indoor environments, a global localization method based on cylindrical features is proposed.

    Methods 

    First, an offline parameterized map is designed, which consists of some map cylinders and a raster map. Because the point cloud map contains a large number of 3D points and complete cylinders, random sample consensus (RANSAC) and geometric models are combined to directly segment the cylindrical points. The raster map is employed to describe the distributions of stable artificial structures. Then, some lightweight binary files are used to offline record the geometric model of cylinders and the feature distribution of the map. Next, based on three unique geometric characteristics of the cylinder (outlier, symmetry, and saliency), a real-time LiDAR point cloud cylinder segmentation method is proposed. Finally, two pose computation strategies are designed. The first is an optimization model based on heuristic search, which searches for the best matching cylinder between the map and real-time point cloud, and calculates the translation and rotation, respectively. The second is an optimization model based on multi-cylinder constraints, which employs both the topological relation (point-to-point and point-to-line constraints) and geometry attributes to find approximately congruent cylinders, then computes optimal pose.

    Results 

    To verify the feasibility of the proposed method, we use a 16-line LiDAR to collect the experimental data in three real-world indoor environments, i.e., lobby, corridor, and hybrid scenarios. The global localization experiment is compared to a similar wall-based localization method, and the loop closure detection is compared to M2DP, ESF, Scan Context, and the wall-based localization. The experimental results show that the proposed method outperforms the baseline methods. The place recognition and localization performance of the proposed method reach the mainstream method level, with a localization success rate of 90% and an error of 0.073 m. Some data can reach millimeter localization accuracy, and the fastest speed is within 100 ms.

    Conclusions 

    The proposed method can effectively realize the global localization and place recognition of the robots in typical open indoor environments. It meets the accuracy and efficiency requirements of autonomous driving for global localization in practical applications. It can be applied to solve the problems of position initialization, re-localization, and loop closure detection.

  • 精密单点定位(precise point positioning, PPP)技术具有定位精度高,数据采集方便,数据处理简单等优点,成为近年来实时精密定位服务的重要手段。实时精密单点定位服务将卫星精密轨道和钟差实时播发给用户[1]。IGS已经开展了实时实验计划(real-time pilot project, RTPP),各个分析中心播发的GPS实时精密轨道精度为4~8 cm,精密钟差精度为0.2~0.8 ns。实时精密轨道通常采用的是超快速预报轨道,由于超快速轨道精度不如最终精密轨道,为了实现高精度实时定位,通过实时估计卫星钟差吸收部分轨道误差。国内外学者对实时精密卫星钟差估计算法进行了大量研究,主要包括非差模式和历元间差分模式。非差模式精密卫星钟差估计方法待估参数过多,计算效率较低[2]。采用历元间差分方法时,模糊度参数被消除,计算速率加快,但初始时刻卫星钟差会引入与卫星相关的偏差[3]。为了消除该项偏差的影响,Zhang等[4]提出了利用非差相位和伪距观测值和历元间差分相位和伪距观测值并行计算的方法。Ge等[5]提出了利用历元间差分相位观测值和非差伪距观测值并行计算的方法。

    全球卫星导航系统发展迅猛,继美国的GPS、俄罗斯的GLONASS后,欧洲正在开发Galileo卫星导航系统,我国已经建立了功能完善的第二代北斗区域卫星导航系统(Beidou Navigation Satellite System, BDS)[6]。相关研究表明多系统融合增加了可观测卫星数目,改善了卫星空间几何结构,提高了定位的准确性,可靠性和连续性[7]。因此,多系统融合逐渐成为了高精度卫星导航定位广大用户的必然选择,而多系统实时卫星钟差的精确估计是实现多系统高精度实时定位服务的前提。本文对基于历元间差分相位观测值和非差伪距观测值的卫星钟差估计方法进行了改进,实现了GPS、GLONASS、Galileo和BDS多系统卫星钟差联合快速估计。

    基于无电离层组合伪距和相位的观测方程为:

    $$ \left\{ \begin{array}{l} P_r^s = \rho _0^s + c\left( {d{t_r}-d{t^s}} \right) + {T_r} + c\left( {{B_r}-{B^s}} \right) + {e_s}\\ L_r^s = \rho _0^s + c\left( {d{t_r}-d{t^s}} \right) - \lambda {N^s} + \\ \;\;\;\;\;\;\;{T_r} + c\left( {{b_r} - {b^s}} \right) + \varepsilon_s \end{array} \right. $$ (1)

    式中,r为测站号;s为卫星号;PrsLrs为无电离层组合伪距和相位观测值;ρ0s为站-星间几何距离;c为光速;dtr为接收机钟差;dts为卫星钟差;Tr为传播路径上对流层延迟误差;Ns为无电离层组合整周模糊度;λ为无电离层组合波长;Brbr分别为接收机端无电离层组合伪距和相位的硬件延迟;Bsbs分别为卫星端无电离层组合伪距和相位的硬件延迟;esεs分别为伪距和相位的测量噪声,多路径误差通常归入到测量噪声内。

    参数估计时,接收机伪距硬件延迟Br被接收机钟差dtr吸收,卫星伪距硬件延迟Bs被卫星钟差dts吸收,固定测站坐标,式(1)线性化为:

    $$ \left\{ \begin{array}{l} {v_{P_r^s}} = c\left( {\delta {t_r}-\delta {t^s}} \right) + m_r^sd{T_r}-{\rm{OM}}{{\rm{C}}_{P_r^s}}\\ {v_{L_r^s}} = c\left( {\delta {t_r}-\delta {t^s}} \right) - \lambda {{\tilde N}^s} + m_r^sd{T_r} - {\rm{OM}}{{\rm{C}}_{L_r^s}} \end{array} \right. $$ (2)

    式中,δtr=dtr+Brδts=dts+Bs;$ {{\tilde N}^s}$=Ns+c(br-bs-Br+Bs)/λ;OMCPrs=Prs-ρ0s;OMCLrs=Lrs-ρ0smrsdTr分别为对流层湿延迟投影函数和残余误差;vPrsvLrs分别为伪距和相位观测值残差。

    由式(2)可得历元间差分的相位观测值为:

    $$ \Delta {v_{L_r^s}} = c\left( {\Delta \delta {t_{r, {\rm{sys}}}}-\Delta \delta {t^s}} \right) + \Delta m_r^sd{T_r}-\Delta \;\;{\rm{OM}}{{\rm{C}}_{L_r^s}} $$ (3)

    式中,sys=G、R、E、B,文中G代表GPS,R代表GLONASS,E代表Galileo,B代表BDS;Δδtr, sys为系统sys相邻历元间接收机钟差改正数之差;Δδts为相邻历元间卫星钟差改正数之差;在规定的弧段内,对流层湿延迟的投影函数mrs发生变化,对投影函数进行历元间做差分得Δmrs;天顶对流层湿延迟残余误差参数dTr作为分段线性常数估计;ΔOMCLrs为相位观测值与计算值之差OMCLrs的历元间差,ΔvLrs为相邻历元间相位观测值残差之差。

    多系统卫星钟差估计时,同一测站不同系统接收机端伪距硬件延迟不同,不同系统接收机钟差存在差异[8]。此时可以估计一个接收机钟差和多个系统时间差,或者同时估计若干个接收机钟差[9]。本文同时估计了4个系统的接收机钟差参数。则多模融合卫星钟差估计误差为:

    $$ \left\{ \begin{array}{l} \Delta {v_{L_r^i}} = c\left( {\Delta \delta {t_{r, G}}-\Delta \delta {t^i}} \right) + \Delta m_r^id{T_r}-\Delta \;{\rm{OM}}{{\rm{C}}_{L_r^i}}\\ \Delta {v_{L_r^j}} = c\left( {\Delta \delta {t_{r, R}}-\Delta \delta {t^j}} \right) + \Delta m_r^jd{T_r} - \Delta \;{\rm{OM}}{{\rm{C}}_{L_r^j}}\\ \Delta {v_{L_r^k}} = c\left( {\Delta \delta {t_{r, E}} - \Delta \delta {t^k}} \right) + \Delta m_r^kd{T_r} - \Delta \;{\rm{OM}}{{\rm{C}}_{L_r^k}}\\ \Delta {v_{L_r^l}} = c\left( {\Delta \delta {t_{r, B}} - \Delta \delta {t^l}} \right) + \Delta m_r^ld{T_r} - \Delta \;{\rm{OM}}{{\rm{C}}_{L_r^l}} \end{array} \right. $$ (4)

    式中,i=1, …, nGj=1, …, nRk=1, …, nEl=1, …, nBnsys为测站r接收到系统sys卫星个数;δtr, Gδtr, R、Δδtr, E、Δδtr, B分别为测站相邻历元间的GPS、GLONASS、Galileo和BDS接收机钟差改正数之差;Δδti、Δδtj、Δδtk、Δδtl分别为第i颗GPS卫星,第j颗GLONASS卫星,第k颗Galileo卫星,第l颗BDS卫星的相邻历元间卫星钟差改正数之差;Δmri、Δmrj、Δmrk、Δmrl分别为第i颗GPS卫星,第j颗GLONASS卫星,第k颗Galileo卫星,第l颗BDS卫星对应的对流层湿延迟投影函数之差;ΔOMCLri、ΔOMCLrj、ΔOMCLrk、ΔOMCLrl分别为第i颗GPS卫星,第j颗GLONASS卫星,第k颗Galileo卫星,第l颗BDS卫星的相位观测值与计算值之差的历元间差;ΔvLri、ΔvLrj、ΔvLrk、ΔvLrl分别第i颗GPS卫星,第j颗GLONASS卫星,第k颗Galileo卫星,第l颗BDS卫星的相邻历元间相位观测值残差之差。

    对式(4)采用均方根信息滤波方法进行参数估计。需要指出的是接收机钟差是相对量,对同一系统的所有跟踪站的接收机钟差采用重心基准$ \sum\limits_{r = 1}^{{m_{sys}}} {\Delta \delta {t_{r, {\rm{sys}}}}} = 0$进行约束,msys为跟踪站到系统sys卫星的测站个数。

    由式(4)可以得到历元k时刻卫星s的历元间差分钟差改正数Δδts(k),则历元k时刻卫星s的钟差改正数为:

    $$ \delta {t^s}\left( k \right) = \delta {t^s}\left( {{i_0}} \right) + \sum\limits_{i = {i_0} + 1}^k {\Delta \delta {t^s}\left( i \right)} $$ (5)

    式中,i0为卫星s初始历元;δts(i0)为初始历元i0对应的卫星钟差改正数;Δδts(i)为历元i对应的卫星钟差改正数历元间差。

    由式(2)可得历元k时刻的非差伪距观测值误差方程为:

    $$ \begin{array}{l} {v_{P_r^s(k)}} = c\left( {\delta {t_r}\left( k \right)-\delta {t^s}\left( k \right)} \right) + \\ \;\;\;\;\;\;\;m_r^s\left( k \right)d{T_r}-{\rm{OM}}{{\rm{C}}_{P_r^s\left( k \right)}} \end{array} $$ (6)

    由历元间差分相位观测值可以得到的非常精确的对流层延迟误差和历元间差分卫星钟差[4-5]。将式(3)求得的dTr和式(5)带入式(6),可得:

    $$ {v_{P_r^s\left( k \right)}} = c\left( {\delta {t_r}\left( k \right)-\delta {t^s}\left( {{i_0}} \right)} \right)-{\rm{om}}{{\rm{c}}_{P_r^s\left( k \right)}} $$ (7)

    式中

    $$ {\rm{om}}{{\rm{c}}_{P_r^s\left( k \right)}} = c\sum\limits_{i = {i_0} + 1}^k {\Delta \delta {t^s}\left( i \right)}-m_r^s\left( k \right)d{T_r} + {\rm{OM}}{{\rm{C}}_{P_r^s\left( k \right)}} $$

    历元间差分方法同时对相位与伪距观测值进行了差分,由式(5)可以看出,求得的卫星钟差受到δts(i0)的影响,当采用导航星历进行计算时,会导致数十纳秒的偏差[2, 4-5]

    式(7)可看做利用精确求得的卫星钟变化来平滑伪距残差,因此δts(i0)经过一段时间才会收敛,才能被用于卫星钟差的计算,经测试,收敛时间大概需要20分钟。

    本文在文献[5]的基础上,利用式(7),对同一系统同一测站观测到的卫星st进行星间做差,消除接收机钟差可得:

    $$ {v_{P_r^{st}\left( k \right)}} = c\left( {\delta {t^t}\left( {{i_0}} \right)-\delta {t^s}\left( {{i_0}} \right)} \right)-{\rm{om}}{{\rm{c}}_{P_r^{st}\left( k \right)}} $$ (8)

    式中,δtt(i0)和δts(i0)分别为卫星ts在历元i0对应的卫星钟差改正数;omcPrst(k)=omcPrt(k)-omcPrs(k)vPrst(k)为卫星ts在历元k对应的伪距观测值残差星间差。

    式(8)与测站无关,采用最小二乘估计即可得到相应卫星的初始时刻钟差改正数δts(i0)。需要指出的是卫星钟差是相对量,采用重心基准$\sum\limits_{s = 1}^n {\delta {t^s}} \left( {{i_0}} \right) = 0 $进行约束,n为历元i0时刻观测到的同一系统卫星个数。

    求出卫星s初始时刻i0的卫星钟差改正数δts(i0)后,历元k时刻卫星s的钟差可以表示为:

    $$ {t^s}\left( k \right) = {t^s}{\left( k \right)_0} + \delta {t^s}\left( {{i_0}} \right) + \sum\limits_{i = {i_0} + 1}^k {\mathit{\Delta }\delta {\mathit{t}^s}\left( i \right)} $$ (9)

    式中,ts(k)0为历元k时刻由导航星历得到的卫星钟差初值;ts(k)为历元k时刻卫星s的钟差。

    为了对本文算法的精度进行分析,采用2014年9月17日(年积日为260天)的全球分布的50个实测跟踪站数据,基于均方根信息滤波单历元解算多系统卫星钟差,测站分布如图 1所示。由于GNSS (Global Navigation Satellite System)观测值是测站与卫星间的相对时间延迟,所以本文所求的卫星钟差是相对于某基准钟的相对钟差。研究表明,基准钟的精度优于10-6 s,相对钟差和绝对钟差对定位的影响是等价的[2]。本文为了保证基准钟的钟差精度及实时估计卫星钟差的需要,以所有跟踪站同一系统的接收机钟差的重心基准作为基准钟,本文所求的同一系统的卫星钟差是相对于该基准钟的相对钟差。

    图  1  GNSS测站分布(地图上中国国界依据中国地图(中国地图出版社出版1:60万,ISBN9787503154032,审图号GS(2009)299)
    Figure  1.  Distribution of GNSS Tracking Stations

    本文对估计的多系统卫星钟差的精度评价采用与武汉大学多系统最终精密卫星钟差做二次差的方法。首先,选取同一系统内某一卫星作为参考星,参考星要尽量选择历元数最多的卫星,做差时GPS、GLONASS、Galileo和BDS选择的参考星依次为G09、R05、E11和C01。为了消除卫星钟差估计时基准钟选择的不同产生的影响,将本文估计的卫星钟差与武汉大学卫星钟差中的相应卫星与参考星的钟差做一次差。然后将计算结果与武汉大学的结果做二次差,这样做可以有效地反映出本文估计的卫星钟差与武汉大学最终精密卫星钟差之间的符合程度[2, 4-5]图 2~图 4分别为GPS、GLONASS、BDS和Galileo系统卫星钟差与武汉大学最终精密卫星钟差二次差的均方根(root mean square,RMS)。从中可以看出,采用本文算法求得的GPS,GLONASS,Galileo和BDS卫星钟差与武汉大学最终精密卫星钟差二次差的均方根都优于0.2 ns,其中GPS所有卫星钟差二次差均方根的平均值为0.145 ns,GLONASS所有卫星钟差二次差均方根的平均值为0.188 ns,BDS和Galileo卫星钟差二次差均方根的平均值为0.139 ns。

    图  2  GPS卫星钟差精度
    Figure  2.  Accuracy of GPS Satellites Clock Offsets
    图  3  GLONASS卫星钟差精度
    Figure  3.  Accuracy of GLONASS Satelllites Clock Offsets
    图  4  BDS和Galileo卫星钟差精度
    Figure  4.  Accuracy of BDS and Galileo Satelllites Clock Offsets

    为了验证算法的正确性,将估计的多模卫星钟差应用于PPP动态定位,并与武汉大学最终精密卫星钟差的定位结果比较。为了排除轨道因素的影响,不同卫星钟差定位解算时,卫星轨道都固定为武汉大学最终精密卫星轨道。选取了多模跟踪站九峰站进行定位试验,本文估计卫星钟差时未使用该站数据,采用GPS、GPS/GLONASS、GPS/BDS、GPS/GLONASS/BDS和GPS/GLONASS/BDS/Galileo 5种不同的动态定位模式,统计了东、北和高三个分量偏差的均方根,从第3小时开始进行精度统计以保证三个方向上偏差小于10 cm。

    图 5图 6分别为采用武汉大学最终精密钟差和本文估计的精密钟差的定位结果。从中可以看出,对于九峰站,本文估计的GPS卫星钟差的定位结果优于武汉大学卫星钟差的定位结果,这主要是因为实验所用的跟踪站在中国境内比较集中,估计的卫星钟差更适用于该区域内测站。无论是对于本文估计的卫星钟差还是武汉大学的卫星钟差,多系统融合定位精度都得到了极大提高,GPS/BDS、GPS/GLONASS/BDS融合定位平面精度优于1 cm,高程方向优于3 cm,由于Galileo卫星数较少,GPS/GLONASS/BDS/Galileo四系统融合定位相对于GPS/GLONASS/BDS融合定位没有明显提高。另外,除了GPS,基于本文估计的卫星钟差的其余四种定位模式的定位结果与基于武汉大学的卫星钟差的定位结果差距在1 cm左右,这一方面可能是由于历元间差分观测值测量噪声变大,估计的卫星钟差精度比基于非差模式的钟差略差,另一方面可能是由于武汉大学估计多系统卫星轨道和钟差时用到九峰站的数据,该站定位结果与武汉大学最终精密卫星钟差内符合性较好。

    图  5  基于武汉大学最终精密钟差的九峰站动态精密单点定位结果
    Figure  5.  Multi-GNSS PPP Results with Satellites Clock Offsets Generated by Wuhan University
    图  6  基于本文估计的精密钟差的九峰站动态精密单点定位结果
    Figure  6.  Multi-GNSS PPP Results with Satellites Clock Offsets Estimated in this Article

    本文多模卫星钟差估计分为两步。首先,采用历元间差分相位观测值求解精确的卫星钟差变化和对流层湿延迟改正;然后,采用非差伪距观测值求解初始时刻卫星钟差改正数。本文不需要采用并行计算的方法,待初始时刻卫星钟差改正数收敛以后即可获得高精度的多模卫星钟差。由于相位观测值历元间差分消除了模糊度参数,而伪距观测值星间差分消除了接收机钟差参数,在保证了卫星钟差精度的基础上,提高了计算效率,该算法非常适合应用于多系统实时卫星钟差估计。

    基于本文算法得到的多模精密卫星钟差与武汉大学最终精密卫星钟差互差优于0.2 ns。精密单点定位结果显示与利用武汉大学最终精密产品的定位结果精度相当,说明基于该算法得到的多模精密卫星钟差完全可以满足高精度导航定位用户的需要。

    http://ch.whu.edu.cn/cn/article/doi/10.13203/j.whugis20220761

  • 图  1   存在柱子的常见场景

    Figure  1.   Common Scenarios with Cylinders

    图  2   全局定位流程图

    Figure  2.   Flowchart of Global Localization

    图  3   激光雷达坐标系

    Figure  3.   Coordinate System of LiDAR

    图  4   地图与实时数据中的圆柱差异

    Figure  4.   Differences Between Map and Online Cylinders

    图  5   非圆柱相似聚类

    Figure  5.   Non-cylinder Similar Clusters

    图  6   对称性约束

    Figure  6.   Symmetry Constraints

    图  7   圆柱间拓扑关系

    Figure  7.   Topological Relationships Among Cylinders

    图  8   实验数据

    Figure  8.   Experimental Data

    图  9   实时LiDAR点云z坐标

    Figure  9.   Online LiDAR Point Cloud’s z Coordinates

    图  10   角度增量设置示意图

    Figure  10.   Explanations of Angle Resolutions

    图  11   圆柱分割评估

    Figure  11.   Evaluations of Pillar Segmentation

    图  12   分割误差与距离的关系

    Figure  12.   Relationship Between Segmentation Error and Distance

    图  13   成功率分布和圆柱数量比例

    Figure  13.   Distribution of Success Rate and Ratio of Pillar Number

    图  14   全局定位结果

    Figure  14.   Results of Global Localization

    图  15   走廊定位效率

    Figure  15.   Localization Efficiency of Corridor

    图  16   定位失败案例

    Figure  16.   Localization Failure Cases

    图  17   位置识别结果

    Figure  17.   Results of Place Recognition

    表  1   实验数据

    Table  1   Experimental Data

    场景场景类型面积/m2扫描数/个圆柱数/个
    1大厅56×285487
    2走廊55×154 5298
    3大厅+走廊60×211 1039
    下载: 导出CSV

    表  2   参数设置

    Table  2   Parameter Setting

    参数
    z1/mz2/mz3/mλωg/mϒε
    -0.32.52.00.20.035.03
    下载: 导出CSV

    表  3   定位成功率

    Table  3   Localization Success Rate

    场景对比方法本文方法
    PWLSWLVWLSPLMPLMPL+SPL
    10.1060.2900.4180.9020.6860.916
    20.1160.4600.4200.6170.4150.589
    30.1120.3660.5230.7940.5520.771
    均值0.1290.3720.4540.7710.5510.759
    下载: 导出CSV

    表  4   平均定位误差/m

    Table  4   Average Localization Errors/m

    场景对比方法本文方法
    PWLSWLVWLSPLMPLMPL+SPL
    10.1070.1410.1530.1090.0730.087
    20.1350.1040.0640.1100.0950.096
    301120.0740.1130.1250.0920.111
    均值0.1180.1060.1100.1150.0870.098
    下载: 导出CSV

    表  5   定位时间/s

    Table  5   Localization Time/s

    场景对比方法本文方法
    PWLSWLVWLSPLMPLMPL+SPL
    10.2240.0722.7001.1820.1220.132
    20.6760.2321.0630.9760.1000.129
    30.6330.2221.3711.6340.1980.213
    均值0.5110.1751.7111.2640.1400.158
    下载: 导出CSV

    表  6   最大F1分数

    Table  6   Maximum F1 Score

    场景M2DPESFScan ContextSPLMPLMPL+SPL
    20.7940.6860.8630.8130.8350.831
    下载: 导出CSV

    表  7   不同候选数量下的成功率

    Table  7   Success Rate Under Different Candidate Numbers

    方法候选数量
    12581015202530354042454850
    M2DP0.7830.7860.7930.7970.8020.8120.8140.8190.8200.8230.8360.8380.8420.8480.850
    ESF0.8620.8800.9050.9170.9250.9350.9400.9430.9450.9460.9500.9510.9520.9520.952
    Scan Context0.9000.9110.9220.9290.9310.9370.9380.9390.9390.9390.9400.9400.9410.9410.941
    SPL0.5730.6560.7680.8170.8550.9020.9300.9390.9450.9490.9520.9520.9520.9530.954
    MPL0.6150.6910.7960.8460.8700.9130.9350.9400.9420.9480.9510.9530.9530.9540.955
    MPL+SPL0.6200.6970.7940.8450.8670.9140.9340.9390.9420.9470.9530.9540.9550.9550.958
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-02-03
  • 网络出版日期:  2023-07-11
  • 刊出日期:  2024-07-04

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