Article(id=1322161756827407091, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322161562689847927, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1725811200000, receivedDateStr=2024-09-09, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793157527405, onlineDateStr=2026-10-28, pubDate=1756051200000, pubDateStr=2025-08-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793157527405, onlineIssueDateStr=2026-10-28, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793157527405, creator=13701087609, updateTime=1793157527405, updator=13701087609, issue=Issue{id=1322161562689847927, tenantId=1146029695717560320, journalId=1225396423026438145, year='2025', volume='45', issue='8', pageStart='1', pageEnd='278', issueExtLink='null', onlineDate='null', pubDate='1756051200000', pubDateStr='2025-08-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793157481119, creator='13701087609', updateTime=1793158854568, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1322167323411198934, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322161562689847927, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1322167323411198935, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322161562689847927, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=200, endPage=208, ext={EN=ArticleExt(id=1322161757049705205, articleId=1322161756827407091, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=Research and Application of Positioning Technology for Mine Inspection Robot Based on UWB and IMU Fusion, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

A fusion positioning method based on UWB (Ultra Wideband) and IMU (Inertial Measurement Unit) was proposed to address the issues of low positioning accuracy and poor real-time performance of underground inspection robots in mines due to environmental influences. Firstly, the UWB ranging module was used to measure the distance between the inspection robot and the UWB base station. Secondly, a GRU (Gated Recurrent Unit) neural network model was constructed, and the UWB measurement distance and real distance were input into the neural network model for training, resulting in a GRU correction model. Then, the GRU neural network was used to correct the model for the measured distance, suppressing NLOS (Non-Line of Sight) distance errors in complex environments and obtaining more accurate distances than before. Finally, the corrected distance information was combined with the data provided by the IMU through ESKF (Error State Kalman Filter) to construct the error state equation and measurement equation, respectively, to evolve and update the system's error state and calculate more accurate position coordinates. The experimental results show that under three different NLOS environments, the corrected static experimental positioning accuracy is improved by 6.09%, 16.56% and 18.89% respectively, and the positioning accuracy in the composite scene is improved by 11.36% compared to before. In the dynamic experiment, the corrected average positioning accuracy is improved by 11.10% compared to before. By correcting the pseudo range measured under non line of sight, the impact of non line of sight can be reduced and the positioning accuracy can be improved.

, authors=Wenbo KUAI1, 2, Hongwei ZHANG1, 2, Zhonghui PU3, Wei XIAO3, authorsList=Wenbo KUAI, Hongwei ZHANG, Zhonghui PU, Wei XIAO, authorCompany=null, correspAuthors=Hongwei ZHANG, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322161765463479123, articleId=1322161756827407091, tenantId=1146029695717560320, journalId=1225396423026438145, language=CN, title=基于UWB和IMU融合的矿井巡检机器人定位技术研究与应用, columnId=1226462295946085268, journalTitle=矿业研究与开发, columnName=矿山机电与矿业智能化, runingTitle=null, highlight=null, articleAbstract=

针对矿山井下巡检机器人因受环境影响而定位精度低、实时性差等问题,提出了一种基于UWB(超宽带)与IMU(惯性测量单元)的融合定位方法。首先,利用UWB测距模块测量巡检机器人与UWB基站间的距离;其次,构建GRU(门控循环单元)神经网络模型,将UWB测量距离和真实距离输入神经网络模型中进行训练,得到GRU修正模型;然后,通过GRU神经网络修正模型对实测距离的修正,抑制复杂环境下NLOS(非视矩)距离误差,得到较之前更为精确的距离;最后,通过ESKF(误差状态卡尔曼滤波)将修正后的距离信息与IMU提供的数据结合,构建误差状态方程和量测方程,分别对系统的误差状态进行演化和更新,解算出更精确的位置坐标。试验结果表明:在三种不同NLOS环境下,修正后的静态实验定位精度较之前分别提升了6.09%、16.56%、18.89%,且在复合场景下定位精度较之前提升了11.36%;在动态实验中,修正后的平均定位精度较之前提升了11.10%。通过对非视距下测量的伪距进行修正可减小了非视距的影响,提高定位精度。

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蒯文博(1997—),男,河南商丘人,硕士研究生,研究方向为煤矿装备智能检测与控制。E-mail:

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张宏伟(1980—),男,安徽宿州人,博士,教授,研究方向为机电设备智能检测与控制。E-mail:
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Study on the posibility of the PIG positioning using MEMS-based IMU[J]. Chinese Journal of Sensors and Actuators, 2016, 29(1): 40-44., articleTitle=Study on the posibility of the PIG positioning using MEMS-based IMU, refAbstract=null), Reference(id=1322161777694069704, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161756827407091, doi=null, pmid=null, pmcid=null, year=2020, volume=7, issue=4, pageStart=3133, pageEnd=3146, url=null, language=null, rfNumber=[20], rfOrder=35, authorNames=FENG D Q, WANG C Q, HE C L, journalName=IEEE Internet of Things Journal, refType=null, unstructuredReference=FENG D Q, WANG C Q, HE C L, et al. Kalman-filter-based integration of IMU and UWB for high-accuracy indoor positioning and navigation[J]. 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figureFileBig=n2BK5TexHk1sVL/fDL4J4Q==, tableContent=null), ArticleFig(id=1322161772618961820, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161756827407091, language=EN, label=Table 1, caption=

Positioning errors of static experiment under different scenarios

, figureFileSmall=null, figureFileBig=null, tableContent=
试验场景评估指标原始误差/cm修正误差/cm
场景1RMSE16.0915.11
MAE15.9714.85
场景2RMSE20.9617.49
MAE20.9017.41
场景3RMSE37.5930.49
MAE37.5830.45
复合场景RMSE54.9148.67
MAE54.8148.56
), ArticleFig(id=1322161772694459293, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161756827407091, language=CN, label=表1, caption=

不同场景下静态试验定位误差

, figureFileSmall=null, figureFileBig=null, tableContent=
试验场景评估指标原始误差/cm修正误差/cm
场景1RMSE16.0915.11
MAE15.9714.85
场景2RMSE20.9617.49
MAE20.9017.41
场景3RMSE37.5930.49
MAE37.5830.45
复合场景RMSE54.9148.67
MAE54.8148.56
), ArticleFig(id=1322161772778345374, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161756827407091, language=EN, label=Table 2, caption=

Positioning errors of dynamic experiment under composite sence

, figureFileSmall=null, figureFileBig=null, tableContent=
评估指标原始误差/cm修正误差/cm
RMSE27.6624.59
MAE24.5520.98
), ArticleFig(id=1322161772849648544, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161756827407091, language=CN, label=表2, caption=

复合场景下动态试验定位误差

, figureFileSmall=null, figureFileBig=null, tableContent=
评估指标原始误差/cm修正误差/cm
RMSE27.6624.59
MAE24.5520.98
), ArticleFig(id=1322161772916757409, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161756827407091, language=EN, label=Table 3, caption=

Partial experiment data

, figureFileSmall=null, figureFileBig=null, tableContent=
序号实际坐标/cm原始定位/cm修正定位/cm
1(250,250)(246.64,257.70)(247.61,257.23)
2(250,250)(248.93,258.51)(245.92,256.06)
3(250,250)(244.17,268.89)(246.17,265,50)
4(250,250)(243.83,266.23)(245.82,262.85)
5(250,250)(222.67,275.29)(229.27,271.65)
6(250,250)(220.27,277.74)(226.79,273.90)
7(355.85,100)(341.49,90.98)(344.73,94.80)
8(400,344.82)(403.81,335.79)(400.95,336.92)
9(233.44,400)(239.92,405.45)(239.47,401.84)
10(100,247.49)(93.42,249.10)(96.60,250.94)
), ArticleFig(id=1322161773009032098, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322161756827407091, language=CN, label=表3, caption=

部分试验数据

, figureFileSmall=null, figureFileBig=null, tableContent=
序号实际坐标/cm原始定位/cm修正定位/cm
1(250,250)(246.64,257.70)(247.61,257.23)
2(250,250)(248.93,258.51)(245.92,256.06)
3(250,250)(244.17,268.89)(246.17,265,50)
4(250,250)(243.83,266.23)(245.82,262.85)
5(250,250)(222.67,275.29)(229.27,271.65)
6(250,250)(220.27,277.74)(226.79,273.90)
7(355.85,100)(341.49,90.98)(344.73,94.80)
8(400,344.82)(403.81,335.79)(400.95,336.92)
9(233.44,400)(239.92,405.45)(239.47,401.84)
10(100,247.49)(93.42,249.10)(96.60,250.94)
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基于UWB和IMU融合的矿井巡检机器人定位技术研究与应用
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蒯文博 1, 2 , 张宏伟 1, 2 , 蒲忠辉 3 , 肖卫 3
矿业研究与开发 | 矿山机电与矿业智能化 2025,45(8): 200-208
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矿业研究与开发 |矿山机电与矿业智能化 2025 , 45 (8) : 200 -208
基于UWB和IMU融合的矿井巡检机器人定位技术研究与应用
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蒯文博1, 2 , 张宏伟1, 2 , 蒲忠辉3, 肖卫3
作者信息
  • 1.河南理工大学 电气工程与自动化学院,河南 焦作市 454003
  • 2.河南省煤矿装备智能检测与控制重点实验室,河南 焦作市 454003
  • 3.河南龙宇能源股份有限公司,河南 商丘市 476600
通讯作者:
张宏伟(1980—),男,安徽宿州人,博士,教授,研究方向为机电设备智能检测与控制。E-mail:
作者简介:

蒯文博(1997—),男,河南商丘人,硕士研究生,研究方向为煤矿装备智能检测与控制。E-mail:

Research and Application of Positioning Technology for Mine Inspection Robot Based on UWB and IMU Fusion
Wenbo KUAI1, 2 , Hongwei ZHANG1, 2 , Zhonghui PU3, Wei XIAO3
Affiliations
  • 1.School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, Henan 454003, China
  • 2.Henan Key Laboratory of Intelligent Detection and Control of Coal Mine Equipment, Jiaozuo, Henan 454003, China
  • 3.Henan Longyu Energy Co., Ltd., Shangqiu, Henan 476600, China
出版时间: 2025-08-25
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针对矿山井下巡检机器人因受环境影响而定位精度低、实时性差等问题,提出了一种基于UWB(超宽带)与IMU(惯性测量单元)的融合定位方法。首先,利用UWB测距模块测量巡检机器人与UWB基站间的距离;其次,构建GRU(门控循环单元)神经网络模型,将UWB测量距离和真实距离输入神经网络模型中进行训练,得到GRU修正模型;然后,通过GRU神经网络修正模型对实测距离的修正,抑制复杂环境下NLOS(非视矩)距离误差,得到较之前更为精确的距离;最后,通过ESKF(误差状态卡尔曼滤波)将修正后的距离信息与IMU提供的数据结合,构建误差状态方程和量测方程,分别对系统的误差状态进行演化和更新,解算出更精确的位置坐标。试验结果表明:在三种不同NLOS环境下,修正后的静态实验定位精度较之前分别提升了6.09%、16.56%、18.89%,且在复合场景下定位精度较之前提升了11.36%;在动态实验中,修正后的平均定位精度较之前提升了11.10%。通过对非视距下测量的伪距进行修正可减小了非视距的影响,提高定位精度。

巡检机器人  /  融合定位技术  /  惯性测量单元  /  GRU神经网络  /  非视距

A fusion positioning method based on UWB (Ultra Wideband) and IMU (Inertial Measurement Unit) was proposed to address the issues of low positioning accuracy and poor real-time performance of underground inspection robots in mines due to environmental influences. Firstly, the UWB ranging module was used to measure the distance between the inspection robot and the UWB base station. Secondly, a GRU (Gated Recurrent Unit) neural network model was constructed, and the UWB measurement distance and real distance were input into the neural network model for training, resulting in a GRU correction model. Then, the GRU neural network was used to correct the model for the measured distance, suppressing NLOS (Non-Line of Sight) distance errors in complex environments and obtaining more accurate distances than before. Finally, the corrected distance information was combined with the data provided by the IMU through ESKF (Error State Kalman Filter) to construct the error state equation and measurement equation, respectively, to evolve and update the system's error state and calculate more accurate position coordinates. The experimental results show that under three different NLOS environments, the corrected static experimental positioning accuracy is improved by 6.09%, 16.56% and 18.89% respectively, and the positioning accuracy in the composite scene is improved by 11.36% compared to before. In the dynamic experiment, the corrected average positioning accuracy is improved by 11.10% compared to before. By correcting the pseudo range measured under non line of sight, the impact of non line of sight can be reduced and the positioning accuracy can be improved.

Inspection robot  /  Fusion positioning method  /  Inertial measurement unit  /  GRU neural network  /  Non-line of sight
蒯文博, 张宏伟, 蒲忠辉, 肖卫. 基于UWB和IMU融合的矿井巡检机器人定位技术研究与应用. 矿业研究与开发, 2025 , 45 (8) : 200 -208 .
Wenbo KUAI, Hongwei ZHANG, Zhonghui PU, Wei XIAO. Research and Application of Positioning Technology for Mine Inspection Robot Based on UWB and IMU Fusion[J]. Mining Research and Development, 2025 , 45 (8) : 200 -208 .
矿业是国民经济发展的重要支柱性产业,但矿山井下工作环境恶劣,灾害频发,造成伤亡事故。矿井机器人在现代矿业中扮演着越来越重要的角色,其中危险气体巡检机器人能够代替人工进入含有危害气体的环境,并能实现长时间井下作业,从而减少人员伤亡[1]。因此,为满足矿业安全生产以及井下救援需求,研发和应用巡检机器人对排除井下安全隐患具有重大意义,而定位精度是实现巡检机器人精确控制的关键因素。但由于矿井中机器人的定位受限于非视距(Non-Line of Sight, NLOS)的影响严重,传统的单个传感器已不满足巡检机器人定位需求[2-4]。
近年来,多个传感器融合定位已然成为研究热点。LANDOLSI等[5]使用UKF算法提供的递归最小均方误差估计技术以及基于视距(Line of Sight, LOS)与非视距假设下的概率密度函数实现了高可靠性的LOS/NLOS分类,使得超宽带(Ultra Wide Band, UWB)定位性能得到了提升。杨秀建等[6]提出了改进的UKF算法将UWB、惯性测量单元(Inertial Measurement Unit, IMU)和里程计编码信息进行集中式融合,利用Sage-Husa滤波器估计更新噪声,引入渐消因子,避免滤波器发散,提高了滤波速率,实现了机器人实时定位。
扩展卡尔曼滤波(EKF)是常见用于融合定位的滤波之一。张晓莉等[7]通过RFID电子标签提供的真实位置信息,结合EKF对捷联惯导产生的累计误差进行修正,提高了巡检机器人的定位精度。张斌飞等[8]使用EKF对UWB和IMU组合定位,并将最小二乘算法和Taylor算法结合,有效抑制了UWB测距精度低、受基站布局影响大的问题。
徐庆坤等[9]设计了一种融合UWB与里程计的定位系统,UWB定位的随机误差和非视距能有效地抑制误差,使移动机器人的定位精度与可靠性都得到了提升。近年来,学者们将神经网络应用于目标定位研究。古玉锋等[10]提出了一种基于神经网络与自调节卡尔曼滤波的超宽带定位算法,利用UWB定位标签和基站之间的距离以及相应的定位信息,建立神经网络模型。将实际位置作为输出进行训练,通过实时测距得到实时的定位坐标。
UWB定位技术具有定位精度高、可靠性强、实时性好等优势,单独使用UWB对机器人定位时,易受多径效应、环境干扰以及非视距等的影响,使得其定位结果有较大的波动性[11]。IMU具有高精度、高稳定性,兼具较强的耐用性和抗干扰性,能够应对巡检机器人在矿井下复杂环境中振动和干扰的影响。但IMU单独定位时,存在积分漂移和累计误差等问题,长时间使用会导致定位误差逐渐增大[12]。因此,为解决矿井下NLOS对巡检机器人定位产生的影响,采取UWB与IMU融合定位,选取对UWB测距修正的方法来减小NLOS带来的误差[13]。引入门控循环单元(Gate Recurrent, GRU)神经网络[14]修正模型,对UWB测量距离进行修正,将修正后的距离作为量测更新,IMU测量数据作为预测,将修正前后的测距信息输入误差状态卡尔曼滤波(Error State Kalman Filtering, ESKF)中进行融合定位,并通过非视距条件下的静态和动态定位试验验证了该方法的有效性。
TOA(到达时间)[15]测距方法是通过UWB基站与标签之间的多次通信实现的。基于TOA测距原理,提出一种双边双向测距算法(Double Sided-Two-WayRanging,DS-TWR),该算法不仅考虑了来自单个标签的数据,还从两个不同方向上同时获取信息,算法模型如图1所示。UWB基站在T1时刻向标签发送数据包,在T′1时刻由标签B接收,然后标签对该数据包加以处理后在T′2时刻同时发射响应性质和请求性质的信号,基站在T2时刻接收,处理一段时间后在T3时刻回复响应信号,模块在T′3时刻接收。计算出两个超宽带模组间的传输时间Tr,再与光速c相乘,即可求出两个基站与标签间的距离,见式(1)、式(2)。
式中:Tro1=T2-T1、Tro2=T′3-T′2、Tre1=T′2-T′1、Tre2=T3-T2;T1、T2分别为基站第一次发出信号与第一次接收到信号的时间;T3为基站第二次发出信号的时间;T′1、T′2分别为标签第一次收到信号与回复信号的时间;T′3为标签第二次接收到信号的时间;c为光速,c=3×108 m/s。
采用UWB对矿井巡检机器人进行定位时,NLOS误差的影响会使UWB信号传播时间变长、信号衰减以及出现反射等现象,这些因素会显著降低测距精度,影响定位精度。
为减小矿井下NLOS环境对巡检机器人定位的影响,通过GRU神经网络模型对测距误差进行修正。GRU神经网络结构如图2所示。相比于长短期记忆(LSTM)神经网络[16],GRU神经网络模型的结构简单,参数更少,训练速度更快,能够有效处理长序列和短序列数据,其灵活的网络结构可以根据具体任务进行调整和优化,适用于不同规模和类型的数据。此外,GRU具有自适应样本权重选择能力,当非视距误差出现异常波动时,GRU会选择忽略,从而提高输出结果的准确性。
根据UWB标签与各个基站之间的距离建立神经网络模型。通过各个节点之间的相互连接关系进行数据处理,对原始UWB数据进行预处理并将其划分为训练集和测试集;训练集输入GRU网络进行模型训练,再使用测试集验证预测效果;将实测距离信息输入训练好的模型,得到修正后的精确距离值。
假设输入序列为UWB模块测量距离值序列{d1,d2,…di,…,dt},将其转换成特征向量序列的形式,计算过程如下[17]:
GRU更新门zt计算:
GRU重置门rt计算:
计算候选隐藏状态n:
更新记忆状态ct和隐藏状态ht:
利用隐藏状态进行最终距离的预测:
式中:Wz、Wr、W分别为更新门、重置门和候选门的权重矩阵;Uz、Ur、U为用于输入和真实距离之间的权重函数;bz、br、b分别为更新门、重置门和候选状态的偏置向量;dt为测量距离值的特征向量;xt为当前步的其他特征向量;σ为Sigmoid函数;[·,·]为向量的串联操作;e为偏置项;Ŝt为输出预测值;V为权重矩阵。
计算模型输出与实际距离之间的损失,并通过方向传播更新模型参数,使得损失最小化。通过最小化损失函数,可以优化网络参数,使得神经网络能更好地预测真实距离。
均方误差损失函数:
式中:m为样本特征维度;Si为真实值;Ŝi为模型输出值。
加权损失函数:
式中,wi为第i个样本的权重。
设定阈值ε,当(Si-Ŝi)2>ε时,wi=0;否则,wi=1。该设定可使训练过程中GRU模型能够忽略那些误差过大的样本,从而提高模型的准确性。
IMU与UWB融合定位时,需要将IMU载体坐标系(B系)转换到UWB所在的导航坐标系(N系)[18]。假设载体坐标相对于导航坐标系的旋转角度ψ为偏航角(Yaw角),则由B系到N系的旋转矩阵为:
式中:为采样周期;为k-1时刻N系的角速度。
IMU定位原理的数学模型为:
式中:pk、vk、qk分别为巡检机器人在k时刻的位置、速度和姿态;ak为k时刻的加速度;g为重力加速度;为k时刻N系下的角速度;Ωk为k时刻四元数更新矩阵。
基于UWB和IMU融合的井下巡检机器人定位原理如图3所示。首先将UWB测距模块在NLOS环境下测量的距离与现场实际距离值输入GRU神经网络进行训练,得到修正模型;采用训练后的GRU神经网络模型对在NLOS环境下测得距离值进行修正;同时,借助IMU采集的加速度和角速度等数据,利用惯性导航系统计算其状态信息[19];将修正后的距离值输入ESKF中,结合IMU计算的位置信息构建测量方程,进行状态更新,从而获得更精确的定位信息。
由于IMU存在固有的定位误差,且这种误差随着时间的推移而逐渐积累和扩展。为了确保定位精度和可靠性,必须确定IMU的当前误差状态,并据此调整其估计值以适应环境变化。为此,设计了一套修正方案,对井下巡检机器人所处的位置、速度、姿态、加速度等参数的误差状态进行系统的评估和更新。通过将这些参数转换为特定的误差状态向量,机器人能够实时监测并更新自身的定位状态。设计巡检机器人的位置误差δp、速度误差δv、姿态误差δΦ、加速度零偏误差δβ以及陀螺仪零偏误差δμ为误差状态向量,误差状态方程为:
式中:δX=[δp δv δΦ δβ δμ]T为误差状态向量;F为误差状态转移矩阵;G为误差状态控制矩阵;α为系统过程噪声。
预测误差协方差矩阵为:
式中:B为预测的误差协方差矩阵;Q为系统过程噪声的协方差矩阵。
在试验过程中,由于IMU采集数据的速度非常快,这就要求将原本用于描述系统动态特性和响应的连续时间方程转换为可以精确刻画离散状态变量的离散系统方程:
式中:Φ为状态转移矩阵;s为噪声;I为单位矩阵。
由于传感器误差累积,IMU在长时间使用后可能出现定位或导航精度下降,因此需要对误差状态进行修正更新,其观测方程为:
式中:Yk为观测量;f(Xk)为系统真实状态的一般非线性函数;τ为高斯白噪声。
在ESKF中,需要针对误差状态构建雅可比矩阵:
计算偏导数对其使用链式法则:
式中,为f(Xk)相对自身参数的标准雅可比矩阵。
通过对雅可比矩阵的计算即可实现量测更新,则误差状态卡尔曼滤波量测更新方程为:
式中:Kk+1为定位标签在k+1时刻的误差卡尔曼滤波增益;Pk+1|k为定位标签在k+1时刻的先验估计协方差;H为定位标签中UWB的状态量到实际测量的转移矩阵;M为定位标签在定位过程中的测量噪声阵;Xk+1|k+1为k+1时刻的后验估计状态矩阵;Pk+1|k+1为k+1时刻的后验估计误差协方差。
至此,已完成IMU误差状态与更新机制设计,通过对误差状态的更新可以进一步提高定位精准度。将IMU误差状态方程纳入ESKF中,利用IMU所获得的数据,计算各时间点巡检机器人与UWB基站的间距l,并与神经网络修改后的UWB测得的距离lk差值建立测量方程,则状态向量更新方程为[20]:
式中:Ek+1为k+1时刻更新后的状态;Ek为k时刻的后验估计值;J为卡尔曼滤波增益;O为惯性导航系统解算的巡检机器人位置;Ou为UWB基站位置。
矿井巡检机器人作业环境具有较高的复杂性和危险性。针对巡检机器人在矿井下复杂环境中会受到不同程度NLOS影响的情况,设计了三种实际场景下的试验方案,如图4所示。
场景1:定位基站与定位标签之间的障碍物采用混凝土、墙壁或岩石等模拟矿井中矿石与岩石等障碍物;场景2:井下矿道错综复杂的分布会导致信号产生多径传播,采用设置多个障碍物来模拟该场景;场景3:定位基站与定位标签之间的障碍物采用金属结构或金属支架模拟矿井中的金属设备等障碍物。
本文采用均方根误差(Root Mean Square Error, RMSE)和平均绝对误差(Mean Absolute Error, MAE)作为性能评估指标,对比分析不同条件下和修正模型下的测距数据,评估定位精度的改进效果。
试验场地为500 cm×500 cm的正方形区域,其中主基站A坐标为(0 cm,0 cm),次基站B、C、D坐标分别为(500 cm,0 cm)、(500 cm,500 cm)、(0 cm,500 cm)。小车以0.1 m/s的速度运行,运动轨迹为300 cm×300 cm的正方形。UWB定位系统集成了先进的DW1000芯片与高性能的STM32F103c8t6微处理器,该系统采用了专为高频信号设计的棒状全向高频天线,可保证信号的全向性和稳定性。其通信能力强大,能在各种环境条件下实现远距离通信,最大通信距离可达130 m。IMU数据通过MPU9250模块采集,该模块采用集成封装技术,体积小、质量轻,适用于移动设备。
在NLOS影响下进行试验并利用UWB测量出的伪距对神经网络模块进行训练。UWB在NLOS环境下的测距值修正步骤如下。
(1)在试验场地使用UWB测距模块沿300 cm×300 cm的四条边各等距选择300个点,测量每个点与基站之间的距离并记录真实距离。在三种试验场景下分别进行测量。
(2)初始化神经网络模型参数,将UWB模块测量的距离作为输入,实际值作为输出对神经网络进行训练,得到神经网络修正模型。
(3)将小车置于三种试验的场景下运动,并通过数据采集模块测得实时数据,将测量出的数据放入GRU修正模型进行修正,得出更为准确的距离,为滤波融合做准备。
完成神经网络训练后,对在NLOS环境下采集的数据进行修正。选取点(250 cm,250 cm)到基站B(500 cm,0 cm)的测距数据进行修正,修正结果对比如图5所示。可见NLOS情况下,标签与基站之间传播信号发生变化,导致UWB测出的伪距发生变化,进而影响定位精准度,修正后的测距精度得到显著提升。
为验证矿井复杂环境下巡检机器人通过UWB和IMU进行融合定位的精度,试验模拟NLOS环境,并通过神经网络修正模型对NLOS环境下的测距进行修正,对修正前后的测距信息分别进行静态与动态定位试验。
试验场景1下,静态试验定位结果与定位误差如图6所示。
试验场景2下,静态试验定位结果与定位误差如图7所示。
试验场景3下,静态试验定位结果与定位误差如图8所示。
选取场景1和3复合障碍物进行静态试验,模拟巡检机器人在矿井中遇到多种复杂环境时的定位情况。复合障碍物下的定位结果与定位误差如图9所示。不同场景下静态试验定位误差见表1。
由表1可知,采用RMSE指标评估时,修正后各场景下的平均定位精度均有显著提升。与修正前相比,修正后场景1、场景2、场景3、复合场景下的定位精度分别提升了6.09%、16.56%、18.89%、11.36%。试验结果表明,针对不同的NLOS环境产生的定位误差,通过修正模型对非视距测量距离进行修正,均能有效提高定位精度。
为模拟巡检机器人在运动时的定位情况,试验将小车置于场景1、场景2、场景3的复合场景下,控制其沿相同的轨迹运动。试验中采集复合场景下UWB模块的原始测距作为修正前的实测距离值,随后采用神经网络对其进行修正,将修正前后的数据作为ESKF的量测输入进行融合定位。通过该试验来模拟巡检机器人在井下受到NLOS环境影响后产生的定位误差,定位结果如图10所示。复合场景下动态试验定位误差见表2,部分试验数据见表3。
由表2可知,采用RMSE指标评估时,复合场景下修正后的定位精度较修正前提升了11.10%,结合图10可以看出,经过神经网络修正后的定位轨迹较修正前更贴近于实际轨迹。
为解决矿井下NLOS对巡检机器人定位精度产生的影响,提出一种基于UWB和IMU的融合定位方法。通过GRU神经网络对UWB测距进行修正,将IMU测量数据作为预测,并将修正前后的数据输入ESKF进行融合定位。
针对巡检机器人在矿井下复杂环境中会受到不同程度NLOS影响的情况,设计了三种实际场景下的试验方案。试验结果表明,三种场景下修正后的静态试验定位精度较修正前分别提升了6.09%、16.56%、18.89%,且在复合场景下平均定位精度较修正前提升了11.36%;修正后的动态试验定位精度较修正前提升了11.10%。通过对非视距下测量的伪距进行修正可减小非视距的影响,提高定位精度。
  • 河南省高校科技创新团队项目(20IRTSTHN019)
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2025年第45卷第8期
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  • 接收时间:2024-09-09
  • 首发时间:2026-10-28
  • 出版时间:2025-08-25
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  • 收稿日期:2024-09-09
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河南省高校科技创新团队项目(20IRTSTHN019)
作者信息
    1.河南理工大学 电气工程与自动化学院,河南 焦作市 454003
    2.河南省煤矿装备智能检测与控制重点实验室,河南 焦作市 454003
    3.河南龙宇能源股份有限公司,河南 商丘市 476600

通讯作者:

张宏伟(1980—),男,安徽宿州人,博士,教授,研究方向为机电设备智能检测与控制。E-mail:
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