[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83970-en":3,"doc-seo-83970-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},83970,687197207639,"Asher","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Quaternion-Averaging-Based Adaptive Complementary Filter for Pedestrian Dead Reckoning With a Foot-Mounted AHRS","Pedestrian Dead Reckoning (PDR) supports indoor navigation by estimating walking trajectories without relying on GPS signals, which degrade near roofs and high-rise buildings. For foot-mounted AHRS-based PDR, position accuracy depends on the attitude estimation algorithm. A Quaternion-Averaging-Based Adaptive Complementary Filter (QAACF) is proposed to improve estimation accuracy and reduce computational cost. QAACF fuses quaternions from angular velocity with quaternions from acceleration and magnetic-field measurements using Markley’s rigorous quaternion averaging. Adaptive weighting accounts for gait phases and magnetic disturbance levels, outperforming existing attitude filters in RMSE with lower computational load than Kalman filters.","Quaternion-Averaging-Based Adaptive Complementary Filter for Pedestrian Dead Reckoning With a Foot-Mounted AHRS  \nShunsei Yamagishi, Lei Jing Member, IEEE  \narXiv :2607 .0545 1v 1 [ cs .RO] 5 Jul 2026  \nAbstract—Pedestrian Dead Reckoning (PDR) can be applied to indoor navigation systems. GPS suffers from signal degradation due to roofs and high-rise buildings, whereas PDR can estimate positions without being affected by such signal degradation. The accuracy of a foot-mounted AHRS(Attitude and Heading Reference System)-based PDR depends on the accuracy of the attitude estimation algorithm used in the AHRS. In this article, a Quaternion-Averaging-Based Adaptive Complementary Filter (QAACF) for PDR with a foot-mounted AHRS is proposed to improve estimation accuracy while reducing computational cost. QAACF fuses a quaternion derived from angular velocity with quaternions derived from acceleration and magnetic field measurements using Markley’s quaternion averaging, which combines two quaternions more rigorously than linear interpolation. In addition, QAACF adaptively adjusts the weights of angular velocity, acceleration, and magnetic field measurements according to gait phases and the level of magnetic disturbances. Experimental results showed that the proposed QAACF achieveslow Root Mean Square Errors (RMSEs) compared to existing attitude estimation filters while requiring lower computational cost than Kalman filters.  \nIndex Terms—Quaternion, Quaternion averaging, Complementary filter, Kalman filter, Pedestrian Dead Reckoning, IMU sensor, AHRS, MARG Sensor.  \nI. INTRODUCTION  \nTHE Pedestrian Dead Reckoning (PDR) is a method for  \nestimating a pedestrian’s walking trajectory by accumulating position changes over short periods using inertial and magnetic field data.  \nPDR has the advantage of not relying on external signals and is therefore suitable for indoor navigation systems, unlike the Global Positioning System (GPS) . GPS suffers from signal degradation due to roofs and high-rise buildings, whereas PDR can estimate positions without being affected by such degradation. However, PDR suffers from accumulated estimation errors caused by acceleration and gyroscope sensor drift. In addition, AHRS-based PDR is affected by magnetic disturbances generated by electronic devices surrounding the measurement area.  \nLiu et al. [1] proposed a high-performance PDR algorithm that estimates accelerometer bias by assuming that the accelerometer bias in the body frame is constant and decomposing the attitude matrix. Kuang et al. [2] proposed a PDR method using MARG (Magnetic, Angular Rate, and Gravity) sensors attached to the foot and waist, which improves  \nThis work was supported by NEDO Intensive Support for Young Promising Researchers Grant 21502121-0, JSPS KAKENHI Grant Number 26K02950, Collaborative Research with Toyota Motor Corporation, and JKA and its promotion funds from KEIRIN RACE.  \nThe authors are with Graduate School of Computer Science and Engineering, The University of Aizu, Aizuwakamatsu, Fukushima 965-8580, Japan (e-mail: [d8271107@u-aizu.ac.jp](d8271107@u-aizu.ac.jp); [leijing@u-aizu.ac.jp](leijing@u-aizu.ac.jp)).  \npositioning accuracy by correcting the waist inertial navigation system (INS) using the foot-mounted MARG sensor and improving heading accuracy using magnetic field vector constraints. Bai et al. [3] presented a robust PDR method using a waist-mounted IMU sensor by fusing the adaptive time thresholding algorithm based on the estimated gait period (ATT-EGP), which dynamically adjusts thresholds, and an improved heuristic drift elimination (HDE) algorithm, which corrects heading estimation by recognizing motion states through turning detection. Yoshida [4] proposed an improved PDR method that classifies walking models, including straight walking, right walking, left walking, and stopping, and classifies gait phases into stance and swing using classifiers based on accelerometer and gyroscope data. Lin et al. [5] pr","cbCaig52iPNGXB8f","https://ap.wps.com/l/cbCaig52iPNGXB8f","pdf",23918459,1,15,"English","en",105,"# Introduction\n## Problem with GPS in indoor environments\n## Error accumulation in inertial sensors\n## Magnetic disturbances affecting AHRS-based PDR\n# Proposed QAACF Approach\n## Quaternion averaging via Markley’s method\n## Adaptive fusion across gait phases and magnetic disturbances\n# Experimental Results\n## RMSE comparison with existing filters\n## Computational cost versus Kalman filters","[{\"question\":\"Why is PDR suitable for indoor navigation compared with GPS?\",\"answer\":\"PDR estimates positions by accumulating inertial and magnetic data without external signals, avoiding GPS degradation caused by roofs and high-rise buildings.\"},{\"question\":\"What limits the accuracy of foot-mounted AHRS-based PDR?\",\"answer\":\"Accuracy depends on the attitude estimation algorithm, and PDR also suffers from accumulated errors from sensor drift and heading errors caused by magnetic disturbances.\"},{\"question\":\"How does QAACF improve attitude estimation while reducing computation?\",\"answer\":\"QAACF fuses quaternions from angular velocity with quaternions from acceleration and magnetic-field measurements using Markley’s quaternion averaging, and adaptively adjusts fusion weights based on gait phases and magnetic disturbance levels.\"}]",1784191750,38,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"quaternion-averaging-based-adaptive-complementary-filter-for-pedestrian-dead-reckoning-with-a-foot-mounted-ahrs","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/quaternion-averaging-based-adaptive-complementary-filter-for-pedestrian-dead-reckoning-with-a-foot-mounted-ahrs/83970/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"Why is PDR suitable for indoor navigation compared with GPS?","Question",{"text":74,"@type":75},"PDR estimates positions by accumulating inertial and magnetic data without external signals, avoiding GPS degradation caused by roofs and high-rise buildings.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What limits the accuracy of foot-mounted AHRS-based PDR?",{"text":79,"@type":75},"Accuracy depends on the attitude estimation algorithm, and PDR also suffers from accumulated errors from sensor drift and heading errors caused by magnetic disturbances.",{"name":81,"@type":72,"acceptedAnswer":82},"How does QAACF improve attitude estimation while reducing computation?",{"text":83,"@type":75},"QAACF fuses quaternions from angular velocity with quaternions from acceleration and magnetic-field measurements using Markley’s quaternion averaging, and adaptively adjusts fusion weights based on gait phases and magnetic disturbance levels.","https://schema.org",{"og:url":51,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":45,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":45,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":45,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":45,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":45,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":105,"slug":137},19,"General","general"]