[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81752-en":3,"doc-seo-81752-105":30,"detail-sidebar-cat-0-en-105":91},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81752,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","Iterated Invariant EKF for 3D Landmark-Aided Inertial Navigation","Inertial navigation aided by 3D landmark measurements is a core robotic perception and state estimation problem. Classical SO(3)-based Extended Kalman Filters can become overconfident in unobservable directions, harming estimation. The Invariant EKF reformulates dynamics on a Lie group, yet its measurement update may violate state compatibility properties. This work applies the Iterated Invariant EKF to landmark-based inertial 3D localization, showing improved accuracy and consistency over SO(3)-EKF, Iterated SO(3)-EKF, and IEKF in simulations.","arXiv :2607 .00145v2 [ cs .RO] 10 Jul 2026  \nIterated Invariant EKF for 3D Landmark-Aided  \nInertial Navigation ⋆  \nHilton Marques Souza Santana 1[0000−0002−2840−2904], Jo˜ao Carlos Virgolino Soares2[0000−0002−6278−378X], and Marco Antonio Meggiolaro 1[0000−0002−6240−8189]  \n1 Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil  \n[hiltonmarques@gmail.com](hiltonmarques@gmail.com)  \n2 Dynamic Legged Systems Lab, Istituto Italiano di Tecnologia, Genova, Italy  \nAbstract. Inertial navigation systems aided by three-dimensional landmark measurements constitute a fundamental problem in robotic perception and state estimation. Classical SO(3)-based Extended Kalman Filter (SO(3)-EKF) approaches provide practical solutions, but suffer from the false observability problem, in which the filter becomes overconfident in unobservable directions, leading to degraded estimation performance.  \nThe Invariant EKF (IEKF) addresses this limitation by reformulating the system dynamics as a group-affine system on a Lie group, although its measurement update does not fully satisfy certain state compatibility properties. More recently, the Iterated Invariant EKF (IterIEKF) was proposed to further improve the IEKF by ensuring, in the low-noise regime, that the estimated state remains on the observed state manifold while the uncertainty is confined to its tangent space. In this work, we formulate and apply the IterIEKF to landmark-based inertial 3D localization for the first time. Through numerical simulations, we show that the proposed approach outperforms the classical SO(3)-EKF, the Iterated SO(3)-EKF, and the IEKF in terms of both estimation accuracy and consistency.  \nKeywords: Kalman Filter · Localization · Sensor Fusion.  \n1 Introduction  \nThe necessity of estimating the state of a mobile system, including its position, orientation, and velocity, has been a fundamental challenge throughout the history of navigation. The use of celestial landmarks for localization spans several millennia. In particular, mariners in the Northern Hemisphere estimated their latitude by measuring the elevation of the North Star (Polaris) above the horizon [1, pg. 2] . These early navigation techniques relied on identifiable, static features in the environment, giving rise to the modern notion of landmarks as fixed  \n⋆ This study was financed in part by the Coordena¸c˜ao de Aperfei¸coamento de Pessoal de N´ıvel Superior – Brasil (CAPES)– Finance Code 001 and the Funda¸c˜ao de Amparo `a Pesquisa do Estado do Rio de Janeiro (FAPERJ) .  \n2 H. Santana et al.  \nreference points that can be repeatedly observed to infer an agent’s state. During the mid-twentieth century, the success of the Apollo missions demonstrated that robust navigation required not only observations of external landmarks, such as stars, but also accurate inertial measurements from accelerometers and gyroscopes. The fusion of inertial and exteroceptive sensing established many of the principles that underpin modern state estimation. Since the early 2000s, the emergence of Micro Aerial Vehicles (MAVs), together with the widespread availability of sophisticated sensing technologies, including RGB-D cameras, LiDARs, and high-performance embedded computing platforms, has enabled realtime state estimation and map reconstruction in increasingly complex environments [11] . These technological advances have made it practical to address the Simultaneous Localization and Mapping problem [9] .  \nThe classical algorithmic foundation for landmark-based localization for autonomous mobile robots was established in [15] . This framework relies on two key stages: landmark detection within the scene, followed by data association (or matching), which evaluates whether an observed feature has been previously cataloged or represents a new landmark. In this work, we consider a 3DMAV navigating with inertial sensors through an environment where a prior map has already been constructed and features are uniqu","cbCaio6pZ5oFNWMu","https://ap.wps.com/l/cbCaio6pZ5oFNWMu","pdf",8988637,2,1,20,"English","en",105,"# Introduction\n## Background and motivation\n## Landmark-aided inertial navigation and filtering approaches","[{\"question\":\"What limitation affects classical SO(3)-EKF in landmark-aided inertial navigation?\",\"answer\":\"Classical SO(3)-EKF suffers from the false observability problem, where the filter becomes overconfident in unobservable directions, degrading estimation performance.\"},{\"question\":\"How does the Iterated Invariant EKF improve on the IEKF?\",\"answer\":\"Iterated Invariant EKF further refines the IEKF so that, in the low-noise regime, the estimated state stays on the observed state manifold and uncertainty is confined to its tangent space.\"},{\"question\":\"What do the numerical simulations demonstrate in this work?\",\"answer\":\"Simulations show the proposed IterIEKF approach outperforms the SO(3)-EKF, Iterated SO(3)-EKF, and IEKF in both estimation accuracy and consistency for 3D landmark-based inertial localization.\"}]",1784175824,50,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"iterated-invariant-ekf-for-3d-landmark-aided-inertial-navigation","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/iterated-invariant-ekf-for-3d-landmark-aided-inertial-navigation/81752/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-25","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What limitation affects classical SO(3)-EKF in landmark-aided inertial navigation?","Question",{"text":75,"@type":76},"Classical SO(3)-EKF suffers from the false observability problem, where the filter becomes overconfident in unobservable directions, degrading estimation performance.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the Iterated Invariant EKF improve on the IEKF?",{"text":80,"@type":76},"Iterated Invariant EKF further refines the IEKF so that, in the low-noise regime, the estimated state stays on the observed state manifold and uncertainty is confined to its tangent space.",{"name":82,"@type":73,"acceptedAnswer":83},"What do the numerical simulations demonstrate in this work?",{"text":84,"@type":76},"Simulations show the proposed IterIEKF approach outperforms the SO(3)-EKF, Iterated SO(3)-EKF, and IEKF in both estimation accuracy and consistency for 3D landmark-based inertial 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