[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83988-en":3,"doc-seo-83988-105":28,"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":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":13,"seo_description":14,"update_tm":26,"read_time":27},83988,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Physics-Regularized Machine Learning for Proprioceptive Vehicle Localization Using Onboard Sensors","Accurate and robust vehicle localization is critical for autonomous mobility in real-world settings, yet GNSS outages cause rapid drift when relying on IMU-only dead reckoning. The document presents Physics-Regularized Machine Learning for Localization (PRML2), a hybrid approach that fuses Kalman filtering with end-to-end data-driven learning. A differentiable EKF regularizes a transformer-based model to improve physical consistency, localization accuracy, and generalization. Results on a public dataset show real-time capability limits and superior accuracy. A new low-friction dataset supports research under degraded conditions.","Physics-Regularized Machine Learning for Proprioceptive Vehicle Localization Using Onboard Sensors  \nAbinav Kalyanasundaram 1 , Karthikeyan Chandra Sekaran 1 , Wolfgang Utschick2 and Michael Botsch 1  \narXiv :2607 .05663v 1 [ cs .RO] 6 Jul 2026  \nAbstract—Accurate and robust localization is essential for autonomous mobility systems in real-world environments. While fusing Inertial Measurement Unit (IMU) data with satellite-based correction signals provides precise vehicle pose estimates, performance degrades substantially during outages. Recent studies indicate that Machine Learning (ML) can improve IMU-based proprioceptive localization, highlighting untapped potential for onboard sensors readily available in production vehicles. This paper introduces Physics-Regularized Machine Learning for Localization (PRML2), a hybrid framework that combines the complementary strengths of Kalman filtering and data-driven learning to estimate vehicle pose directly from onboard sensors. A key aspect of PRML2 is its physics-regularized learning, enabled by end-to-end training of an ML model through a differentiable Kalman filter. This improves consistency with vehicle motion models, thereby enhancing both localization accuracy and generalization across driving conditions. We evaluate the performance limits of MLenhanced onboard odometry on a publicly available dataset and show that PRML2 achieves superior localization accuracy and demonstrates real-time capability. This work also introducesa novel dataset to support vehicle localization research under low-friction conditions. The proposed framework provides a robust and cost-effective solution for vehicle localization under degraded sensing conditions by integrating learning with physics-based priors.  \nI. INTRODUCTION  \nPrecise localization is crucial for the safe and reliable operation of autonomous vehicles. The knowledge about the ego vehicle’s pose acts as a foundation for critical downstream tasks such as path planning, motion control, and decisionmaking [1] . Accurate localization is typically achieved by fusing an IMU with Global Navigation Satellite System (GNSS) measurements [2] . However, during GNSS outages, dead reckoning based on commercial-grade IMUs rapidly degrades due to drift accumulation [3] . While fusing IMUs with cameras and LiDAR can reduce drift, such approaches increase system cost, complexity, and are sensitive to environmental conditions [4] . Alternatively, commonly available onboard sensors such as steering wheel angle, wheel speeds, and yaw rate provide valuable odometry signals for vehicle localization [5], [6] . Being proprioceptive, they can measure vehicle motion independently without reliance on external signals or the environment. Therefore, exploring the achievable performance of vehicle localization using only onboard sensors is critical for robust and cost-effective autonomy under degraded GNSS conditions.  \n1AImotion Bavaria, Technische Hochschule Ingolstadt, Germany, [firstname.lastname@thi.de](firstname.lastname@thi.de)  \n2Technische Universitt M¨unchen, Germany, [utschick@tum.de](utschick@tum.de)  \nFig. 1: Overview of the test vehicle configuration and the objective of PRML2 for proprioceptive localization.  \nState-of-the-art (SOTA) methods for vehicle localization during GNSS outages can be broadly categorized into three groups: HD map–based methods, multi-sensor fusion techniques, and dead-reckoning approaches [7] . HD map–based methods achieve high localization accuracy but require prebuilt and continuously maintained maps [4] . Multi-sensor fusion techniques, such as VINS, LiDAR-IMU odometry, and SLAM, often require expensive sensors and can be sensitive to environmental conditions [4], [8] . In contrast, dead reckoning based on IMUs or onboard sensors is proprioceptive and inexpensive, yet prone to drift [8] . Classical Bayesian filters for IMUs generalize well but are limited by noise accumulation, leading to significant drift during GNSS outa","cbCaij14rNdUYHJ4","https://ap.wps.com/l/cbCaij14rNdUYHJ4","pdf",3061869,1,"English","en",105,"# Introduction\n## Localization challenges during GNSS outages\n## Proprioceptive onboard sensing and odometry\n## Motivation for hybrid ML with physics priors\n# PRML2 Framework\n## End-to-end training via differentiable EKF\n## Transformer-based model with physics guard layer\n## Contributions and evaluation direction","[{\"question\":\"Why does vehicle localization degrade during GNSS outages?\",\"answer\":\"When GNSS signals are unavailable, pose estimation relies on dead reckoning from IMUs, where drift accumulates rapidly, reducing accuracy.\"},{\"question\":\"What is PRML2 and how does it combine learning with physics?\",\"answer\":\"PRML2 is a hybrid framework that trains a transformer-based model end-to-end through a differentiable EKF, using the Kalman filter as a physics-regularized constraint to enforce physical and temporal consistency.\"},{\"question\":\"What sensors does PRML2 use and what problem does this address?\",\"answer\":\"PRML2 relies exclusively on onboard sensors such as steering wheel angle, wheel speeds, and yaw rate, enabling robust and cost-effective localization without external satellite or environment-dependent measurements.\"}]",1784191882,20,{"code":4,"msg":29,"data":30},"ok",{"site_id":23,"language":22,"slug":31,"title":13,"keywords":32,"description":14,"schema_data":33,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":26},"physics-regularized-machine-learning-for-proprioceptive-vehicle-localization-using-onboard-sensors","",{"@graph":34,"@context":84},[35,52,67],{"@type":36,"itemListElement":37},"BreadcrumbList",[38,42,46,49],{"item":39,"name":40,"@type":41,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":43,"name":44,"@type":41,"position":45},"https://docshare.wps.com/document/","Document",2,{"item":47,"name":12,"@type":41,"position":48},"https://docshare.wps.com/document/research-report/",3,{"item":50,"name":13,"@type":41,"position":51},"https://docshare.wps.com/document/physics-regularized-machine-learning-for-proprioceptive-vehicle-localization-using-onboard-sensors/83988/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":22,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":39,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"Why does vehicle localization degrade during GNSS outages?","Question",{"text":74,"@type":75},"When GNSS signals are unavailable, pose estimation relies on dead reckoning from IMUs, where drift accumulates rapidly, reducing accuracy.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What is PRML2 and how does it combine learning with physics?",{"text":79,"@type":75},"PRML2 is a hybrid framework that trains a transformer-based model end-to-end through a differentiable EKF, using the Kalman filter as a physics-regularized constraint to enforce physical and temporal consistency.",{"name":81,"@type":72,"acceptedAnswer":82},"What sensors does PRML2 use and what problem does this address?",{"text":83,"@type":75},"PRML2 relies exclusively on onboard sensors such as steering wheel angle, wheel speeds, and yaw rate, enabling robust and cost-effective localization without external satellite or environment-dependent 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