[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86386-en":3,"doc-seo-86386-105":30,"detail-sidebar-cat-0-en-105":92},{"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},86386,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","Rethinking Gaussian Trajectory Predictors Calibrated Uncertainty for Safe Planning","Accurate trajectory prediction underpins safe autonomous navigation in crowded environments, yet many Gaussian trajectory predictors provide confidence values whose statistical reliability is rarely enforced. This work introduces a calibration-focused loss that uses Kernel Density Estimation to approximate the empirical distribution of predicted confidence levels and matches it to the Chi-squared distribution to respect Gaussian assumptions. A Mean Squared Error term preserves mean accuracy. Experiments on real-world datasets show improved confidence reliability and better collision-free planning when integrated with an uncertainty-aware Model Predictive Controller.","Rethinking Gaussian Trajectory Predictors: Calibrated Uncertainty for Safe Planning  \nFatemeh Cheraghi Pouria, Mahsa Golchoubian, and Katherine Driggs-Campbell  \narXiv :2603 . 10407v2 [ cs .RO] 12 Jul 2026  \nAbstract—Accurate trajectory prediction is critical for safe autonomous navigation in crowded environments. While many trajectory predictors output Gaussian distributions, the reliability of their confidence levels often remains unaddressed. This limitation can lead to unsafe or overly conservative motion planning when the predictor is integrated with an uncertainty-aware planner. Existing Gaussian trajectory predictors primarily rely on the Negative Log-Likelihood loss, which is prone to predict over- or under-confident distributions, and may compromise downstream planner safety. This paper introduces a novel loss function for calibrating prediction uncertainty which leverages Kernel Density Estimation to estimate the empirical distribution of confidence levels. The proposed formulation enforces consistency with the properties of a Gaussian assumption by explicitly matching the estimated empirical distribution to the Chi-squared distribution. To ensure accurate mean prediction, a Mean Squared Error term is also incorporated in the final loss formulation. Experimental results on real-world trajectory datasets show that our method significantly improves the reliability of confidence levels predicted by different State-Of-The-Art Gaussian trajectory predictors. We also demonstrate the importance of providing planners with reliable probabilistic insights (i.e., calibrated confidence levels) for collision-free navigation in complex scenarios. For this purpose, we integrate Gaussian trajectory predictors trained with our loss function with an uncertainty-aware Model Predictive Controller on scenarios extracted from real-world datasets, achieving improved planning performance through calibrated confidence levels.https://github.com/fate-79/Rethinking-GaussianTrajectory-Predictors.git  \nI. INTRODUCTION  \nTrajectory prediction is a core challenge for interactive autonomous systems [1] . The importance of trajectory prediction is evident in the context of safe autonomous crowd navigation. When endowed with informative trajectory predictors, downstream planners can effectively maneuver through pedestrian crowds while avoiding collisions.  \nPreviously, researchers focused on deterministic models, which predict a single most-likely future trajectory represented  \nas a sequence of points. However, the need for more realistic motion forecasting drew attention to the probabilistic and multi-modal nature of pedestrian behavior. As a result, later works utilized generative and probabilistic formulations, such as bivariate Gaussian models and Gaussian Mixture Models (GMMs) which enable generation of multiple plausible future trajectories through sampling [2]–[9] . Such predictors facili  \nFatemeh Cheraghi Pouria and Katherine Driggs-Campbell are with the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Champaign, IL 61820 USA (e-mail: fate[meh5@illinois.edu](meh5@illinois.edu); [krdc@illinois.edu](krdc@illinois.edu)) Mahsa Golchoubian is with the Department of Mathematical and Computational Sciences, University of Toronto, Toronto, Canada ([e-email:mahsa.golchoubian@utoronto.ca](e-email:mahsa.golchoubian@utoronto.ca)) (Corresponding  \nauthor: Fatemeh Cheraghi Pouria.)  \ntate uncertainty-aware planning by providing multiple future trajectories and associated probabilities.  \nAs a common practice in the trajectory prediction literature, the assessment of whether a predictor outperforms others and consequently is favorable for integration with a planner is often based only on point-wise accuracy metrics such as Average Displacement Error (ADE) and Final Displacement Error (FDE), or their Best-of-N (BoN) variants for multimodal probabilistic models [10]–[12] . However, a trajectory predictor that exc","cbCailrMUf6DWuJy","https://ap.wps.com/l/cbCailrMUf6DWuJy","pdf",5877672,5,1,9,"English","en",105,"# Introduction\n## Motivation: safe crowd navigation and probabilistic forecasting\n## Limitations of point-wise metrics and unreliable confidence\n# Proposed approach: calibrated uncertainty loss","[{\"question\":\"Why does confidence calibration matter for Gaussian trajectory predictors in planning?\",\"answer\":\"Because the planner relies on the predictor’s probabilistic confidence to judge likely future positions; unreliable confidence can cause unsafe behavior or excessive conservatism.\"},{\"question\":\"What loss function does the paper propose to calibrate uncertainty?\",\"answer\":\"It introduces a model-agnostic loss that estimates the empirical distribution of confidence levels via Kernel Density Estimation and matches it to the Chi-squared distribution under a Gaussian assumption, with an added Mean Squared Error term for mean accuracy.\"},{\"question\":\"How is the method validated and how does it affect motion planning?\",\"answer\":\"Experiments on real-world trajectory datasets show more reliable predicted confidence levels, and the calibrated predictors improve performance when integrated with an uncertainty-aware Model Predictive Controller on scenarios extracted from real-world data.\"}]",1784211431,23,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"rethinking-gaussian-trajectory-predictors-calibrated-uncertainty-for-safe-planning","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/rethinking-gaussian-trajectory-predictors-calibrated-uncertainty-for-safe-planning/86386/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"Why does confidence calibration matter for Gaussian trajectory predictors in planning?","Question",{"text":76,"@type":77},"Because the planner relies on the predictor’s probabilistic confidence to judge likely future positions; unreliable confidence can cause unsafe behavior or excessive conservatism.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What loss function does the paper propose to calibrate uncertainty?",{"text":81,"@type":77},"It introduces a model-agnostic loss that estimates the empirical distribution of confidence levels via Kernel Density Estimation and matches it to the Chi-squared distribution under a Gaussian assumption, with an added Mean Squared Error term for mean accuracy.",{"name":83,"@type":74,"acceptedAnswer":84},"How is the method validated and how does it affect motion planning?",{"text":85,"@type":77},"Experiments on real-world trajectory datasets show more reliable predicted confidence levels, and the calibrated predictors improve performance when integrated with an uncertainty-aware Model Predictive Controller on scenarios extracted from real-world data.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,110,115,120,123,127,130,134],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":22,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":20,"slug":137},19,"General","general"]