[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83148-en":3,"doc-seo-83148-105":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},83148,687197207057,"Sage","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Neural-Enhanced Micro-Kalman Filtering for Satellite Tracking: A Comparative Study","Satellite state estimation is essential for orbital navigation, tracking, and autonomous space operations, yet performance is degraded by uncertainty in process and measurement noise that limits conventional Kalman filtering. The paper introduces a Neural-enhanced micro-Kalman filter (µKF) within an information-form state estimation framework. Using a linearized orbital dynamics model, a lightweight neural scaling mechanism adapts process and measurement noise covariances online while retaining Bayesian filtering structure. Numerical simulations on a linear Gaussian satellite tracking model compare Neural-µKF against KF, EKF, UKF, and an adaptive KF, showing low mean square estimation error with computational advantages.","arXiv :2607 .06830v1 [ ee ss . SY] 7 Jul 2026  \nNEURAL-ENHANCED MICRO-KALMAN FILTERING FOR SATELLITE TRACKING: A COMPARATIVE STUDY  \nMoh Kamalul Wafi  \nDepartment of Engineering Physics  \nInstitut Teknologi Sepuluh Nopember (ITS)  \nSurabaya, Indonesia  \n{[kamalul.wafi}@its.ac.id](kamalul.wafi}@its.ac.id)  \nABSTRACT  \nSatellite state estimation plays a fundamental role in orbital navigation, tracking, and autonomous space operations. Accurate estimation remains challenging due to uncertainties in process and measurement noise, which may degrade the performance of conventional Kalman filtering techniques.  \nThis paper presents a Neural-enhanced micro-Kalman filter (µKF) for satellite tracking based on an information-form state estimation framework. Starting from a linearized state-space model of orbital dynamics, a lightweight neural scaling mechanism is introduced to adapt the process and measurement noise covariances online while preserving the underlying Bayesian filtering structure.  \nThe proposed estimator is formulated within the information-form µKF framework and evaluated through numerical simulations using a linear Gaussian satellite tracking model. Its performance is compared with the classical Kalman filter (KF), the extended Kalman filter (EKF), the unscented Kalman filter (UKF), and an adaptive Kalman filter under identical operating conditions. Simulation results demonstrate that the proposed Neural-µKF accurately tracks the satellite states with consistently low mean square estimation errors (MSEE) . Furthermore, the proposed method achieves estimation performance comparable to, and for selected states slightly better than, the baseline Kalman filter while retaining the computational advantages of the information-form formulation. These results demonstrate that integrating lightweight neural covariance adaptation into the µKF provides an effective and flexible framework for satellite state estimation.  \nKeywords Satellite Tracking · State Estimation · Micro-Kalman Filter · Information Filter · Neural Networks · Adaptive Covariance Scaling  \n1 Introduction  \nSatellite tracking plays a fundamental role in modern aerospace engineering, including orbital navigation, Earth observation, deep-space exploration, and communication systems. Accurate knowledge of a satellite’s position and velocity is essential for trajectory prediction, collision avoidance, attitude determination, and autonomous mission planning. Since direct measurements are inevitably corrupted by sensor inaccuracies and environmental disturbances, reliable state estimation algorithms remain an indispensable component of satellite navigation systems [1,2] .  \nAmong the available estimation techniques, the Kalman filter has become one of the most influential methods for linear stochastic systems since its introduction by Kalman in 1960 [3] . By recursively combining a mathematical model with noisy measurements, the Kalman filter provides the minimum mean-square error estimate under linear Gaussian assumptions. Its theoretical foundation and numerous engineering applications have been extensively studied in the literature, making it a standard tool for aerospace, robotics, navigation, and signal processing problems [4–6] . Numerous improvements have subsequently been proposed to enhance the performance of the classical Kalman filter, including covariance adaptation and gradient-based optimization techniques for uncertain environments [7] .  \nAs estimation problems become increasingly complex, several extensions of the classical Kalman filter have been proposed. For nonlinear systems, the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) ap-  \nFiltering Module on Satellite Tracking  \nproximate the Bayesian filtering problem using linearization and sigma-point transformations, respectively. Adaptive Kalman filtering techniques further improve estimation performance by adjusting the process and measurement noise statistics online when these quantities are unce","cbCaic9p5pxQ8q4g","https://ap.wps.com/l/cbCaic9p5pxQ8q4g","pdf",888238,2,1,15,"English","en",105,"# Introduction\n## Satellite tracking and state estimation challenges\n## Kalman filter and common extensions\n## Information filter and micro-Kalman filter\n## Motivation and paper contributions","[{\"question\":\"Why is satellite state estimation difficult with classical Kalman filtering?\",\"answer\":\"Uncertainties in process and measurement noise can degrade performance, because conventional Kalman filtering relies on assumptions that may not hold under noisy or varying conditions.\"},{\"question\":\"What is the key idea of the Neural-enhanced µKF proposed in the paper?\",\"answer\":\"A lightweight neural scaling mechanism adapts process and measurement noise covariances online, integrated into an information-form micro-Kalman filtering framework while preserving the Bayesian structure.\"},{\"question\":\"How does the proposed Neural-µKF compare to KF, EKF, UKF, and an adaptive Kalman filter?\",\"answer\":\"Simulation results show consistently low mean square estimation errors, with performance comparable to the baseline Kalman filter and slightly better for selected states, while maintaining computational benefits of the information-form formulation.\"}]",1784185620,38,{"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},"neural-enhanced-micro-kalman-filtering-for-satellite-tracking-a-comparative-study","",{"@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/neural-enhanced-micro-kalman-filtering-for-satellite-tracking-a-comparative-study/83148/",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","2026-07-24","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},"Why is satellite state estimation difficult with classical Kalman filtering?","Question",{"text":75,"@type":76},"Uncertainties in process and measurement noise can degrade performance, because conventional Kalman filtering relies on assumptions that may not hold under noisy or varying conditions.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the key idea of the Neural-enhanced µKF proposed in the paper?",{"text":80,"@type":76},"A lightweight neural scaling mechanism adapts process and measurement noise covariances online, integrated into an information-form micro-Kalman filtering framework while preserving the Bayesian structure.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the proposed Neural-µKF compare to KF, EKF, UKF, and an adaptive Kalman filter?",{"text":84,"@type":76},"Simulation results show consistently low mean square estimation errors, with performance comparable to the baseline Kalman filter and slightly better for selected states, while maintaining 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