A Guaranteed Geometric Approach and Most Efficient Algorithm for Satellite Collision Avoidance

A Guaranteed Geometric Approach and Most Efficient Algorithm for Satellite Collision Avoidance | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A Guaranteed Geometric Approach and Most Efficient Algorithm for Satellite Collision Avoidance Bao Michael Nguyen, Dale Francis Reding This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8809208/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract A novel geometric collision risk assessment method is introduced that determines the unique minimum separation distance between two covariance ellipsoids representing the positional uncertainty of space objects.By reformulating the problem to find the unique point at which the normal vectors of the uncertainty envelopes are parallel,we eliminate the need for complex sextic polynomial root-finding. The methodology employs a characteristic bisection algorithm generalisable to n-dimensions, guaranteeing a real solution with O(1) complexity regardless of dimensionality. This provides a critical enabling technology fornext-generationAI-enabled Space Traffic Management (STM), facilitating both real-time autonomous decision-making and the integration of high-dimensional non-spatial risk factors. MSCClassification: 65D18,70F16,93C95 Characteristic Bisection Collision Avoidance Covariance Ellipsoid Hyper-ellipsoids Missile Defence O(1) Complexity Space Debris Space Situational Awareness (SSA) Space Traffic Management (STM) Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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