{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T05:04:50Z","timestamp":1790139890185,"version":"4.0.1"},"reference-count":35,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T00:00:00Z","timestamp":1789603200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12472359"],"award-info":[{"award-number":["12472359"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]},{"name":"National Natural Science Foundation of China","award":["U2441205"],"award-info":[{"award-number":["U2441205"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]},{"award":["12472359"],"award-info":[{"award-number":["12472359"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"award":["U2441205"],"award-info":[{"award-number":["U2441205"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"State Key Laboratory of Space System Operation and Control"},{"name":"National Key Laboratory of Air-based Information Perception and Fusion"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Persistent angle-only tracking with Walker low-Earth-orbit constellations requires repeated geometric assessment, but optimal sensor-subset selection is computationally costly. To support efficient assessment, a symmetry-reduced differentiable neural information field is proposed to approximate the A-optimal potential of the best feasible sensor subset of a prescribed size. Its two-stage network replaces absolute time with bounded phases derived from axial and finite-permutation symmetries of a relative-periodic Walker constellation under J2. For a 25\u00d725 constellation, symmetry reduction decreased the three-seed mean root-mean-square error from 7.664\u00d710\u22123 to 1.154\u00d710\u22123 relative to a matched two-body encoding; altitude-gradient correlation reached 0.9960. Finite-symmetry closure was verified for Delta, Star, and Rosette. Field accuracy remained within prescribed thresholds for 30 days under matched J2 dynamics. Without orbit maintenance, high-fidelity propagation yielded median and minimum sampled validity horizons of 1.50 and 1.25 days. On historical Iridium trajectories reconstructed from orbital records, three independently trained fields maintained the prescribed accuracy for at least 30 days, demonstrating long-horizon applicability to an operational Walker constellation. Neural triggering reduced penalized mean regret by 91.6% and candidate-pool searches by 93.4%. Full-grid neural inference achieved 17.5-fold CPU and 5567-fold GPU speedups over CPU candidate-pool evaluation.<\/jats:p>","DOI":"10.3390\/s26185902","type":"journal-article","created":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T09:04:17Z","timestamp":1790067857000},"page":"5902","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Symmetry-Reduced Differentiable Neural Information Field for Geometric Angle-Only Trackability Assessment Across Walker Low-Earth-Orbit Sensor Constellations"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-0912-5110","authenticated-orcid":false,"given":"Hengguo","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6488-5990","authenticated-orcid":false,"given":"Kebo","family":"Li","sequence":"additional","affiliation":[{"name":"College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4144-6418","authenticated-orcid":false,"given":"Yangang","family":"Liang","sequence":"additional","affiliation":[{"name":"College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-3434-9039","authenticated-orcid":false,"given":"Yunxiao","family":"Lv","sequence":"additional","affiliation":[{"name":"College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.actaastro.2025.02.019","article-title":"Preliminary Analysis and Design of an Optical Space Surveillance and Tracking Constellation for LEO Coverage","volume":"231","author":"Felicetti","year":"2025","journal-title":"Acta Astronaut."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.actaastro.2018.06.033","article-title":"Non-Iterative Angles-Only Initial Relative Orbit Determination with J2 Perturbations","volume":"151","author":"Perez","year":"2018","journal-title":"Acta Astronaut."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"13227","DOI":"10.1109\/JSEN.2024.3370696","article-title":"On the Information Evolution and Sensor Deployment for Multi-Spacecraft Cooperative Visual 3-D Sensing of Orbital Targets","volume":"24","author":"An","year":"2024","journal-title":"IEEE Sens. 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