A Symmetry-Reduced Differentiable Neural Information Field for Geometric Angle-Only Trackability Assessment Across Walker Low-Earth-Orbit Sensor Constellations

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 25×25 constellation, symmetry reduction decreased the three-seed mean root-mean-square error from 7.664×10−3 to 1.154×10−3 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.