Polygon Closure Initial Orbit Determination for Low Earth Orbit Space Debris: J2-Corrected Lambert in an Over-Determined Framework

The state-of-the-art optical-only method, Systematic Ranging (Farnocchia et al., 2010), parameterizes each orbit by range (ρ) and range-rate (ρ̇) at a single epoch, and is susceptible to near-zenith degeneracy. This work introduces PC-IOD (M = 4), which overcomes this limitation by using four anchor observations connected through three Lambert arcs with J₂ correction, forming an overdetermined 6 × 4 constraint matrix with a unique solution. A controlled experiment on identical synthetic data (400 km LEO, inclination i = 32.4°, 0.5 arcsec noise, 8-minute optical pass) shows a clear contrast. Systematic Ranging converges to a physically incorrect orbit(a = 4477 km, e = 0.50, angular residual 75 143 arcsec, zero survivors),whereas PC-IOD (M = 4) accurately reconstructs the orbit(a = 6778 km, e ≈ 0, inclination error Δi = 0.00117°) in 227 ms on ARM Cortex-X3 (NEON). The J₂ perturbation contributes approximately 1.27 km of positional drift per pass (≈ 74× the astrometric noise), making J₂-corrected propagation mandatory. Improved TLE quality reduces false-positive collision-avoidance maneuvers, yielding an estimated $2.2M/year in propellant savings for Starlink-scale constellations. CubeSats and nanosatellites with ≤ 1 kg propellant benefit proportionally more. A C++ implementation with NEON optimization (227 ms on Snapdragon 8 Gen 2) is provided, together with Python validation code, a Systematic Ranging comparison script, and complete licensing documentation.