Black and Gold VII -External Geometric Quality, Cooperative Ranging, and Admission under the Common Integrity Gate

Black and Gold VII -External Geometric Quality, Cooperative Ranging, and Admission under the Common Integrity Gate C. J Tully Independent Researcher, Engineer Tamworth, NSW, Australia ORCID: 0009-0007-5661-7332 October 2026 This paper is the seventh of the black-and-gold series. It places external geometric quality and cooperative ranging under the common Quasi-Equivalence Index gate. A surrounding beacon array supplies a Fisher information matrix whose smallest eigenvalue is maximized by E-optimal placement. A 22-state north-east-down extended Kalman filter fuses inertial data with bottom-lock and water-track Doppler, depth, acoustic position, heading, and scalar range evaluated at the emission epoch. In a controlled two-vehicle, two-beacon simulation both filters, initialized 4 m from truth, finished a 40 s cruise with 0.02 m terminal error. An external measurement or a cooperative range is admitted into the series only when the updated state continues to satisfy QEI ≥ 0.12. The result is a geometry result under a matching truth model; it is not a sea trial. Golden scaling may be applied afterwards without further check.