Error analysis for laser-based metric calibration of the Naval Space Surveillance System

The Naval Space Surveillance System is a network of continuous-wave VHF interferometer stations designed to detect Earth satellites. Angular metric data from the system are used in real time to update the catalog of known space objects maintained by the Air Force and Naval components of United States Space Command. For many years, the system has operated with a near real-time calibration of the detector electronics but without a rigorous tie to an external reference frame. One way to establish such a tie is by comparing system measurements with data derived by Satellite Laser Ranging. In principle, public-domain laser ranging data on geodetic satellites can always be used to generate a few high-precision reference orbits whose ephemerides can be compared with surveillance measurements. In the right circumstances, special laser tracking data on aml suitable satellite can be taken simultaneously with surveillance measurements and compared directly. Both approaches offer benefit to space surveillance operations, and both have been demonstrated in previous work. This analysis initiates the analytical investigation of how precisely we can resolve errors in the surveillance measurements, using laser ranging-derived data. Equations are presented which relate surveillance measurement uncertainties to reference data uncertainties in explicit terms. Simple geometric measurement models are considered, rather than detailed physical measurement models, in order to provide fundamental understanding of how errors transform in the two types of calibration considered. The resulting formulae are suitable for deriving calibration requirements and simplified error budgets, either analytically or by numerical simulation.