Initial Orbit Determination Using Very Short Arc Data Based on Double-Station Observation

A method of initial orbit determination (IOD) of a space object, which uses very short arc (VSA) data of double-station observations, is presented. Closed-form solutions of the initial orbit are derived, and these solutions utilize radial measurements (the range, velocity, and acceleration) from two radar stations. The performance of the method based on the geometric dilution of precision (GDOP) metric is analyzed in detail. The analytical approximation expressions of the GDOP metric are also derived, and these expressions can serve as guidance for choosing an observation arc in order to obtain better IOD performance. Comparison of the analytical results with Monte Carlo simulations shows good consistency. Theoretical analysis and simulation results show that several seconds of VSA data can produce an IOD accuracy of several kilometers in position and several meters per second in velocity, provided that highly accurate measurements of phase-derived velocity and acceleration are available.