Initial Relative-Orbit Determination using Heterogeneous TDOA

This paper presents a solution for the initial orbit determination of a space-based RF transmitter using time-difference- of-arrival (TDOA) measurements obtained from space-based receivers in known orbits. Orbit determination requires six independent TDOA measurements spread over time. The TDOA measurement can be expressed as a quadratic equation for the instantaneous transmitter position. The orbital motion of the transmitter is linearized relative to a reference orbit, which allows the TDOA measurement to be transformed to a quadratic equation for the relative position and velocity components at a chosen initial time. The system of six quadratic equations are solved using homotopy continuation.