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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.