An analytical initial orbit determination method using two observations from a bistatic radar

An analytical initial orbit determination (IOD) method using two observations from a bistatic radar is proposed. Each observation contains bistatic range and the doppler frequency shift, azimuth angle and elevation angle. This problem arises from the challenging catalogue process for small space debris, which features sparse radar observations. By incorporating doppler measurements into the original Lambert's IOD problem which uses two position vectors and can only be solved iteratively, we show that an analytical solution can be obtained. The specific angular momentum conservation equation and the specific mechanical energy equation are used as kinematic constraints. An ad hoc coordinate system is proposed to derive the solution. The geometric dilution of precision (GDOP) metric is analysed to express the IOD accuracy using a linearization method. Simulations are carried out to demonstrate the performance of the proposed method.