Initial Orbit Determination Method for Low Earth Orbit Objects Using Too-Short Arc Based on Bistatic Radar

Abstract

The problem of initial orbit determination (IOD) for low Earth orbit (LEO) objects using bistatic radar too-short arc (TSA) observations is addressed. For TSA observations, the traditional IOD methods suffer low accuracy. For LEO objects with stable attitude, the high order kinematic parameters can be obtained from the time derivatives of the radar echo phase. In this paper, we propose an analytical IOD method using bistatic radar TSA observations, which contain the position measurements (bistatic range, azimuth angle, and elevation angle) and the high order kinematic measurements (bistatic velocity, acceleration, and jerk). As the undetermined target state variables constitute a complex system of equations that can only be solved iteratively, we define an auxiliary coordinate system based on the bistatic geometry to help reduce the equations to one unary quartic equation. Further, we derive closed-form expressions of the orbital state. The performance of the proposed method is evaluated using linearization approximations. Numerical simulations are carried out for several typical LEO observation scenarios to demonstrate the performance of the proposed method.