Observability Analysis of Initial Relative Orbit Determination of Space Targets with Optical Measurements

Autonomous spacecraft relative navigation has a wide range of applications in the field of on-orbit services. By virtue of its advantages of simplicity, reliability, small size, light weight and long acting distance, the optical camera has become the main measurement device for spacecraft relative navigation. However, since the optical camera can only acquire the line-of-sight information of the target and lacks the distance information, this limits the accuracy of spacecraft relative state estimation. Meanwhile, accurate initial relative orbiting is the foundation and key prerequisite for optical relative navigation. In order to improve the estimation accuracy and convergence speed of optical relative navigation, this paper proposes a method for analysing the observability of the initial relative state based on optical relative navigation. The observability of the initial relative state is analysed, and the method does not involve the operation of the Lie derivative, which significantly reduces the computational complexity of the observability analysis. Finally, the effects of orbital inclination, eccentricity and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$J_{2}$</tex> ingestion on LEO are simulated and analysed.