Analysis on error propagation in velocity vector synthesis of deep-space celestial autonomous navigation based on radial velocity measurement

According to the spatial geometrical relations of velocity measurement navigation principle, the determination of the spacecraft's velocity vector in inertial space requires measuring at least three stars' radial velocities. In view of the error propagation problem due to the inevitably existed radial velocity measurement errors, the mapping relationship between the radial velocity measurement error and the velocity determination error is derived. The probability distribution function of velocity determination errors is obtained when the radial velocity measurement errors subject to zero-mean Gaussian distribution, and the analytical expressions of the velocity determination errors' mean and variance under certain condition are achieved. Theoretical and simulation analyses show that the influence of the radial velocity measurement errors on the velocity determination error achieves minimum when the line-of-sights of three stars are orthogonal to each other. Simulation analyses also show how the error propagation process is influenced by the angles between stars. These research results can be used as theoretical bases for the star selection of the celestial autonomous navigation system based on velocity measurement.