摘要：The technology of satellite formation flying has being a research focus in flight application. The relative position and velocity between satellites are basic parameters to achieve the control of formation flight during the satellite formation flying mission. In order to improve the navigation accuracy, a new filter different from Extended Kalman Filter (EKF) should be adopted to estimate the errors of relative position and velocity, which is based on the nonlinearity of the kinetic model for the satellite formation flying. A nonlinear Divided Difference Filter (DDF) based on Stirling interpolation formula was proposed in this paper. According to the linearity of the measurement equation for the filter, a simplified differential filter was designed by means of expanding the polynomial of the nonlinear system equation and linear approximating of the finite differential interpolation. Digital simulation experiment for the relative positioning of satellite formation flying was carried out. The result demonstrates that the filter proposed in this paper has a higher filtering accuracy, faster convergence speed and better stability. Compared with the EKF, the estimation accuracy of the relative position and velocity has improved by 77.1%and 47% respectively in the method of simplified DDF, which indicates the significance for practical applications.
