A simplified version of the nonlinear divided difference filter (DDF) algorithm based on Stirling’s interpolation formula called simplified divided difference filter (SDDF) was applied to relative navigation for spacecraft formation, using a limited divided difference items of the Taylor’s expansions as an approximation to the real nonlinear system equations. Numerical simulation results indicate that the SDDF filter algorithm has the obvious advantages than that of the EKF, including the higher navigation precision, faster convergence and better stability; the accuracy improvement of the SDDF compared with the EKF are 79% and 52% for relative position and velocity. This algorithm can be applied to relative navigation for spacecraft formation flying and is worthy of application.

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