Abstract: To solve the collaborative relative navigation problem for near circular orbiting small satellites in close range formation under GNSS denied environment, a novel consensus constrained relative navigation algorithm based on the lever arm effect of the sensor offset from the spacecraft center of mass is proposed. Firstly, the orbital propagation model for the relative motion of the multi spacecraft formation is established based on the Hill Clohessy Wiltshire equations and the line of sight measurement under sensor offset condition is modeled in the Local Vertical Local Horizontal frame. Secondly, the consensus constraint model for the relative orbit state is constructed by introducing the geometry constraint between the spacecraft, based on which the consensus extended Kalman filter is designed. Next, the observability analysis is done and the conditions of the sensor offset to make the state observable are obtained. Lastly, the digital simulations are conducted to verify the proposed algorithm, where the comparison to the unconstrained case is also done. The results show that the estimate error of the relative position converges very quickly, the location error is smaller than 10 m under the condition of 10 -3 rad level camera and 5 m offset.

Key words: Spacecraft formation, Relative navigation; Observability analysis, Angles only measurement