Abstract
The purpose of this paper is to investigate the observability of autonomous navigation system of two satellite system using relative position measurements only. The concept of local $k$-order observability is proposed and introduced into analysis of nonlinear system. Necessary and sufficient conditions of local 4-order, 5-order and 6-order observability of the autonomous navigation system are presented and mathematically proved. The relationships between these three conditions as well as the sufficient and necessary condition of satisfying observability rank condition for the autonomous navigation system are given and proved.
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