Relative navigation of circumlunar satellite formation in DSL mission: Real-time solution for incomplete observations

DSL (Discovering the sky at the longest wavelengths) mission is crucial for probing the cosmic dawn and dark ages through ultra-long wavelength observations. However, it presents significant navigation challenges due to GNSS signal loss, difficulty in obtaining relative measurements and severe orbital ambiguity problem. Considering these factors, this paper proposes a cooperative relative navigation strategy for the DSL mission's incomplete inter-satellite observations, consisting of three main parts: unanchored positioning, anchor nodes positioning and coordinate registration. Firstly, we obtain unanchored positions using inter-satellite range information through a multi-satellite cooperative localization method, which can quickly resolve relative positions even with missing range measurements. Secondly, considering the incomplete angle measurements caused by field of view limitations and illumination conditions, we design a new information fusion and complementary method to determine positions of the ANS (Anchor Node Satellites). Thirdly, to achieve high-precision coordinate registration, we propose a covariance-weighted Procrustes analysis algorithm based on positioning accuracies of different anchor nodes to transform unanchored satellite positions into the desired coordinate system. These three proposed algorithms are combined as a fused navigation strategy. Numerical simulations of two practical cases, clustering and trailing formation in the DSL mission, validate the effectiveness of the proposed method, showing the efficiency dealing with incomplete measurement information. Specifically, even with only 30 % angle measurements and 70 % range measurements, the proposed method can still maintain 5-meter accuracy within a distance of 100 km under 50 μrad angle-measuring error and 0.1 m ranging error.