Error Covariance Analyses for Celestial Triangulation and Its Optimality: Improved Linear Optimal Sine Triangulation

This study presents an improved methodology for celestial triangulation optimization in spacecraft navigation, addressing limitations in existing approaches. While current methods like Linear Optimal Sine Triangulation (LOST) provide statistically optimal solutions for position estimation using multiple celestial body observations, their performance can be compromised by suboptimal measurement pair selection. The proposed approach, called the Improved-LOST algorithm, introduces a systematic method for evaluating and selecting optimal measurement pairs based on a Cramér–Rao Lower-Bound (CRLB) analysis. Through theoretical analysis and numerical simulations on translunar trajectories, this study demonstrates that geometric configuration significantly influences position estimation accuracy, with error variances varying by orders of magnitude depending on observation geometry. The improved algorithm outperforms conventional implementations, particularly in scenarios with challenging geometric configurations. Simulation results along a translunar trajectory using various celestial body combinations show that the systematic selection of measurement pairs based on CRLB minimization leads to enhanced estimation accuracy compared to arbitrary pair selection. The findings provide valuable insights for autonomous navigation system design and mission planning, offering a quantitative framework for assessing and optimizing celestial triangulation performance in deep space missions.