Analytical Methods in Triangulation-Based Celestial Localization

Optical measurements are a key part of modern interplanetary navigation. This work applies the statistically optimal Linear Optimal Sine Triangulation (LOST) algorithm to the problem of celestial navigation. In addition to optimal triangulation methods, celestial navigation requires the consideration of target ephemeris errors, light aberration, and light time-of-flight. In most cases, only light aberration and light time-of-flight change the expected direction of the measured line-of-sight. These effects are found to be non-negligible at typical observer velocities (for light aberration) and planet velocities (for light time-of-flight). The effects of the position uncertainty of planets are only important when the observer is close to them. The LOST framework provides a mechanism to conveniently consider all of these effects.