This paper presents a method for simultaneous deep-space navigation and attitude determination using angles-only measurements. Using planetary ephemerides and observations of three known celestial bodies in the spacecraft body frame, a geometric construction is developed to derive an equation for the spacecraft’s distance to one body. The derivative of the associated zero-finding function is obtained for Newton’s method, which enables efficient equation solving. A sign ambiguity arises in the process, yielding nine possible combinations; a resolution strategy is proposed to identify the correct solution. Once the distance is determined, the spacecraft’s position is triangulated in the inertial frame, after which any attitude determination algorithm can be applied using the body measurements. The method eliminates the need for matrix inversions and employs a computationally efficient Newton iteration, making it suitable for onboard navigation. Numerical examples, simulating measurements of the Sun and two additional celestial bodies, demonstrate the proposed approach, and an accuracy analysis is conducted considering measurement uncertainties.
Choi et al. (Wed,) studied this question.