Deterministic relative attitude determination of three-vehicle formations

This paper proves that deterministic relative attitude determination is possible for a formation of three vehicles. The results provide an assessment of the accuracy of the deterministic attitude solutions, given statistical properties of the assumed noisy measurements. Each vehicle is assumed to be equipped with sensors to provide line-of-sight, and possibly range, measurements between them. Three vehicles are chosen because this is the minimum number required to determine all attitudes given minimal measurement information. Three cases are studied. The first determines the absolute (inertial) attitude of a vehicle knowing the absolute positions of the other two. The second assumes parallel beams between each vehicle to determine relative attitudes, and the third assumes nonparallel beams for relative attitude determination, which requires range information to find deterministic solutions. Covariance analyses are provided to gain insight on the stochastic properties of the attitude errors and the observability for all three cases.