Fisher Information Based Analysis of Deterministic Relative Attitude Observability in Planar Vehicle Formations

This paper examines the problem of relative attitude observability for formations of three, four and five vehicle formations. The analysis is rooted in within the principles of maximum likelihood estimation insomuch as the metric for observability is the resulting Fisher information matrix for the small attitude errors. For formations of three and four vehicles it is shown that the relative attitudes are not observable by proving that the Fisher information matrix is singular for these cases. For formations of five vehicles, the observability relies on the number of LOS vector pairs available within the formation. It is shown that a minimum number of 8 LOS vector pairs is necessary for the attitudes to be observable, with all configurations of less LOS vector pairs yielding a singular Fisher information matrix.