Analysis of Non-Linear Attitude Observers for Time-Varying Reference Measurements

This paper provides a comprehensive stability analysis of a suite of nonlinear attitude observers that have been developed over the last few years. The observers considered are based on vectorial measurements of an a priori known reference direction. By treating the reference direction and the measurement in the same analysis framework, and allowing time-variation of either, we are able to define general persistency of excitation criteria that incorporate and generalize convergence criteria used in prior work. A key outcome is conditions that ensure almost global asymptotic and local exponential stability of attitude observers based on a single vector measurement as long as the excitation conditions are met on the reference and system trajectory. The approach generalizes stability results provided in prior work, based on rank conditions, that required at least two or more vector measurements.