A geometric framework for rigid body attitude estimation

Abstract

In this paper, we present a geometric framework to solve two common attitude estimation problems: (i) a geometric problem using measurement of two reference directions, and (ii) a geometro-kinematic problem using measurement of a single reference direction and rate measurement. Both the aforementioned problems may be formulated as angle optimization problems, which can then be solved to obtain exact closed-form solutions. Since the proposed framework preserves the special nonlinear geometry associated with the space of attitudes, and since we present analytic solutions, the proposed framework yields faster and more accurate solutions than those that are based upon linearization techniques. Furthermore, the framework may be extended beyond traditional output error least-squares, to accommodate other practical, but unconventional, optimality metrics. Of special note, we may generalize the classic vector Triad solution, which uses a primary and a secondary measurement, to one with multiple secondary measurements. Lastly, the presented method can be used to derive previous solutions under a single unifying framework, and thus establishes how they are related to each other in a fundamental way. The geometric framework has been verified in simulations as well as experiments.