Nonlinear attitude observers on SO(3) for complementary and compatible measurements: A theoretical study

This paper considers the question of designing an attitude observer exploiting the structure of the Special Orthogonal Group SO(3) for both inertial and body-fixedframe measurements. We consider measurements from a minimal sensor suite, typically a rate gyroscope along with several measurements of inertial and/or body-fixed vector directions. We propose fully nonlinear pose observers based directly on the vector measurements, allowing a mix of both inertial and body-fixed measurements.We provide a comprehensive stability analysis of the observer error dynamics. We show that even with a single vector measurement it is often possible to recover asymptotically stable observer error dynamics.