Attitude and earth velocity estimation - Part II: Observer on the special orthogonal group

This paper presents a novel cascade attitude observer based on measurements of a single body-fixed vector, in addition to high-grade rate gyro readings. First, a second body-fixed vector, related to the angular velocity of the Earth around its own axis, is dynamically estimated. Then, an attitude observer is built based upon the measured body-fixed vector, the estimated one, and the angular velocity provided by the rate gyros. The topological characteristics of the attitude estimates are preserved by construction and the estimation error is shown to converge to zero. The region of convergence is characterized and the result is best described as semi-global. Simulation results are included that show the achievable performance of the proposed solution. Finally, the results and characteristics of the observer are compared with that proposed in a companion paper, which considers attitude estimates on ℝ^3×3.