Stability of a nonlinear attitude observer on SO(3) with nonideal angular velocity measurements

This paper presents a nonlinear observer for attitude estimation on SO(3) and studies the stability properties of the system in the presence of nonideal inertial sensor measurements. Exploiting vector observations and biased angular velocity readings in the feedback law, almost global asymptotic stability of the origin is obtained and exponential convergence is guaranteed for an explicit region in the state space. Sufficient conditions in the observer design are proposed to yield exponential stability of the origin given worst-case initial alignment errors. Stability of the observer in the presence of angular measurement noise is obtained, and convergence to a desired neighborhood of the origin, for any initial condition in a known region, can be guaranteed by properly defining the observer parameters. The properties of the observer are illustrated in simulation for inertial sensor characteristics and initial alignment errors commonly found in practical setups.