Finite time stable attitude estimation of rigid bodies with unknown dynamics

An almost global finite time stable attitude estimation scheme for a rigid body that does not require the knowledge of the dynamics or the probability distribution of the sensor noise is presented. The attitude of the rigid body is estimated from measurements of at least two linearly independent known vectors and the angular velocity in the body-fixed frame. The estimation scheme is shown to be almost globally finite time stable using a Lyapunov analysis in the absence of measurement errors. A generalized Wahba's cost function, designed to be a Morse function on SO(3), is used to derive the nonlinear estimation scheme and show its stability. The proposed scheme is discretized as a geometric variational integrator for digital implementation. The stability and convergence of the estimation scheme are shown analytically, and validated through numerical simulations.