  A geometric estimator is proposed for the rigid body attitude under
multi-rate measurements using discrete-time Lyapunov stability analysis in this
work. The angular velocity measurements are assumed to be sampled at a higher
rate compared to the attitude. The attitude determination problem from two or
more vector measurements in the body-fixed frame is formulated as Wahba's
problem. In the case when measurements are absent, a discrete-time model for
attitude kinematics is assumed in order to propagate the measurements. A
discrete-time Lyapunov function is constructed as the sum of a kinetic
energy-like term that is quadratic in the angular velocity estimation error and
an artificial potential energy-like term obtained from Wahba's cost function. A
filtering scheme is obtained by discrete-time stability analysis using a
suitable Lyapunov function. The analysis shows that the filtering scheme is
exponentially stable in the absence of measurement noise and the domain of
convergence is almost global. For a realistic evaluation of the scheme,
numerical experiments are conducted with inputs corrupted by bounded
measurement noise. Simulation results exhibit convergence of the estimated
states to a bounded neighborhood of the actual states.
