  This paper addresses the problem of estimating the attitude and angular
velocity of a rigid object by exploiting its second order kinematic model. The
approach is particularly useful in cases where angular velocity measurements
are not available and the attitude and angular velocity of an object need to be
estimated from accelerometers and magnetometers. We propose a novel sensor
modality that uses multiple accelerometers to measure the angular acceleration
of an object as well as using magnetometers to measure partial attitude. We
extend the approach of equivariant observer design to second order attitude
kinematics by demonstrating that the special Euclidean group acts as a symmetry
group on the system considered. The observer design is based on the lifted
kinematics and we prove almost global asymptotic stability and local uniform
exponential stability of the estimation error. The performance of the observer
is demonstrated in simulation.
