  This work presents a contracting hierarchical observer that fuses position
and orientation measurements with an IMU to generate smooth position, linear
velocity, orientation, and IMU bias estimates that are guaranteed to converge
to their true values. The proposed approach is composed of two contracting
observers. The first is a quaternion-based orientation observer that also
estimates gyroscope bias. The output of the orientation observer serves as an
input for another contracting observer that estimates position, linear
velocity, and accelerometer bias thus forming a hierarchy. We show that the
proposed observer guarantees all state estimates converge to their true values.
Simulation results confirm the theoretical performance guarantees.
