Adaptive Identification on the Group of Rigid-Body Rotations and its Application to Underwater Vehicle Navigation

This paper reports a novel stable adaptive identifier on the group of rigid-body rotations, and its application to a sensor-calibration problem arising in underwater vehicle navigation. The problem addressed is the identification of an unknown rigid-body rotation map from input-output data. General least-squares (LS) and adaptive identification techniques are commonly employed to identify general linear maps from input-output data, but do not guarantee that the resulting identified map is a rigid-body rotation. At present, an LS singular value decomposition approach is the standard method for identification constrained to the group of rigid-body rotations. This paper reports the first exact adaptive identifier on the group of rigid-body rotations, together with a proof of asymptotic stability. Techniques for navigating underwater vehicles are reviewed, and the Doppler-alignment calibration problem is posed. The reported adaptive identifier is employed to solve this problem, and performance of this adaptive identifier is evaluated on both laboratory and field experimental data. The results reported herein compare favorably with results obtained via previously reported LS techniques. The methodology reported herein may be of broader interest because of its applicability to more general problems in the identification, dynamics, and control on the group of rigid-body motions