Globally exponentially stable attitude and gyro bias estimation with application to GNSS/INS integration

This paper deals with the construction of nonlinear observers for navigation purposes. We first present a globally exponentially stable observer for attitude and gyro bias, based on gyro measurements and two or more pairs of vector measurements. We avoid the well-known topological obstructions to global stability by not confining the attitude estimate to SO(3), but rather estimating a full rotation matrix with nine degrees of freedom. We also show how the attitude can be estimated under a relaxed persistency-of-excitation condition, with a single vector measurement as a special case. Next, we use the attitude observer to construct a globally exponentially stable observer for gnss/ins integration, based on accelerometer, gyro, and magnetometer measurements, as well as gnss measurements of position and (optionally) velocity. We verify the stability properties of the design using experimental data from a light fixed-wing aircraft.