Passive and Explicit Attitude and Gyro-Bias Observers Using Inertial Measurements

This article addresses the problem of estimating the attitude and gyro bias using biased gyro and inertial vector measurements. Two nonlinear observers are presented. One of the two is the passive observer evolving on the semisphere of quaternion, which decouples the gyro measurements from the reconstructed attitude. The other is the explicit observer evolving on the SO(3), which uses directly body-frame measurements of known inertial vectors. The proposed observers achieve faster convergence for large attitude estimation errors than similar observers in literature, guarantee asymptotical stability for almost arbitrary initial conditions, achieve similar steady-state performance with lower computational cost than multiplicative extended Kalman filter, which is the workhorse of attitude estimation, and are suitable for implementation using a low-cost inertial measurement unit. Simulation and experimental results prove the fast convergence and steady-state performance of the proposed observers.