Globally exponentially stable cascade observers for attitude estimation

Globally exponentially stable attitude observer with Earth velocity estimation

“…Further suppose that Assumptions 1 and 2 hold. Then, the origin of the error dynamics (16) is a globally exponentially stable equilibrium point.…”

“…In uncertainty ellipsoids were employed in the design of a deterministic attitude estimator. Previous work by the authors includes and , where two different attitude estimators are proposed that avoid common problems of attitude estimation such as singularities, unwinding phenomena, or topological limitations for achieving global asymptotic stabilization, see for a thorough discussion of these issues.…”

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

“…These topological obstructions can be avoided by allowing the attitude estimate to evolve on a larger state space; this strategy has recently been employed by Oliveira (2011a,b, 2012b) and by the authors (Grip, Saberi, & Johansen, 2011, by estimating a matrix with nine degrees of freedom that converges to a rotation matrix on SO(3). Batista et al (2012b) and Batista, Silvestre, and Oliveira (2012c) also considered the use of a separate observer to produce globally exponentially stable gyro bias estimates, although their approach requires stationary reference vectors. Attitude estimation using a single vector measurement has been considered by several authors (Batista et al, 2011b;Batista, Silvestre, & Oliveira, 2012a;Kinsey & Whitcomb, 2007;Lee, Leok, McClamroch, & Sanyal, 2007;Mahony, Hamel, Trumpf, & Lageman, 2009) and is possible under a persistency-of-excitation (pe) condition.…”

Cascade attitude observer for the SLAM filtering problem

“…The gyro bias estimate is then sent to a simplified complimentary filter from Mahony et al [10]. This makes the gyro bias estimation and attitude estimation decoupled, as in Batista et al [14], so that the erroneous initialization of the attitude does not affect the convergence of the gyro bias estimate, resulting in a smoother and faster transition phase for the attitude estimate, which becomes more apparent for large gyro biases. The performance is compared against the complimentary filter, where simulation results are made in R 3 .…”

“…An attitude and gyro bias estimation scheme is presented in Batista et al [13], where the dynamics are given as an LTV system and solved with a Kalman filter. A computational efficient gyro bias attitude observer is also presented by Batista et al [14], where the gyro bias is in cascade with the attitude estimation. The mentioned methods use reference vectors from global phenomena.…”