“…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.…”