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We propose a new algorithm for estimating constant biases in gyro measurements of angular velocity, and demonstrate that the resulting estimates converge to the true bias values exponentially fast. The new observer is then combined with a nonlinear attitude tracking control strategy in a certainty equivalence fashion, and the combination shown via Lyapunov analysis to produce globally stable closed-loop dynamics, with asymptotically perfect tracking of any commanded attitude sequence. The analysis is then extended to consider the effects of stochastic measurement noise in the gyro in addition to the bias. A simulation is given for a rigid spacecraft tracking a specified, time-varying attitude sequence to illustrate the theoretical claims.