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This study investigates the effect of noisy measurements of the angular rate in a non-linear attitude estimator for satellites. The attitude estimator uses measurement of a single attitude sensor such as Sun, Earth-horizon, star tracker or magnetometer together with a rate gyro, and guarantees exponential convergence of the attitude estimation error to zero under a no-noise condition. In view of a realistic situation where the presence of noise in gyro measurement is not negligible, this study presents stochastic and deterministic upper bounds for the attitude estimation error resulting from noisy angular rate measurement. A realistic simulation is presented to illustrate the results.