In this paper, fine attitude estimation using low-cost sensors for attitude pointing missions of spacecraft is addressed. Attitude kinematics and gyro models including bias models are in general utilized to estimate spacecraft attitude and angular rate. However, a linearized model and a transition matrix are derived in this paper from nonlinear spacecraft dynamics with external disturbances. A Kalman filtering technique is applied and offers relatively high estimation accuracy under dynamic uncertainties. The proposed approach is demonstrated using numerical simulations.