An extended Kalman filtering technique is addressed for gyroless spacecraft to estimate the angular rate and attitude vectors of spacecraft and the alignment of reaction wheels using only vector measurement. In this work, it is assumed that the angular momentum and control torque of the reaction wheels are measurable and usable for the filter formulation. Because there is no angular rate sensor, a dynamic model of a spacecraft equipped with reaction wheels is required to estimate the angular rate of the spacecraft. In this formulation, misalignment of the reaction wheels is considered a state variable to be estimated. For actual implementation, the external torque disturbance is regarded as a first-order Markov process, and is also exploited in this Kalman filter formulation. Finally, effectiveness of the estimation algorithm proposed in this paper is demonstrated using numerical simulations.