This paper presents the development and performance of a special algorithm for estimating the attitude and angular rate of a spacecraft. The algorithm is a pseudolinear Kalman filter, which is an ordinary linear Kalman filter that operates on a linear model whose matrices are current state estimate dependent. The nonlinear rotational dynamics equation of the spacecraft is presented in the state space as a state-dependent linear system. Two types of measurements are considered; one type is a measurement of the quaternion of rotation, which is obtained from a newly introduced star tracker based apparatus. The other type of measurement is that of vectors, which permits the use of a variety of vector measuring sensors like sun sensors and magnetometers. Several measurement models are presented, a linear model for the case where the measured quantity is the quaternion, and two measurement models, one of which is pseudo-linear, when the measured quantities are vectors. In the latter situation, one model is for the case where the attitude is represented by a quaternion, and the other is for the case where it is represented by a direction cosine matrix. A special observability enhancement algorithm is introduced for the latter case. The state-dependent pseudo-linear filter is tested using simulated spacecraft rotations.