REQUEST is a recursive algorithm for least-squares estimation of the attitude quaternion of a rigid body using vector measurements. It uses a constant, empirically chosen gain and is, therefore, suboptimal when filtering propagation noises. The algorithm presented here is an optimized REQUEST procedure, which optimally filters measurement as well as propagation noises. The special case of zero-mean white noises is considered. The solution approach is based on state-space modeling of the K-matrix system and uses Kalman-filtering techniques to estimate the optimal K matrix. Then, the attitude quaternion is extracted from the estimated K matrix. A simulation study is used to demonstrate the performance of the algorithm.