For state estimation of space gravitational wave detection spacecraft, the well-known Kalman filter (KF) and its simple variants cannot be applied because of their restrictive assumptions that the process and measurement noises are white and their first two moments are known. In contrast, the specially designed robust estimators are more promising. In this paper, we linearize the quaternion measurements by introducing guidance information. On this basis, a residual normalized adaptive strong tracking filtering algorithm based on variational Bayes (VB-RNSTF) is proposed to deal with the spacecraft state estimation problem with complex colored noises. This algorithm combines adaptive KF based on variational Bayes with strong tracking filters to adjust the covariance matrix of process noise and estimate the covariance matrix of measurement noise. The proposed VB-RNSTF also introduces residual normalization to improve estimation accuracy. Simulation results demonstrate the effectiveness and performance superiority of the proposed algorithm for spacecraft state estimation compared to the existing filtering algorithms.