The Kalman filtering (KF) is widely used in the low-cost MEMS-SINS/GPS integrated navigation system. In such a system, the quaternion method is usually used to calculate the attitude angles, and then the attitude angular error correction is made by the periodic Kalman filtering. This will result in two different effects. One is the produced angular divergence if the filtering cycle is long; another is the increased complexity and the affected real-time effects if the filtering cycle is short. To trade off the filtering performance and the real-time effect, the KPCA (Kernel principal component analysis) based KF is proposed in this paper. The quaternion reconstruction error by KPCA is used to decide whether KF is carried out or not. That is, if the KPCA reconstruction error is beyond the set threshold, the KF is carried out, otherwise, the quaternion solution is utilized. The experimental results show the relative superiority of KPCA-based KF compared to KF.