Abstract： To solve the problem that a robust covariance matrix cannot be obtained because of insufficient samples in principal component analysis, the covariance matrix was transformed into the feature subspace estimation problem by introducing the idea of CS decomposition Bayesian spatial estimation. First, the SPE (squard prediction error) statistic threshold and failure mode feature subspace matrix library were established using a large number of historical data using PCA offline. When there exists an abnormal condition in the online system, only a small sample of failure data can be obtained due to the effect of a certain environment. However, the feature subspace matrix can be obtained using a small sample data. Then, fault diagnosis was completed by comparing the similarity between the feature subspace and the failure mode subspace. Finally, the feasibility and effectiveness of this method was verified by simulation.