Model identification and error covariance matrix estimation from noisy data using PCA

Principal components analysis (PCA) is increasingly being used for reducing the dimensionality of multivariate data, process monitoring, model identification, and fault diagnosis. However, in the mode that PCA is currently used, it can be statistically justified only if measurement errors in different variables are assumed to be i.i.d. In this paper, an iterative algorithm for model identification using PCA is developed for the case when measurement errors in different variables are unequal and are correlated. The proposed approach not only gives accurate estimates of both the model and error covariance matrix, but also provides answers to the two important issues of data scaling and model order determination.