Recursive iterative Principal Component Analysis
Recursive iterative P rincipal Component Analysis (RIPCA) is a specialized technique developed for real-time model identification and error variance estimation in time-varying processes. It combines the recursive update capabilities of Recursive PCA (RPCA) with the noise-handling power of Iterative PCA (IPCA). Core Components The RIPCA algorithm operates by integrating three distinct methodologies: Iterative PCA (IPCA): Originally designed by Narasimhan and Shah to solve the "errors-in-variables" problem, where both input and output measurements contain noise. It iteratively estimates both the linear model and the specific error variances (heteroskedastic noise) for each variable. Recursive PCA (RPCA): A technique that updates the data covariance matrix incrementally as new samples arrive. This eliminates the need to store massive amounts of past data, making it ideal for online monitoring. The Recursive Iterative Approach: In RIPCA, these are combined to track changes in a...