Model-order selection for analyzing correlation between two data sets using CCA with PCA preprocessing

I have worked on development and application of statistical signal processing and machine learning algorithms for a variety of applications. I have worked on tracking and filtering, TDOA estiamtion, and guidance algorithms related orbital craft, self-propelled systems, and unmanned/autonomous vehicles (UAS, etc.). I have developed link budget models for satellite communications and radar signal degradation analysis. I am interested in the theoretical under-pinnings of tracking algorithms and hidden behaviors of ML algorithms and what can be understood better about them in terms of classical statistics. I also love problem solving and working on challenging practical problems, whether it is algorithm development or developing applications that are useful for the customer.