Numerically Sane Construction of Polynomial Least Squares Filters via QR Factorization

Abstract

We carefully develop a numerically sane algorithm for constructing polynomial least squares filters using the QR factorization. Filters of this type appear in a range of practical techniques and are extremely important. Many published methods for constructing these filters rely on algorithms and derivations that are numerically unwise, that are unnecessarily complex, or that are simply incorrect. Moreover there is a lack of proper historical context. We address both issues here.