Unitary orthogonalization processes

All methods for solving least-squares problems involve orthogonalization in one way or another. Certain fundamental estimation and prediction problems of signal processing and time-series analysis can be formulated as least-squares problems. In these problems, the sequence that is to be orthogonalized is generated by an underlying unitary operator. A prime example of an efficient orthogonalization procedure for this class of problems is Gragg's isometric Arnoldi process, which is the abstract encapsulation of a number of concrete algorithms. In this paper, we discuss a two-sided orthogonalization process that is equivalent to Gragg's process but has certain conceptual strengths that warrant its introduction. The connections with classical algorithms of signal processing are discussed.