Reformulating least mean squares in the data domain

It is often the case that an idea is clearly obvious once it becomes ubiquitous. This is why it is so difficult to judge the innovation content of a new idea or concept. A creative, but familiar, idea invariably seems less brilliant than something new and esoteric. A theoretically complex notion first heard may stimulate the mind but generally cannot compare in innovation with, say, something as simple, but ultimately culture transforming, as the wheel. Only the test of time can separate the truly great ideas from the merely clever ones. By this measure, Widrow´s work on adaptive processing is unambiguously seminal. Though Dr. Widrow initiated data adaptive least squares processing, the initial optimal noise filtering concept was conceived by Norbert Wiener (1949) and Andrey Kolmogorov (1941) (independently), both whom developed stochastic least squares theory. These prior efforts, while a tour de force of mathematics-one that provided essential insight and analytical tools-suffered from an assumption of the presence of prior knowledge of time series statistics.