On the Recursive Solution to the Normal Equations: Some Other Results [Lecture Notes]

The recursive solution of the autocorrelation normal equations was recovered in a recent article by Baran and Oppenheim [1]. The algorithm they obtained is slightly different from the one currently described in the literature [9]. However, they did not reallize the importance of the difference. I discovered it almost 30 years ago [4], [6] and used it to propose a modified Burg method as alternative to the well-known Burg method [2] that emerged directly from the classic Durbin-Levinson algorithm. In fact, the solution of the normal equations Baran, Oppenheim, and I obtained leads to predictors that are different from those acquired with the classic Durbin-Levinson algorithm. We will see the difference by looking into the recursions verified by the corresponding prediction error filters.