ABSTRACT
This chapter presents the normal equations from linear algebra. It emphasizes the similarity between the normal equations and Wiener filtering. Both can be used to provide a linear, least mean square estimate of a signal from a set of measurements. There are two differences between the normal equations and Wiener filtering. The first difference is that the normal equations deal with linear estimation whereas Wiener filtering deals with linear, time invariant estimation. The second difference is that the normal equations produce an estimate which minimizes the error in terms of the measured signal while Wiener filtering produces an estimate which minimizes the error in terms of the unknown signal. The chapter focuses on the estimation of a vector in terms of a set of vectors. A common practical method of solving large matrix problems is to use an iterative solution. Iterative solution is particularly useful when the matrix is sparse — when the matrix contains a high proportion of zeros.
