Motivation
In general, the RLS can be used to solve any problem that can be solved by adaptive filters. For example, suppose that a signal d(n) is transmitted over an echoey, noisy channel that causes it to be received as
where represents additive noise. We will attempt to recover the desired signal by use of a -tap FIR filter, :
where is the vector containing the most recent samples of . Our goal is to estimate the parameters of the filter, and at each time n we refer to the new least squares estimate by . As time evolves, we would like to avoid completely redoing the least squares algorithm to find the new estimate for, in terms of .
The benefit of the RLS algorithm is that there is no need to invert matrices, thereby saving computational power. Another advantage is that it provides intuition behind such results as the Kalman filter.
Read more about this topic: Recursive Least Squares Filter
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