Abstract
Least-squares algorithms aim at the minimization of the sum of the squares of the difference between the desired signal and the model filter output [1,2]. When new samples of the incoming signals are received at every iteration, the solution for the least-squares problem can be computed in recursive form resulting in the recursive least-squares (RLS) algorithms. The conventional version of these algorithms will be the topic of this chapter.
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Notes
- 1.
The a posteriori error is computed after the coefficient vector is updated, and taking into consideration the most recent input data vector x(k).
- 2.
The expression for ξmin,p can be negative, however, ξ(k) is always non-negative.
- 3.
Again the reader should recall that when computing the gradient with respect to w ∗(k), w(k) is treated as a constant.
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Diniz, P.S.R. (2013). Conventional RLS Adaptive Filter. In: Adaptive Filtering. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-4106-9_5
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DOI: https://doi.org/10.1007/978-1-4614-4106-9_5
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