The algorithms given for un-normalized LRLS and normalized LRLS filters on Wikipedia are transcribed from Adaptive Filtering Algorithms and Practical Implementation by Paulo S. R. Diniz. In reading the book, I noticed the author has this to say of the forgetting factor λ.
Another interesting feature of the normalized lattice algorithm is that the forgetting factor λ does not appear in the internal updating equations; it appears only in the calculation of the energy of the input and reference signals. This property may be advantageous from the computational point of view in situations where there is a need to vary the value of λ.
I do not understand whether the author is saying that updating the factor is impossible with the un-normalized form, or computationally expensive. Nor do I understand what prevents one from updating the factor over time when using the un-normalized form. To me, it looks simple to parameterize the forgetting factor in terms of k for either algorithm. Could someone help me shed light on precisely what is meant here and why it is true?