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?

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    $\begingroup$ Hi: I don't know the answer to your question but I'm interested in this field of adaptive filtering. ( I'm familar with kalman filter and background is econometrics/stat time-series ). Is this book good for an introduction. I have some experience with numerical optimization and time series methods so I'm interested in what is meant by "adaptive". Thanks and I'm sorry that I can't help you with your question. $\endgroup$ – mark leeds Oct 27 '19 at 1:08
  • $\begingroup$ The book is extremely math heavy and goes very in-depth. It's a good comprehensive text, but I think if you want an intro to the subject you're better off with a chapter from a signal processing textbook. I don't really have a favorite to recommend; the best intro I got was a professor's slide set + lecture. $\endgroup$ – Void Star Oct 27 '19 at 16:29
  • $\begingroup$ Thanks for suggesting that. You make a good point. I'm sorry that no one has responded. If I could respond with something intelligent, I would. Unfortunately, I'm not familiar with this topic. $\endgroup$ – mark leeds Oct 28 '19 at 1:32

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