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invfreq: computation using LS-TLS approach

From: Pascal A. Dupuis
Subject: invfreq: computation using LS-TLS approach
Date: Thu, 23 Dec 2004 08:45:16 -0600
User-agent: Mutt/1.5.6+20040907i


invfreq solve the problem of fitting some parametrised frequency
response to some given data. The main step are:
- construct a design matrix (R) and a target vector (P)
- find the set of parameters (Theta) which best maps the design matrix to the
target vector

The actual code uses LS, meaning only P is supposed to be noised. But
some columns of R are constructed from the target frequency response,
and are thus also noised. Furthermore, if the frequency is noised, the
whole R matrix is noised.

I have coded an alternative to solving Theta=R\P using QR, where the
noised part is handled by TLS, and the unnoised part by standard LS.

I have performed a few simulations, and it appears that this mixed
approach gives parameters which are more accurate than with ordinary LS.

Before submitting patches, I would like to ask to other octave users
what should be the best way to pass one supplemental argument to
invfreqs and invfreqz, namely the resolution method. I imagine a
string with possible values: 'LS' (default), 'TLS', or 'LS-TLS'.

Pascal Dupuis

Dr. ir. Pascal Dupuis
K. U. Leuven, ESAT/ELECTA (formerly ELEN):
Kasteelpark Arenberg, 10; B-3001 Leuven-Heverlee, Belgium
Tel. +32-16-32 10 21 -- Fax +32-16-32 19 85

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