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Mon Nov 16 14:34:17 CET 2009

## HSVD

A summary of [1].
CHAPTER 2
Explains basic principles of Linear Prediction (LP) and State Space
(SS) based methods for parameter estimation.
The flow of HSVD is like this:
1. start with a signal of length N
2. create a hankel matrix (N-q x q) -> choose q
3. compute SVD
4. truncate: take first n singular vectors -> choose n
5. LS solve shift equation
6. compute eigenvectors
The two values to be chosen are n (signal space dimension) and q
(signal + noise space dimension). The n parameter follows from what
one is looking for, but how to determine q?
Translating LP to an AR problem shifts the statistics but makes it
easier to estimate using LS.
The essence seems to be this: trunctation by SVD is essentially noise
reduction. This then makes the LS or TLS-based estimation for LP and
SS approaches more precise. However, the statistically optimal (ML)
estimates require nonlinear optimization.
In general SS methods are better for larger number of poles since they
obtain poles from an eigenvalue decomposition instead of polynomial
rooting, which is ill-conditioned for large order.
[1] ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/vanhamme/phd.ps

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