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Sat, 24 Mar 2018 15:58:56 GMT
20180324T15:58:56Z

Comparison of least squares and exponential sine sweep methods for Parallel Hammerstein Models estimation
http://hdl.handle.net/10985/12468
REBILLAT, Marc; SCHOUKENS, Maarten
Comparison of least squares and exponential sine sweep methods for Parallel Hammerstein Models estimation
Linearity is a common assumption for many reallife systems, but in many cases the nonlinear
behavior of systems cannot be ignored and must be modeled and estimated. Among
the various existing classes of nonlinear models, Parallel Hammerstein Models (PHM) are
interesting as they are at the same time easy to interpret as well as to estimate. One way to
estimate PHM relies on the fact that the estimation problem is linear in the parameters and
thus that classical least squares (LS) estimation algorithms can be used. In that area, this
article introduces a regularized LS estimation algorithm inspired on some of the recently
developed regularized impulse response estimation techniques. Another mean to estimate
PHM consists in using parametric or nonparametric exponential sine sweeps (ESS) based
methods. These methods (LS and ESS) are founded on radically different mathematical
backgrounds but are expected to tackle the same issue. A methodology is proposed here
to compare them with respect to (i) their accuracy, (ii) their computational cost, and (iii)
their robustness to noise. Tests are performed on simulated systems for several values of
methods respective parameters and of signal to noise ratio. Results show that, for a given
set of data points, the ESS method is less demanding in computational resources than the
LS method but that it is also less accurate. Furthermore, the LS method needs parameters to
be set in advance whereas the ESS method is not subject to conditioning issues and can be
fully nonparametric. In summary, for a given set of data points, ESS method can provide a
first, automatic, and quick overview of a nonlinear system than can guide more computationally
demanding and precise methods, such as the regularized LS one proposed here.
Sun, 01 Jan 2017 00:00:00 GMT
http://hdl.handle.net/10985/12468
20170101T00:00:00Z
REBILLAT, Marc
SCHOUKENS, Maarten
Linearity is a common assumption for many reallife systems, but in many cases the nonlinear
behavior of systems cannot be ignored and must be modeled and estimated. Among
the various existing classes of nonlinear models, Parallel Hammerstein Models (PHM) are
interesting as they are at the same time easy to interpret as well as to estimate. One way to
estimate PHM relies on the fact that the estimation problem is linear in the parameters and
thus that classical least squares (LS) estimation algorithms can be used. In that area, this
article introduces a regularized LS estimation algorithm inspired on some of the recently
developed regularized impulse response estimation techniques. Another mean to estimate
PHM consists in using parametric or nonparametric exponential sine sweeps (ESS) based
methods. These methods (LS and ESS) are founded on radically different mathematical
backgrounds but are expected to tackle the same issue. A methodology is proposed here
to compare them with respect to (i) their accuracy, (ii) their computational cost, and (iii)
their robustness to noise. Tests are performed on simulated systems for several values of
methods respective parameters and of signal to noise ratio. Results show that, for a given
set of data points, the ESS method is less demanding in computational resources than the
LS method but that it is also less accurate. Furthermore, the LS method needs parameters to
be set in advance whereas the ESS method is not subject to conditioning issues and can be
fully nonparametric. In summary, for a given set of data points, ESS method can provide a
first, automatic, and quick overview of a nonlinear system than can guide more computationally
demanding and precise methods, such as the regularized LS one proposed here.