(k)
a
d.(t)= dcd + d (k)(k) (6.23)
.q(t.p)
k∈Kd dd
1+ e
(k)aw
g.
w = dcw + (6.24)
(k)(k)
.qw (t.pw )
1+ e
k∈Kw
The choice of model order Kd and Kw is discussed in the following.
6.4. SIGMOID PROGRESSION ANALYSIS
6.4.2 Estimation Methods
The sigmoid sum model proposed above is underdetermined and non-linear, and cannot be estimated by matrix inversion like polynomial models. The problem of .nding the set of model parameters which causes the model d.to obtain a the best possible approximate of d is a non-linear optimization problem. A solution to this problem is .nding the set of model parameters which generates the most balanced power spectrum for r.. Provided that the model order is .xed, this can be simpli.ed to the problem of .nding the set of model parameters which minimizes the r.sum of squares [48].
However, if model order is itself a model parameter, minimizing square sum r.will estimate a model d.generating an r.equal to zero. I.e. d.models both d and
r.
For the noise gain parametrization, it is su.cient to minimize the sum square di.erence between g.w and g.
w. If model order is itself a parameter, it is however not possible to validate the model by evaluating the residual power spectrum. This because the sum square di.erence between g.w and g.
w is expected to assume a power spectrum of mainly low frequency, even for a correct model. Consequently, a traditional model validation technique like r2 or adjusted r2 must be used.
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