These parameters are kept for the modeling of the data set presented previously
(since the waveforms of the data are similar), where the amplitude of the flow is quite
constant but there are two different kinds of breaths. It can be noted that in the second
data set, the flow is not centered around zero but around a positive offset (likely caused
by a measurement error), this might be a reason which the non-linear models did not
perform well, and outlines the high dependency of modeling and segmentation methods
to data preprocessing.
3.4.2 Linear Experts
In most system identification cases, the data is non-linear, but can be fitted to a
linear model within an acceptable error range. As noted before though, the presence of
both sharp changes and flat parts in the data will make it harder for a linear model to
perform a good prediction, because the first would require a high filter order whereas the
latter would on the contrary require a low order. Therefore non-linear models might be a
better option.
To train the experts, we use a Wiener filter [23]. With this approach, the final
weights of the model are computed in one step. The correlation matrix of the input vector
is computed using a sample breath sequence (mandatory or spontaneous). The Wiener
optimal filter coefficients W,, are computed by simply inverting the autocorrelation
matrix, as shown in (3.4).
pt= R-'P (3.4)
Then the least mean square algorithm (LMS) [23] is used for the online update of
the experts. Usually the recursive least squares (RLS) algorithm is faster and more robust
than the LMS, but in our framework of online segmentation, using the LMS gives a