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140 Control theory in biomedical engineering

Fig. 6 Cross-validation of the Arabic letter “SIN” by MKS model (Chihi et al., 2015).

The MKS model is a parametric model that needs adjustment every time we
change data, even if the data presents the same kind of graphic trace, written
by the same person. Simulation results show significant error between esti-
mated and real data especially in cross-validation (Fig. 6). We note that the
solid line denotes measured data and the dotted line presents the response of
the MKS model.

5.3 Interval observer for robust handwriting characterization
In the preceding section, we presented different handwriting models to
characterize several kinds of graphic traces: numbers, geometric forms, let-
ters, and so on. However, these models are limited in terms of accuracy and
need parametric adjustment each time we change the data. This can be
explained by the stochastic nature of the EMG signals. Based on the exper-
imental approach previously presented in Chihi et al. (2017), a linear fourth-
order model to generate handwriting traces according to x and y directions
was developed to characterize the handwriting process from only two EMG
signals of the forearm. This model is given by the following equations:
4 4 5 5
X X X X
^
a
c
ð
ð
b ix x e k ið
x e kðÞ ¼ ^ ix y e k iÞ + ^ Þ + ^ ix e 1 k i +1Þ + d ix e 2 k i +1ð Þ
i¼1 i¼1 i¼1 i¼1
4 4 5 5
X X X X
^
^
c
ð
y e kðÞ ¼ a ^ iy x e k iÞ + b iy y e k ið Þ + ^ iy e 1 k i +1Þ + d iy e 2 k i +1ð Þ
ð
i¼1 i¼1 i¼1 i¼1
(4)