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Modeling simple and complex handwriting based on EMG signals 133

We also note:
x
s t ¼ x t , y , _x t , _y , € t , €, …, x t K +1 , y , _x t K +1 , _y , € t K +1 ,
y
x
½
t t t t K +1 t K +1
T
€ y Š is the state vector that contains the coordinates of the pen. In addi-
t K +1
tion, it contains the first and second rates of change for the window of K time
moments starting from t; A is the state transition matrix that describes the
relationship between the state vectors at two consecutive moments; v t con-
tains the noise of the process.
Based on the KF, the fusion is realized by the multiplication of functions
of dynamical and measurement models. The gain of the KF allows estimat-
ing the contribution of each model.
The KF is based on the fusion of two noisy information sources to esti-
mate the dynamical system’s state vector. In the Okorocova model, the first
information source is a dynamical model based on the physical properties of
the handwriting system. This source is presented as a multivariate autore-
gressive process. The parameter estimation is computed from the recorded
data. The second information source is the noisy vector of the measured
EMG signals. The relationship between these signals and the pen coordinate
is presented using a multivariate linear regression model (Okorokova
et al., 2015).
Based on eight inputs and six states, this method is suitable for real-time
operations. It requires the computation and the adjustment of 48 parameters.
Furthermore, the use of eight inputs increases the complexity of the model
and the computation time. The KF is considered a powerful and effective
method, especially for stochastic signals, but it requires some assumptions
(e.g., white noise) that might be difficult to meet in practice. This may affect
the response of this method in terms of accuracy, especially in real-time
applications (Thomassen and Meulenbroek, 1993). Fig. 1 shows the
response of the cross-validation of the KF-based model. We remark that
the estimated numbers are not easily identifiable, especially for “0” and
“5,” which can be confused with “6” and “0,” respectively. In summary,
cross-validation shows the limitation of this approach despite the use of eight
inputs and 48 parameters.

4 Zhang-Kamavuako model (ZK)

Zhang and Kamavuako (ZK) proposed a handwriting model to reconstruct a
pen tip moving on an XP-PEN Deco 02 Digital Graphics Drawing Tablet
from EMG signals recorded from three muscles (opponens pollicis, first