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132 Control theory in biomedical engineering
problems related to the complexity of this biological process, models using
several kinds of graphic traces generated by one or more writers and taking
into account their individual properties such as speed, fluctuation, inclina-
tion, and preferential direction have also been proposed (Chihi et al., 2015;
Chihi and Benrejeb, 2018). The following sections focus on the presentation
of the most important handwriting models based on different experimental
data (numbers, geometric forms, Arabic letters, etc.).
3Kalman filter-based model
In order to reconstruct handwriting traces, numbers from zero to nine, using
eight channels of EMG activities of the forearm muscles, Okorokova et al.
(2015) proposed an approach based on the KF, which allows the fusion of
two information sources, presented by two models: dynamical and measure-
ment models (Linderman et al., 2009; Okorokova et al., 2015). These
models are defined as follows:
• Dynamical models present the physical characteristics of handwriting
motion. It allows computing the dependence between the state vector
s at the time t and the state vector in the past and the position of the
pen moving in the plane, according to x and y directions.
(1)
s t ¼ As t 1 + v t
with:
s t : state vector [6K 1]
s t ¼ x t , y t , _x t , _y , €x t , €y , …, x t K +1 ,½
t t
x
y
y t K +1 , _x t K +1 , _y , € t K +1 , € T
t K +1 t K +1
A: state transition matrix; [6K 6K]
v t : vector containing process noise [6K 1]
K: samples time relative to the dynamical model
• Measurement model to compute the dependence between the state vec-
tor and eight EMGs signals inputs of this model.
(2)
s t ¼ Hz t + w t
with:
z t : state vector [6L 1]
H: measurement transformation matrix [6K 1L]
w t : vector containing measurements noise [6L 1]
L: samples time relative to measurements model
