THE DYNAMICAL MODEL OF THE PEN TIP 

The model that we are currently using is a second order model that is appropriate to describe the dynamics of a point object moving on a plane. The following figures shows the differential equations that describe the model. 
where x(t), v(t) and a(t) are the two dimensional-components of the position, velocity and acceleration of the tracked point, and na(t) is additive zero-mean, Gaussian, white noise. The state of the filter X(t) includes three 2-dimensional variables x(t), v(t) and a(t). This model is a second order model that is appropriate to describe the dynamics of a punctual object moving on a plane. The
output of the model y(t) is the estimated position of the pen tip.
 

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 Mario Enrique Munich - mariomu AT vision DOT caltech DOT edu