# How to model a system for tracking a person using kalman filter?

I need to model a system for human motion. The following link shows for to build a system for a plane.

I am currently reading the documentation for a kalman filter library http://kalman.sourceforge.net/doc/example.html. I have an accurate position(x, y, z) of a person, but I need to shine a light on the person with a device that is not very fast so I need to predict where the person will be to keep the light on them.

I understand that for motion on the x-y plane a person motion can be modeled using the equation(I need to also account for the z-axis):

$$S(t) = S(0) + V(0)*t + (1/2)*a(0)*t^2$$

But I'm not sure how to build the state vector used for estimate $\vec x$ using this information.

Note: I am currently using polynomial extrapolation with some degree of success.

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– Alex R. Jan 2 '13 at 19:23

After a lot of research I have resolve this issue and found the kalman state vector $\vec x_{k}$ which I need to track and predict a persons movements.
$\vec x_{k} = f(\vec x_{k-1}, \vec u_{k-1}, \vec w_{k-1}) = (p_x, v_x, a_x, p_y, ..., p_z, ...)^T$ Where $p, v, a$ represent: position, velocity, and acceleration respectively.
using this information and the Equation $P(t) = P(0) + V(0)*t + a(0)*\frac{t^2}{2}$ I can now start to model the system.