# How to model the dynamics of human movement?

I am trying to derive a state space equation for human movement (i.e. walking, running, standing still) in some normal distribution sense. The following equations should not be so hard to follow:

If the state $\bar{x} = (x, \dot{x})$

The state equation will be $\bar{x}(t) = A\bar{x}(t-1)$

With the covariance matrix $C(t) = AC(t-1)A^{-1} + Q$

Where $A = \begin{bmatrix} 1 & T \\ 0 & 1 \end{bmatrix}$

where $T$ is the time period,

and where $Q$ a "process noise" covariance matrix.

$Q = \begin{pmatrix} \sigma_x^2 & \sigma_x \sigma_{\dot{x}} \\ \sigma_x \sigma_{\dot{x}} & \sigma_{\dot{x}}^2 \end{pmatrix}$

In my view, the key of a correct model lies in getting correct values of $\sigma_x$ and $\sigma_{\dot{x}}$.

According to wiki, the fastest human speed recorded is 44.72 km/h.

What do you think?

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What is the use of covariance matrix? It seems that it has no effect on the state. Also, if you are considering a periodic motion, then there is no need for the velocity in the state. –  hwlau Jan 13 '11 at 11:11
I am not sure I follow. What is the $x$ variable supposed to represent? Distribution of traveled distance? Also, do I understand it correctly that $t$ denotes number of steps so this is just a Markov chain? Why are you working in a discrete setting? Also, where do $C$ and $Q$ matrices come from? –  Marek Jan 13 '11 at 11:18
And human is not a rigid body in context of motion analysis. –  mbq Jan 13 '11 at 14:26
This is a very important topic especially in the context of the rapidly developing field of robotics. –  user346 Jan 13 '11 at 18:21