Relationship of accelerometer and velocity and position state space?

Question

I have a accelerometer and I’m measuring distance and velocity by integration. I want to build a state space model of this. How would I go about it? I know $a = \mathrm{d}v/\mathrm{d}x \cdot \mathrm{d}x/\mathrm{d}t$. So is this right? $$ x \dot{x} = \ddot{x} $$

Answer 1

No, $\ddot x=\frac {dv}{dt},$ not $\frac {dv}{dx}$. It is true that $a=\ddot x = \frac {dv}{dx}\dot x$ but that is different from $\dot x x$