# Acceleration to Displacement

I'm doing an experimental program.

I've a smartphone fixed on the car dashboard with a support, during the travel i read from an application some value from inertial sensor,

Accelerometer Data Time (at fixed interval) of each registration in second.

So now i would to pass from vertical acceleration to vertical displacement, to do this I should do a double integration,

I tried, euler method. From initial condition like

$v_{0} = 0.$ this is initial velocity at time zero.

$x_{0} = 0.$ this is initial position at time zero.

define,

$\Delta T =$ registration interval. (in my case 0,04s)

then for each registration made, i do:

$v_{i} = v_{i-1} + ay_{i} *\Delta T.$

$x_{i} = x_{i-1} + v_{i} * \Delta T.$

where i represent the current, and i-1 precedent.

But the chart that I get is not very realistic, in fact both the speed and the displacement are only grow, instead the effect that I had to get is that the vertical displacement came out as something similar to the acceleration graph.

Given that applying this procedure, I also a high error, it is possible that the graph is only growing, and I do not see any kind of vertical oscillation?

I also read the Kalman filter can be applied in advance to clean the signal, could be a solution?

Or should I change the method of integration and switch to the Euler from Runge Kutta? (The lastes, however, I have not the slightest idea of ​​how it could be set)

Here is an example of the data registered. It can be helpful