I have the accelerometer and gyroscope data series with a sample rate of 60HZ. I want to convert this data and track the real motion that took place while recording the data.
Hello,
use https://en.wikipedia.org/wiki/Inertial_navigation_system for starters. It provides a lot of informations, including some good estimates about the precision achievable.
The basic problem is that both devices measure acceleration. Plus the fact that the gravitational acceleration overlays any acceleration that's measured my the accelerometer. If you do not know the direction of graviation with respect to the orientation of the accelerometer, you cannot calculate the addtional acceleration component.
Thus the gyrometer is required to track the orientation of the accelerometer (starting from a static start position where no acceleration other than graviation is in effect). nd only with the 'corrected' orientation of the accelerometer you can calculate actual 'effective' acceleration.
So much about acceleration. To get total displacement, you have to integrate the values from gyrometer and accelerometer twice. (The first integration gives rotational resp. linear speed, the second - the integrate of rotational resp. linear speed - gives the 'way' or 'displacement.)
Aside from the aspect that acceleration values depend on the precision of tracking the orientation of the accelerometer, the double integration integrates all errors that occurred until now: analog asymmetries, digitization errors, not-perfectly-symmetrical noise, calculation errors (eg. rounding errors) and so on.
This is why 'normally' acceleration-based inertial sensors are assisted by further sensors (eg. magnetometers or GPS). Thus the drift of the double integration can be corrected periodically by the measurements from the additional sensors.
You may as well look up "sensor fusion" at wikipedia, which will give you additional informations. Though the above link should be really great for starters - giving quite a number of links to documents about details.
Wish you success
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