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Originally Posted by Invictus3593
What if the time variable was such a very short amount of time, like 50ms,
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Shorter integration times are generally better. You will still see some drift due to the double integration and the fact that the measured accel has error.
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...and you just took the average acceleration over that time period?
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That's what trapezoidal integration tries to do.
Play around with it in a spreadsheet or Maxima or Octave or SciLab and see for yourself.