integrate to get displacement from acceleration over time

I tried this before, but didn't get accurate results and stopped.

The idea in integration is to sum the difference between consecutive
values of your data stream multiplied by the duration of the interval
between these values (like computing a surface):
-> sum [ (value[timeX]-value[timeX-1])*(timeX-(timeX-1)) ]

should give you the speed. And if you apply the same process on speed,
you'll get the position.

You probably won't get your data on a regular time interval, so
timeX-(timeX-1) will vary over time.

The problem is that the datas, and especially the time intervals, are
not extremely accurate, so after a while, your speed won't be 0
although the accelerometer doesn't move anymore because the sum of
acceleration and deceleration won't _perfectly_ match. And so the
positions will move too.

As an accelaration of 0 doesn't mean that there is no movement (I was
surprised to notice that the violin player I worked with moved her bow
with a perfectly stable speed, i.e. no acceleration!), it is not easy
to add some "reset" function to the speed and position; it depends on
the physical properties of your moving object (in the case of a bow,
you know the range of the movement, and could eventually manually reset
the position when an extremity of the bow is reached).

Another issue is that your accelerometer will probably return 0->1 G
values if it's only rotated, without changing its position within the
world.

Good luck.

_____________________________
Patrick Delges

Centre de Recherches et de Formation Musicales de Wallonie asbl
http://users.skynet.be/crfmw/max