State observer <-> Accelerometer

Hi,
I'm starting to learn control (state space approach) and have a question:
Most of the time the states (eg. position and velocity) can not be
measured directly, therefore we need a state observer. What if in the case where the states are position and velocity, however, only the acceleration can be measured? How can we use the measurement of acceleration to help designing the state observer?
I am not sure if it's true that as long as we know the initial velocity, we can integrate the acceleration measured to give the velocity so that we only need a reduced-order observer (because velocity are known by integrating the measured acceleration).
Thanks for reading and advices.
YongTze
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yongtze wrote:

If you are only measuring acceleration in a single axis then the velocity is unobservable. Integrating the acceleration twice to get position is theoretically possible, but very difficult to do in practice. Even relatively bad position feedback will markedly improve your accuracy.
You might want to google on "inertial navigation" -- it sounds like that's what you're talking about, and there's a whole body of knowledge on how to do it.
--

Tim Wescott
Wescott Design Services
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