Question: Is it possible to use the accelerometer to detect height? For instance, if I'm holding the phone on my hand and then detect the height after raising my arm?

Thanks

Answer: 
You get position by integrating the linear acceleration twice but **the error is horrible. It is useless in practice.**

Here is [an explanation why (Google Tech Talk)](http://www.youtube.com/watch?v=C7JQ7Rpwn2k) at 23:20. I highly recommend this video.

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First of all you measure Linear acceleration and gravity together (also some noise)
So it means when you are using accelerometer you will get
Accelerometer Readings = Linear Acc. + Gravity + Noise
Here you just only need Linear Acc. but the Accelerometer reads all the values