There has been an ongoing discussion/debate about whether accelerometers are actually useful for attitude estimation on flying rotorcraft (quadrotors, in particular). The simple, one sentence answer is "yes, they are."
However, the accelerometer measurements are non-intuitive. If the estimation algorithm uses the accelerometers incorrectly (which is, incidentally, the norm on hobby and even some professional aircraft) then there will be significant errors.
There is some good literature available now that describes the problem. Martin and Salaun published a very good paper describing quadrotor flight dynamics. I also just finished my MS thesis, wherein I address the subject in detail.
In my thesis (the last link), Chapter 5 is what you'll want to look at.
Thanks for your helpful post Caleb. Would you possibly know an answer to the following question:
Attitude estimation with ONLY 3axis ACCELEROMETERS. and nothing else, based on a lowpass filter? where can I find an opensource way to do this?
Nice analysis. Of course there is always more work to be done... But it looks like a nice step in the right direction.
You appear to have an error in formula 5.15. Fortunately it does not appear to carry forward anywhere.
I can follow the math but cannot intuitively see how the LPF filter model corrects the phase lag between the accelerometer estimated and actual angles. Do you have an intuitive understanding of this that you can put in words?
Thanks Caleb for your great work and for being willing to share it with us.
FYI, Salaun's PhD thesis is also available (its mostly in English - don't be fooled by the first few pages)