I don't believe that the system you describe is "observable" using just a single accelerometer -- the basic problem from what I understand is that a single accelerometer cannot tell if the change in measured acceleration is from DV/dt or changes in gravity from changes in angle.
I think it would be possible to use several (at least 2) accelerometers to do the angle calculation BUT... ...you will have practical problems.
To get angle from a yaw rate sensor you only have to integrate once (from Omega to Theta) . In general, integration is more friendly than differentiation, but it does involve that Constant term and there is that drift problem (small errors add up).
To get angle from acceleration, I think you will have to effectively integrate twice (once to go from Acceleration to Velocity, then again to go from Velocity to Position). This adds 2 Constant terms and there is a REALLY tough drift problem (small errors add up FASTER AND FASTER as time goes by).
I think a gyro (an angular rate sensor) is probably the better way to go.
Joe J.
P.S. I'm not here and you didn't read this ;-) I am much too busy at
Robotic Amusements, Inc., getting ready for our product launch at the
AMOA Show in Sept. Wish us luck...