Kalman for 3D position and 1D orientation
Reading your link in more detail, it says:


  Acceleration ($\ddot{x}$ &amp; $\ddot{y}$) as well as position ($x$ &amp; $y$) is measured.


which, to me, is not a constant acceleration.  What it is doing is a discretized changing acceleration model, assuming that the acceleration is constant between each sample period.

Now to your question: is inclusion of $\phi, \dot \phi,$ and $\ddot \phi$ in the state vector valid?

The answer is yes, but you need to include the dynamics of how those states interact with the other states.  



OK, so now you've added the extra information, I can take a stab at it.

It should work with the following provisos:


The noise distribution on the angle $\phi$ will be uniform not Gaussian.  I can't find a good reference, but this discussion on comp.dsp mentions it.  That means the KF equations for $\phi$ won't be quite right.  I don't think this is a big deal.
There will be some coloration between the noise on $\phi$ and the noises on $x$ and $y$.  I'm not sure what this should be, but it may mean you need to introduce some off-diagonal terms in the $Q$ matrix in the KF formulation.