Converting coordinate system is really the main reason the Extended Kalman Filter was invented.

Yet I will tell you tip, it doesn't work well in those cases.  
If you use Non Linear Transformation use something that will both make things easier and better (Yea, usually it doesn't work like that, but in this case it does) - Use the Unscented Kalman Filter (UKF) which is based on the [Unscented Transform][1].

It is easy to see that linearization doesn't work well for propagating the mean and the covariance in many (Most) cases.  
The UKF directly approximate the calculation of the integration of the non linear function which calculates the mean and covariance.

It will make things easier as you'll be able to skip the linearization step and only know the coordinate transformation function.


  [1]: https://en.wikipedia.org/wiki/Unscented_transform