I'm successfully using an Extended Kalman Filter for object tracking. My state vector ($x, y, v_x, v_y$) needs to be in cartesian coordinates. The measurement data is transmitted in polar coordinates.
The state transition equations (and thus the state transition matrix) are linear: \begin{align} x_{k+1} &= x_{k} + v_{x,k} \cdot \Delta t \\ y_{k+1} &= y_{k} + v_{y,k} \cdot \Delta t \\ v_{x,k+1} &= v_{x,k} \\ v_{y,k+1} &= v_{y,k}. \end{align}
So the non-linear relation of the measurement vector in polar coordinates to my state vector in cartesian coordinates is the only reason why I used an EKF.
A simpler approach could include a "classic" transformation of my measurement data from polar to cartesian coordinates before feeding it into a standard Kalman Filter.
Assuming that I transform my measurement noise covariance matrix accordingly: Would this have an impact on the filter performance (e.g. because the measurement noise can't be assumed as gaussian any more)?