A parameter estimation system includes a first coil configured to be loosely inductively coupled to a second coil. A controller is programmed to output parameters of the first coil and second coil. The controller is programmed to estimate the parameters based on voltage and current measurement from only the first or the second coil. The voltage and current measurements may be used in a Kalman filter. In some configurations, the controller is further programmed to command a short circuit between terminals of the second coil and apply a test voltage to the first coil. The first coil may be part of a vehicle charging station and the second coil may be part of a vehicle. The parameters may be utilized to control charging of the vehicle.