Apply Kalman filter to remove process noise, given zero measurement error
You're misunderstanding how the Kalman filter framework works. Your measurements are a reflection of what the underlying state of the system is at each time instant. If you have zero measurement covariance, then your measurements perfectly reflect the system state, so there's no need for any filter whatsoever. It's not likely that this is truly the case.

Process noise is a representation of uncertainty in the model for how your system's state changes as time goes on. It's not something to be "removed" by the Kalman filter. Instead, it gives you the ability to accommodate higher-order effects that you aren't modeling in your state transition matrix.