Improved capacitive touch and hover sensing with a sensor array is provided. An AC ground shield positioned behind the sensor array and stimulated with signals of the same waveform as the signals driving the sensor array may concentrate the electric field extending from the sensor array and enhance hover sensing capability. The hover position and/or height of an object that is nearby, but not directly above, a touch surface of the sensor array, e.g., in the border area at the end of a touch screen, may be determined using capacitive measurements of sensors near the end of the sensor array by fitting the measurements to a model. Other improvements relate to the joint operation of touch and hover sensing, such as determining when and how to perform touch sensing, hover sensing, both touch and hover sensing, or neither.