An electronic device may be provided with wireless circuitry that includes first, second, and third antennas used to determine the position and orientation of the electronic device relative to external equipment. The antennas may include patch elements on respective substrates mounted to a flexible printed circuit. Each substrate may include fences of conductive vias that are coupled to ground and that laterally surround the corresponding patch element. Control circuitry may identify phase differences between the first and second antennas and between the second and third antennas and may identify an angle of arrival of received ultra-wideband signals using the phase differences. The control circuitry may compare the phase differences to a set of predetermined surfaces of phase differences to identify environmental loading conditions for the antenna. The control circuitry may correct the angle of arrival using offsets identified based on the environmental loading conditions.