A position determination system is provided comprising one or more fixed base units and one or more mobile units, wherein the system is arranged to determine the horizontal position of a mobile unit based on the proximity of said mobile unit to at least one base unit and wherein the system is arranged to determine the height of said mobile unit based on the air pressure sensed at the mobile unit and the air pressure sensed at one or more of the base units. The use of pressure sensors to determine height reduces the complexity of the infrastructure required for 3D positioning. The invention finds particular benefit in patient care and monitoring environments and in object tracking and inventory systems. The invention also extends to mobile units for use in the system, intelligent buildings fitted with the system and to methods of determining the position of mobile units.