Current mobile robot ultrasonic localisation techniques use sensor systems which rely on features in a horizontal plane. The implicit assumption is that the room boundary on the horizontal plane is not obstructed by objects such as furniture. This assumption is often not realistic and restricts the versatility and portability of these systems. The solution proposed in this paper is the provision of sensing flexibility to use other 3D room boundaries (e.g. ceiling-wall intersections) as 3D natural beacons. We propose a 3D ultrasonic sensor array that uses a Maximum Likelihood Estimator to match the echo arrival times to different object classes and to determine the location of the 3D target. This method does not require fast data acquisition or powerful computing. It has been implemented on a robot localisation application with the Extended Kalman Filter. This paper is the first of two parts, and presents theoretical results on target classification and minimum transducer requirements. The second part, in the next issue of Robotica, presents experimental results on the characterisation of the sensor and its application to robot localisation, and includes the references for the both papers.