Geometrical modeling of a two-dimensional sensor array for determining spatial position of a passive object

This paper presents a model of an active sensor array which can determine the spatial position of a passive object by illuminating the object via a small set of emitters and measure the intensity of the reflection by means of a small set of receivers. All emitters and receivers are located in the same two-dimensional plane. The model is based on geometrical observations and provides a mapping of the measured reflected intensities to spatial position. The mapping is derived from intersection sets of prolate spheroids with emitters and receivers in the focal points, and it is shown that the mapping, therefore, has a series of interesting properties. The optimal positions of emitters and receivers are also derived.