In this paper, we describe an original mathematical technique for calculating the position and orientation of an electromagnetic coil from a minimum of four collinear magnetic field measurements. This problem arose in the development of a system for evaluating the efficacy of inflatable back rafts designed to mitigate complications that arise from the immobilisation of patients with suspected spinal injuries on spinal boards during transport to hospital. Electromagnetic markers are attached to points of interest on the back of an immobilised test subject. Spinal curvature is then measured by passing a magnetometer underneath the board