In this paper, we propose a novel method for estimating the position and posture of a smartphone which has a magnetic dipole inside a speaker by using the weighted integral method with a linear magnetic sensor. We derive a system of linear equations relating the dipole position and the weighted integrals of the magnetic flux density on the linear sensor. We prove that, although the coefficient matrix for a single linear sensor is possible to be singular, use of two linear sensors that do not exist on the same plane enables us to uniquely localize the dipole. Based on the simulations, we develop a non-coplanar, cruciform array of magnetic impedance sensors. We demonstrate that the method is applicable to position and posture estimation of a neodymium magnet and a smartphone.
