On the singular problem in linear algorithm for the magnetic dipole positioning

Magnetic dipole positioning technique has attracted more and more attention recently, for its increasing applications in medical, traffic, and the tracking of motion objective, because it provides high accuracy and fast velocity. Typically, a nonlinear optimization algorithm is applied to such a problem, but a linear algorithm is preferable for faster, more reliable computation, and lower complexity. We proposed a linear algorithm to determine the 5D dipole´s position and orientation parameters. However, there exist several singular problems in the linear algorithm that cause failure computation and discontinuous results. These singular problems are related to 1 or 2 zero orientation parameters, lower than 4 rank of sensing matrix for computation, and singularity in solution vector. In this paper, we present these singular problems and propose some methods to handle them. Simulations were done and results show that by solving these problems, the linear positioning algorithm is much more stable and accurate.