GELS: Gradiometer-Based Electromagnetic Localization System Achieves Closed-Form 6-DoF Pose Estimation for Medical Tools

The authors propose GELS, a gradiometer-based electromagnetic localization system that uses a compact magnetometer array as an embedded quasi-gradiometer to estimate the local magnetic field and gradient tensor, then maps displacements via the Euler homogeneous relation and uses Procrustes registration with at least three noncollinear sources to recover the array's orientation and position. The closed-form algorithm requires only known source positions and array geometry, with no pre-calibrated workspace field maps, initial pose guesses, or calibrated source magnetic moments; in benchtop experiments, the solver's median runtime was 172.00 microseconds. Perturbation analysis identifies inter-sensor inconsistency and dipole model mismatch as the main accuracy limits.