Information-based Unified Design Framework for NMR Magnetic Tracking System

Abstract: Nuclear magnetic resonance (NMR) magnetic tracking offers a promising alternative to magnetic resonance imaging (MRI)-based localization for medical robotic guidance. However, scalar field measurements and field-aligned marker moments constrain position and orientation tracking, requiring careful configuration design. We present a unified information-based framework that uses local covariance analysis to evaluate receiver geometry, marker separation, and external source configuration in on/off-board NMR tracking. Numerical evaluation shows that planar-array precision depends jointly on receiver count and geometry, with triangular lattice arrays achieving the lowest best-case position uncertainty among the evaluated layouts for 9--20 receivers. Two spatially separated, field-aligned markers enable device-axis tracking, with predicted angular uncertainty below $2<sup>\circ$ at the evaluated workspace center for suitable marker separations. We further establish point-dipole source--receiver duality, unifying the analysis of on/off-board NMR tracking. These