Global uniqueness of NMR magnetic tracking

Establish global uniqueness of position and device-axis estimation for scalar NMR magnetic-tracking configurations with field-aligned markers, including whether nonlocal measurement ambiguities exist beyond the local covariance analysis.

Background

The paper analyzes local position and device-axis uncertainty using covariance matrices derived from linearized measurement models. Such local covariance results characterize sensitivity near a given state but do not determine whether distinct, widely separated states produce identical measurements.

The scalar NMR readout, planar receiver geometries, field-aligned marker moments, marker-exchange symmetry, and reflection symmetries can create potential nonlocal ambiguities. The paper therefore identifies global uniqueness as unresolved and notes that its analysis does not establish whether the measured configurations are globally identifiable.