Unscented transform-based uncertainty analysis of rotating coil transducers for field mapping

The uncertainty of a rotating coil transducer for magnetic field mapping is analyzed. Unscented transform and statistical design of experiments are combined to determine magnetic field expectation, standard uncertainty, and separate contributions of the uncertainty sources. For nonlinear measurement models, the unscented transform-based approach is more error-proof than the linearization underlying the “Guide to the expression of Uncertainty in Measurements” (GUMs), owing to the absence of model approximations and derivatives computation. When GUM assumptions are not met, the deterministic sampling strategy strongly reduces computational burden with respect to Monte Carlo-based methods proposed by the Supplement 1 of the GUM. Furthermore, the design of experiments and the associated statistical analysis allow the uncertainty sources domain to be explored efficiently, as well as their significance and single contributions to be assessed for an effective setup configuration. A straightforward experimental case study highlights that a one-order-of-magnitude reduction in the relative uncertainty of the coil area produces a decrease in uncertainty of the field mapping transducer by a factor of 25 with respect to the worst condition. Moreover, about 700 trials and the related processing achieve results corresponding to 5 × 106 brute-force Monte Carlo simulations