Performance Analysis for Estimating a Target's Relaxation Frequencies from Frequency-Domain Electromagnetic Induction Data

We present three analyses that explore the behavior of the Cramer–Rao lower bounds (CRBs) on estimating a target’s relaxation frequency response from frequency-domain electromagnetic induction (EMI) data. In the first analysis, we show that the CRB on a given relaxation frequency is independent of the amplitudes of the other relaxations present in the target’s relaxation frequency response. In the second, we show that the presence of a second relaxation frequency closer than one decade in frequency greatly increases the CRB on that relaxation frequency. Finally, we illustrate the behavior of the minimum root-mean-square error (RMSE) per relaxation frequency as a function of the number of relaxation frequencies present in the target’s relaxation frequency response.