Performance Analysis of Parameter Estimation in Electromagnetic Induction Data

Abstract

We derive the Cramer–Rao lower bound (CRB) for target tensor amplitudes and target location parameters that can be estimated from electromagnetic induction (EMI) measurements of a target. In deriving the bound, no restrictions are placed on the target type, target orientation, quantity, or location of the measurement positions, nor the geometry of the EMI sensor or sensor array. The analysis is applicable to both a scanned sensor and a stationary array, as well as both time- and frequency-domain sensors. We show how the bound varies as a function of target type, orientation, depth, and signal-to-noise ratio. In addition, we illustrate the ways to use the CRB and the Fisher information matrix to analyze the relationships between the tensor amplitudes and location parameters. We show results of the CRB analysis applied to an experimental frequency-domain Georgia Tech sensor for a few target types for a nominal 2-D scan geometry as well as the Time-domain Electromagnetic Multi-sensor Towed Array Detection System. We also provide an algorithm for estimating the target location and tensor that achieves the CRB.