The objective of this project was to explore alternatives to conventional dipole inversion for extracting target features from multi-axis electromagnetic induction (EMI) sensor array data. Conventional dipole inversion searches for the target parameter values (location and polarizabilities) that minimize the difference between measured signals and those calculated using the dipole response model. An alternative approach was considered that sought to determine the parameter values that would minimize an objective function based on the dispersion in estimates of the target’s polarizability using different combinations of transmitters and receivers.

Technical Approach

The alternative inversion approach exploits rotationally invariant properties of the polarizability tensor. Focusing the processing on the primary invariant (trace of the polarizability tensor) significantly limits the search space that is required to invert EMI data. Conventional dipole inversion requires that one search over target (x, y, z) location, target (θ, φ, ψ) orientation, and (β1, β2, β3) principal axis polarizabilities to minimize the difference between the measured response and response predicted by the dipole model fit. With tensor invariant processing, one only needs to search on (x, y, z) to find the target location that minimizes the dispersion in calculated values for the rotationally invariant trace. The principal axis polarizabilities can then be calculated directly.


This project documented results on the convergence properties of a downhill simplex based algorithm for determining a target’s location (and polarizabilities) using this approach. Specifically, this work examined convergence of the algorithm for data collected with the 2x2 TEM array at the former Camp Beale in 2011 and found no impact due to signal-to-noise ratio (SNR) and background leveling effects. However, the minimum polarizability dispersion does vary systematically with SNR—targets with higher SNR tend to have less uncertainty (dispersion) in the polarizability estimate than those with lower SNR.

Testing shows that polarizability dispersion based inversion can produce more accurate polarizabilities than conventional dipole inversion in some cases. However, the fraction of targets in the ESTCP classification demonstrations that cannot be accurately analyzed using conventional dipole inversion may be small enough (<5%) that modest improvements in calculating the polarizability are likely to have very little effect on classification performance.

This project also documented a new size-shape classification algorithm for comparing unknown target polarizabilities with those of munitions items and other targets of interest. It appears to produce better classification performance than the library comparison procedure that this project had been using. The performance of the size-shape classification algorithm was also compared using the average polarizability (equivalent to the trace of the polarizability tensor) with the performance for the full set of three principal axis polarizabilities using data from the ESTCP demonstrations at Camp San Luis Obispo, Camp Butner, Camp Beale, and Pole Mountain. The differences are not large, but the 3β receiver operating characteristic (ROC) tends to rise a bit faster than the <β> ROC. Because the two approaches can emphasize slightly different features in the EMI response, different targets tend to drive the ROC behavior of the different classifiers.


By its very nature, polarizability dispersion based inversion provides a direct measure of the uncertainty in the polarizabilities calculated from EMI data collected using advanced sensor arrays. The benefits of the new classification algorithm are both quantitative and qualitative. Re-processing data from the recent Camp Beale demonstration using this approach produced a ROC that rises more rapidly and hits the 100% target of interest (TOI) recovered level with 50% fewer clutter digs beyond the training set than the ROC from conventional processing. Improved classification performance improves munitions response efficiency. The procedure operates in an intuitive and easily visualized feature space. It is transparent, objective, and easily automated. All of this is likely to facilitate transition to production work and ease regulatory acceptance.