Difficult terrain and vegetation make it difficult to collect high-quality data with currently available sensors. Current handheld sensors suitable for use in such environments must be supported by costly and/or cumbersome ancillary systems capable of precisely determining sensor location while data are being collected. This project is a proof-of-concept study for a simple handheld electromagnetic induction (EMI) sensor that would be capable of detecting and classifying buried objects and that does not require precise sensor position information. The basic system concept is a compact three-element handheld EMI array that can simply be waved over some suspected target location and then classify the target on the basis of its intrinsic EMI response in real time using a simple procedure initially introduced in SERDP project MR-1572 for purposes of estimating the number of targets within a sensor array’s field of view. 

Target classification using standard physics-based processing of EMI data collected over a target entails inverting the data to determine the target’s location, orientation, and three principal axis polarizability curves. The inversion is based on a dipole response model in which the polarizabilities specify the target’s intrinsic electromagnetic response. In order for this procedure to yield accurate results, measurements of the response at many locations and/or from many directions are needed and the locations of the sensor readings relative to each other must be precisely known. However, it turns out that by using the MR-1572 joint diagonalization procedure a set of data eigenvalues can easily be calculated that often mimic the shapes of the principal axis polarizabilities. This project focused on whether or not data eigenvalues can serve as surrogates for principal axis polarizabilities.

Technical Approach

The relationship between data eigenvalues and principal axis polarizabilities depends on the location of the target relative to the array elements and on the target orientation. To systematically examine the effects, the project team ran numerical simulations using a simple three-element array and a 37-mm target at various locations and orientations below the array. Polarizabilities and data eigenvalues were plotted, and in each plot a single scale factor was applied to the set of data eigenvalues to line them up with the polarizabilities.

From review of the plots, a “sweet spot” was visible 27 cm directly below the center of the array where the data eigenvalues match the polarizabilities perfectly. Moving off from the sweet spot introduces differential scaling of the data eigenvalues and mixing of the polarizabilities contributing to the different data eigenvalues. These effects can even be perverse enough to make the data eigenvalues look like the polarizabilities for a plate-like object.

Target orientation has no effect on the data eigenvalues at the sweet spot, but can exert a significant influence at locations where the data eigenvalues are not scaled replicas of the polarizabilities. The dominant effect appears to be target location relative to the array elements. Monte Carlo simulations were run to quantify the effects, looking at the extent of polarizability mixing in the data eigenvalues.

For the calculations reported below, the project team used 20-cm radius transmit/receive loop pairs set in a circle of radius 25 cm. Other calculations confirmed that array geometry details had no effect on the general conclusions. A 37-mm target was used and its location and orientation was randomly varied relative to the sweet spot 27-cm directly below the center of the array. At each location/orientation combination, data matrices for each time gate were calculated using a standard forward model. Each set was then jointly diagonalized for all the time gates to get data eigenvalues as functions of decay time. These data were reduced by calculating the best fit linear combinations of the 37-mm transverse and axial polarizabilities to the data eigenvalues.


With the target location unknown, the sensor array cannot be positioned in the “optimum” location where data eigenvalues are simply scaled replicas of the polarizabilities. Classification using data eigenvalues has to accommodate arbitrary linear combinations of the polarizabilities. Classification performance is seriously degraded with forced admission of arbitrary linear combinations of polarizabilities in the classification algorithm. As the spread of locations progressively increases, the data eigenvalues can no longer be considered as scaled replicas of the individual principal axis polarizabilities, but rather must be recognized as linear combinations of all of the target’s polarizabilities. Adding more sensors does not alter conclusions regarding the relationship between data eigenvalues and principal axis polarizabilities.


Although data eigenvalues have proved useful for identifying situations where there are multiple targets in the sensor’s field of view and often give an indication that a target of interest (TOI) may be present, they cannot replace principal axis polarizabilities as the primary data-derived parameters for classification. The loss of classification performance to clutter items whose principal axis polarizabilities can be closely reproduced using linear combinations of TOI polarizabilities is too large.

Consequently, a simple handheld EMI sensor that relies on data eigenvalues to reliably classify targets without precise sensor position information is not realistic. The polarizabilities needed for reliable classification can only be obtained by inverting the data, and a lot of data are required to reliably constrain the target location in the inversion process.