The objective of this project was to develop an algorithm that automatically determines the number of sources and their respective locations based on measure electromagnetic induction (EMI) sensor data. An algorithm was developed to enumerate, locate, and characterize individual signal sources given observation of their combined signals. No a-priori estimate for the number of sources is required. It is assumed a forward model exists, and that superposition holds, i.e. coupling between sources is ignored. A system of linear equations y = Ax is set up in which columns of matrix A contain expected signals from many hypothesized sources, and y contains the observed signal. Recently developed solvers designed for linear systems with sparse non-negative solutions make this approach feasible even when large numbers of sources are involved. With each iteration, the collection of hypothesized sources is refined using a Harmony Search algorithm. Application is demonstrated on the problem of locating multiple buried conductors based on EMI signals observed at ground surface.
This algorithm is designed to locate and identify buried conductive metal targets based on EMI signals collected at ground surface, and it addresses the case of multiple targets spaced so closely together that their signals overlap, and it is not possible to get isolated solutions on individual targets. The algorithm proceeds by successively refining a large collection of hypothesized point sources, whose number (parameter p) is typically 100 or more, intended to be larger than the number of actual buried targets present. As the algorithm iterates, the spatial distribution of sources evolves to produce better and better agreement with the observed EMI signals. After convergence, a clustering algorithm is run on the cloud of sources, and prominent clusters are identified as individual buried targets.
These data were collected with the Naval Research Lab (NRL) time-domain electro-magnetic induction (TEM) array, a state-of-the-art sensor with 25 transmitter coils and 25 receiver coils, each square in shape and about 40cm on a side, arranged in a 5 by 5 grid on a horizontal plane, making the overall instrument about 2 by 2 meters in size. This system is designed to discriminate buried unexploded ordnance from harmless clutter, to reduce the cost of cleanup at former Department of Defense sites.
The TEM operates by pulsing current sequentially through the 25 transmitter coils to develop transient magnetic fields in the sub-surface, which induce eddy currents in buried conductors, giving rise to secondary magnetic fields that are detected in the receive coils. Analysis of these signals is based on the dipole model, which assumes each buried conductor behaves as a point source, producing a transient dipolar field proportional to the transmitted primary field, where the coefficient of proportionality is a symmetric tensor with six unique elements. Each source is therefore fully characterized by nine values: three position coordinates and six tensor entries.
Three data sets are analyzed, representing three different kinds of data: the first is test-stand-data collected indoors at Blossom Point, MD, with the TEM array held approximately 6 feet off the ground on non-conducting supports, and metal targets carefully positioned below. This arrangement allows for testing the instrument without soil effects, and with accurate knowledge of the true distribution of sources. The second data set is field data from Aberdeen Proving Ground (APG), MD. It was collected on calibration target A1, which is a 155mm artillery round buried at about 1m depth. Here, soil is present, and the true target location is less accurately known. The third data set is the same A1 target from APG, but with four additional synthetic clutter targets added into the data.
An algorithm has been presented and demonstrated to locate and characterize multiple signal sources based on observation of their combined signals. The method relies on new solvers designed to provide sparse non-negative solutions for underdetermined linear systems of equations, permitting many hypothetical sources to be evaluated jointly with each iteration. Most of these sources receive zero weight, but those with positive weight drive successive refinement of the collection. A crucial consideration is the grouping of non-negative weights into local neighborhoods to estimate true sources which may be located inside. This grouping is done by partitioning the volume into tetrahedrons, each vertex of which is a non-zero source that received weight in the preceding iteration. Approximation of the presumed true source inside is accomplished by locating the tetrahedron centroid and then assigning source parameters to best match the summed signal from the four vertices. The overall number of sources in the system is indicated by the number of clusters in the output, which may be detected by clustering algorithms capable of counting clusters, such as quality threshold clustering.
Application to the problem of electromagnetic induction is demonstrated, using signals from the NRL TEM array. Results show successful location of multiple sources for both in-air test stand measurements and field measurements. Future research is needed in speed improvements, automatic background removal, and the application to data acquired while moving.