Low-Rank Model for Wideband Electromagnetic Induction Sensors

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Wideband electromagnetic induction (WEMI) sensors are used to detect, classify, and locate obscured targets. WEMI sensors can be designed to measure the magnetic fields either in the time domain or frequency domain. They also capture multiple location measurements from a target by either a physical sensor array, a synthetic sensor array created by scanning the sensor, or a combination of the two. This letter uses a physical model for the sensor to develop a low-rank model for WEMI data. The data are organized into a matrix where the rows contain the time/frequency measurements and the columns contain the multiple locations so all of the data can be exploited jointly. It is shown that this data matrix can be processed directly with singular value decomposition (SVD) to extract three independent terms—one for target signature, one related to location, and one for tensors that define the orientation. The low-rank model predicts a maximum rank for WEMI measurements and is exploited to provide a relationship between the rank of the measurements and the number of linearly independent tensors for the target. Results are presented from the laboratory data to validate the low-rank model and demonstrate the connection between the data’s rank and the physical target. The low-rank model leads to a new “filterless” processing paradigm for exploiting WEMI data by using the SVD to perform sensor calibration, hardware debugging, as well as target detection.