On the low-frequency natural response of conducting and permeable targets

Abstract

Abstract-The low-frequency natural response of conducting, permeable targets is investigated. We demonstrate that the source-free response is characterized by a sum of nearly purely damped exponentials, with the damping constants strongly dependent on the target shape, conductivity, and permeability, thereby representing a potential tool for pulsed electromagnetic induction (EMI) identification (discrimination) of conducting and permeable targets. This general concept is then specialized to the particular case of a body of revolution (BOR), for which the Method-of-Moments (MoM)-computed natural damping constants from several targets are compared with measurements. Moreover, theoretical natural (equivalent) surface currents and damping coefficients are shown for other targets of interest. Finally, we investigate the practical use of such natural signatures in the context of identification, wherein Cramer-Rao bound (CRB) studies address signal-to-noise ratio (SNR) considerations.

Statistical Classification of Buried Unexploded Ordnance Using Nonparametric Prior Models

“…The objects include the following: a 3-in long by 1-in diameter stainless steel cylinder (S1), a 6-in long by 1-in diameter stainless steel cylinder (S2), a 3-in long by 1-in diameter aluminum cylinder (A1), and a 6-in long by 1-in diameter aluminum steel cylinder (A2). The target responses were generated with a four-pole per axis dipole model in which the sums in (3) are terminated after the four terms [21], [24]. The poles used for this simulation were generated using the methods in [21].…”

“…The processing model used here is based on [24], which is a truncated version of the EMI physical model in [9] and [21]. Using this model, the scattered signal collected at M time gates or frequencies (depending on the sensor) at each of L locations in space can be written as …”

“…1 shows an example of a library (feature space) built for a steel cylindrical object corresponding to five possible object depths, seven possible values for each of the three Euler angles, and no horizontal variation of target. Data were generated using a four-pole per axis dipole model in which the sums in (3) are terminated after four terms [21], [24]. In our previous work [24], classification was done in feature space using a pole library in a fairly simplistic manner.…”

“…In theory, the veracity of this model requires illumination of an infinitesimally small target by a uniform field, which is a condition that is not generally met in practice. Moreover, given limited noisy data, at most, a single term in each of the three sums can be estimated reliably [21], leading some investigators to use forms of the model employing only two exponentials [21], [23] on the assumption that targets of interest are spheroidal and, therefore, have two equal eigenvalues. These theoretical and practical limitations of the dipole model impart a position and orientation dependence on the object-specific parameter estimates required for an accurate classification.…”

“…The model directly captures both the features for classification and the parameters required to infer the location and orientation of the buried object. The model uses a singlepole per axis version of the PAPF expansion introduced in [21] which results in a 3-D feature space with one-pole per body axis. Because of this approximation, the features are no longer independent of the object orientation and location.…”