Statistical classification of buried objects from spatially sampled time or frequency domain electromagnetic induction data

Abstract

[1] Methods for classifying objects based on spatially sampled electromagnetic induction data taken in the time or frequency domain are developed and analyzed. To deal with nuisance parameters associated with the position of the object relative to the sensor as well as the object orientation, a computationally tractable physical model explicit in these unknowns is developed. The model is also parameterized by a collection of decay constants (or equivalently Laplace-plane poles) whose values in theory are independent of object position and orientation. These poles are used as features for classification. The overall algorithm consists of two stages. First, we estimate the values of the unknown parameters and then we do classification. Classification is done by comparing either the raw data or some low-dimensional collection of features extracted from the data to entries in a library. The library can be constructed using either simulated or calibration data. A maximum likelihood method is developed and analyzed for the problem of joint pole, location, and orientation parameter determination. Here we examine and compare two classification schemes. The first classification method is based on data residuals generated from estimated signal parameters. This scheme performs well in low SNR cases. The second is based on estimated pole values themselves, which performs well in high SNR cases. We validate our methods on both simulated and field data taken from frequency and time domain sensors.

Statistical Classification of Buried Unexploded Ordnance Using Nonparametric Prior Models

“…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.…”

“…More specifically, for each object in the library, this distance metric was constructed using the mean pole vector and covariance matrix for the associated pole cloud. In essence then, our work in [24] and [25] was predicated on the implicit assumption that the pole cloud was Gaussian. As is evident from Fig.…”

“…In our previous work [24], [25], a processing algorithm was developed based on the fusion of the dipole scattering model and a parametric model for the eigenvalues of the MPT which are referred to here as principle axis polarizability functions (PAPFs). The model directly captures both the features for classification and the parameters required to infer the location and orientation of the buried object.…”

“…In terms of processing, a simple nonlinear least square method was used in [24] and [25] to extract poles, location, and orientation information from the data. Using the estimated poles, classification was performed using Mahalanobis distance metric.…”