Modeling position error probability density functions for statistical inversions using a Goff–Jordan rough surface model

Abstract

Buried unexploded ordnance (UXO) continues to be a difficult remediation problem from both a sensing and a discrimination point of view. Modern approaches to both the sensing and discrimination problems utilize high bandwidth electromagnetic induction (EMI) sensors to collect geo-referenced data which is then inverted, or fit, using a forward model in order to obtain features that can be directly interpreted using the physics associated with electromagnetic induction-based sensing. These features are then used in a variety of classification architectures. One aspect of this process that has captured recent interest is that uncertainty in the positions at which data was collected can degrade the inversion performance and thus the subsequent classification. Several mechanisms to address this issue have been explored that range from filtering and prediction of actual positions to exploiting Bayesian approaches for uncertainty mitigation. In the Bayesian approach, a statistical model of the position errors is used as a prior for integrating over the uncertainty in the inversion process. In this study, we demonstrate that errors in the statistical priors used in this process can negatively impact subsequent classification performance, thus highlighting the need for an accurate statistical model for the position errors. Next, we propose a mechanism by which to obtain such models. Specifically, we utilize a Goff–Jordan rough surface model and simulate the sensor data collection system motion over the simulated ground or ocean surfaces to calculate errors and generate statistical models. Our results suggest that this approach can be used to develop the statistical models necessary for mitigating uncertain position information.