Incorporating Uncertainty in Unexploded Ordnance Discrimination

We examine representations of feature vector uncertainty in the context of unexploded ordnance (UXO) discrimination with electromagnetic data. We compare a local uncertainty estimate derived from the curvature of the misfit function with global estimates of the model posterior probability density (PPD) obtained with Markov chain sampling. For well-posed experiments (i.e., with high SNR and adequate spatial coverage), the two methods of uncertainty appraisal agree. However, when the inverse problem is ill posed, we find out that the PPD can be multimodal. To incorporate these uncertainties in discrimination, we first develop an extension of discriminant analysis which integrates over the posterior distribution of the model. When dealing with multimodal PPDs, we show that an effective solution is to input all modes of the PPD-corresponding to all models at local minima of the misfit-into discrimination and, then, to classify on the basis of the model which is most likely a UXO.