Wednesday (Group 2) - SERDP-ESTCP - Strategic Environmental ...

Munitions Management (MM)
Poster Number 45 – Wednesday
Ground Based Detection and Discrimination — EMI & Magnetometers / Modeling & Processing
ROBUST STATISTICS FOR UXO DISCRIMINATION
DR. STEPHEN BILLINGS
Sky Research, Inc.
2386 East Mall, Suite 112A
Vancouver, BC V6T1Z3 CANADA
(541) 552-5185
stephen.billings@skyresearch.com
CO-PERFORMERS: Laurens Beran and Douglas Oldenburg (University of British Columbia)
T
he objective of SERDP MM-1629 is to provide more statistically rigorous solutions to the
inversion problems that occur as integral parts of any UXO discrimination scheme.
Experience from demonstration projects has shown that inversion of TEM data with low SNR is
susceptible to outlying data, so that the global minimum of the misfit does not provide a model
which can be reliably used for discrimination. This problem can be addressed by using a misfit
function which is less sensitive to outliers, or by iteratively updating data uncertainties so that
data which cannot be fit are downweighted during inversion. In the former approach, L1 type
norms replace the conventional L2 misfit. This introduces additional nonlinearity to the inverse
problem, and the resulting algorithm in fact requires iterative reweighting of data uncertainties.
Hence robust norms can be regarded as equivalent to iterative update of an L2 norm. We have
investigated the latter approach by developing a formal Bayesian technique to updating data
uncertainties. Application to real data reduced the effect of outliers on the inversion process, and
resulted in improved parameter estimates.
Discrimination requires estimation of features which provide information regarding target size,
shape or composition. Inversion of TEM data extracts useful features which can then be used to
make discrimination decisions. However, parameters estimated in the inversion process are not
point estimates but have an associated uncertainty which is a function of the uncertainty in the
data and the curvature of the misfit function at its minimum. For example, when the model
parameters are well constrained (i.e., have a small uncertainty), the misfit function will have a
high curvature at the final model. For a nonlinear inverse problem, the posterior distribution of
the final model can then be approximated as a Gaussian distribution with covariance inversely
proportional to the curvature of the misfit. To investigate the utility of including parameter
uncertainty in discrimination, we have developed a “Gaussian product” classifier which uses
feature vectors and their associated uncertainties to make discrimination decisions. The classifier
discounts parameters that are highly uncertain from the discrimination process. For example,
when applied to TEM data from Camp Sibert, we found that the decay of the primary
polarization had a large uncertainty relative to the amplitude of the polarization. Consequently,
the Gaussian product classifier made discrimination decisions based primarily upon the
amplitude of the polarization.
G-13