Landmine detection can be cast as a model selection problem in which probability theory is used as logic for inductive inference. Using this method, the landmine detection decision is based on the values of calculated posterior probabilities for two propositions: 'The received signal is from a landmine' and 'The received signal is from the background.' The posterior probability for a proposition is the probability for the proposition given the observed data signal and the information known prior to the observation. Calculation of the posterior probability requires the numerical integration of a multi-dimensional probability density function. Until the beginning of the last decade, there were few robust methods available to perform these numeral integrations and no methods that could be generally applied. As a result, probability theory as logic for inductive inference found only infrequent use in practical detection algorithms. Because of the increasing power of computers and new research in the areas of Markov chain Monte Carlo and multi-dimensional adaptive-quadrature integration methods, practical detection algorithms based on the use of probability theory as logic for inductive inference are now being developed and used. This paper describes our model selection formulation of the landmine detection problem and presents results obtained using multi-dimensional adaptive quadrature.
Probability as logic is used to estimate the surface velocity of a patch of soil driven by an incident acoustic wave. The data used by the estimation procedure is obtained from a laser Doppler vibrometer (LDV). The output of the LDV is an intermediate-frequency carrier that is frequency- modulated by the soil surface velocity. Additionally, the LDV output is amplitude modulated by an undesirable variation in the returned laser signal due to dynamic optical speckle. The effect of the amplitude modulated by an undesirable variation in the returned laser signal due to dynamical optical speckle. The effect of the amplitude modulation on the estimate of the soil surface velocity is illustrated with results obtained using the Markov chain Monte Carlo method.
Sound waves from a powerful loudspeaker can excite a certain type of vibration of the surface of the ground when a mine is present and near the surface. In turn, a laser-Doppler vibrometer can be employed to acquire information about the surface vibrations. In particular, the portion of the ground surface that is vibrating has the shape of the projection of the mine onto the surface. This paper discusses a method based on Bayesian probability theory for processing laser- Doppler vibrometer data to infer the periphery of any surface vibration pattern. Difficulties with using a phase- lock loop in determining a surface map are also discussed.