Characterization of binary string statistics for syntactic landmine detection

Syntactic landmine detection has been proposed to detect and classify non-metallic landmines using ground penetrating radar (GPR). In this approach, the GPR return is processed to extract characteristic binary strings for landmine and clutter discrimination. In our previous work, we discussed the preprocessing methodology by which the amplitude information of the GPR A-scan signal can be effectively converted into binary strings, which identify the impedance discontinuities in the signal. In this work, we study the statistical properties of the binary string space. In particular, we develop a Markov chain model to characterize the observed bit sequence of the binary strings. The state is defined as the number of consecutive zeros between two ones in the binarized A-scans. Since the strings are highly sparse (the number of zeros is much greater than the number of ones), defining the state this way leads to fewer number of states compared to the case where each bit is defined as a state. The number of total states is further reduced by quantizing the number of consecutive zeros. In order to identify the correct order of the Markov model, the mean square difference (MSD) between the transition matrices of mine strings and non-mine strings is calculated up to order four using training data. The results show that order one or two maximizes this MSD. The specification of the transition probabilities of the chain can be used to compute the likelihood of any given string. Such a model can be used to identify characteristic landmine strings during the training phase. These developments on modeling and characterizing the string statistics can potentially be part of a real-time landmine detection algorithm that identifies landmine and clutter in an adaptive fashion.