Upper bound on false alarm rate for landmine detection and classification using syntactic pattern recognition

Recently, there has been considerable interest in the development of robust, cost-effective and high performance non-metallic landmine detection systems using ground penetrating radar (GPR). Many of the available solutions try to discriminate landmines from clutter by extracting some form of statistical or geometrical information from the raw GPR data, and oftentimes, it is difficult to assess the performance of such systems without performing extensive field experiments. In our approach, a landmine is characterized by a binary-valued string corresponding to its impedance discontinuity profile in the depth direction. This profile can be detected very quickly utilizing syntactic pattern recognition. Such an approach is expected to be very robust in terms of probability of detection (Pd) and low false alarm rates (FAR), since it exploits the inner structure of a landmine. In this paper, we develop a method to calculate an upper bound on the FAR, which is the probability of false alarm per unit area. First, we parameterize the number of possible mine patterns in terms of the number of impedance discontinuities, dither and noise. Then, a combinatorial enumeration technique is used to quantify the number of admissible strings. The upper bound on FAR is given as the ratio of an upper bound on the number of possible mine pattern strings to the number of admissible strings per unit area. The numerical results show that the upper bound is smaller than the FAR reported in the literature for a wide range of parameter choices.