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A robust ground penetrating radar (GPR) signal processing approach is developed and applied to the sensing of surface soil and ice/water layers as well as near-surface buried objects. The principal technique relies on a reference set of waveforms, which are tested for optimal matching with measured radar reflections to be analyzed. In principle, the reference set can be based on measurements as well as on model output, with the latter employed. Even when layers are quite thin relative to the incident wavelength or pulse, the approach provides accurate information on layer characteristics, particularly thickness. The method assumes a well-defined transmit signal and hence is best used with antennas elevated shove the surface, In tests using UHF pulses on lab and field ice and on thawing soil, the system offers approximately an order of magnitude improvement in layer resolution relative to more traditional methods. Also, in the process of its signal-matching calculations, the procedures provide a numerical indication of the reliability of each result. In application to thawing soil, simulations suggest that one can address a wide variety of conditions using quite a limited set of reference signals. By detecting the thin-layer effect from soil over a buried metallic object, the system also locates near-surface targets when their reflections cannot be separated in time from ground surface returns. An alternative system also succeeds in detecting near-surface objects under the same conditions by detecting wavelet dispersion. This is done without reliance on specific details of transmit wavelet or reflected signals. A mine-like target is detectable in a wet clay soil when the ground is frozen but not when it is thawed.