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Estimation of the basic parameters, wall thickness and dielectric constant, is important in through-the-wall radar imaging. Ambiguities in wall characteristics will degrade the image focusing quality of synthetic-aperture radar. In order to obtain a quick and precise estimation of wall parameters, an equivalent propagation model of an electromagnetic wave in the air-wall-air medium is first developed in this paper. According to the developed propagation model, two filter-based approaches, denoted respectively as the echo-domain-filter-based method and the image-domain-filter-based method, are proposed to estimate wall thickness and dielectric constant by adjusting the two corresponding parameters of the echo-domain filter or the image-domain filter to obtain the best focusing quality of behind-the-wall targets. The processing schemes of the two methods show that the image-domain-filter-based method is more efficient because it does not involve imaging processing in each adjustment. Moreover, the image-domain-filter-based method is accelerated by reducing the dimension of searching space to better the computational efficiency further. Simulation results show that the proposed accelerating image-domain-filter-based method can provide quick and precise estimation of wall parameters.