Wideband radars are sensors of new generation used for target detection and classification. Detection of moving targets with wideband radar faces range migration phenomenon which is used to resolve velocity ambiguities in low pulse repetition frequency mode. The resolution is equivalent to a bi-dimensional spectrum estimation problem with non-uniform sampling, while the ability to resolve velocity ambiguity depends on spectral resolution of the method used. Recently Iterative Adaptive Approach (IAA) was shown an attractive solution of this problem. Nevertheless straightforward implementation of IAA for wideband signal suffers from high computational requirements. In this paper fast implementation of IAA for wideband data is proposed and studied with numerical simulations. Proposed solution decreases computational cost by an order of magnitude for realistic data sizes.