<p>This paper focuses on the sparse representation direct position determination (SR-DPD) method in motion scenarios with a single station. In contrast to the conventional two-step positioning method, the SR-DPD method eliminates the need to estimate intermediate positioning parameters, but directly processes the original sampled signal to determine the position estimate of the source, resulting in higher positioning accuracy even at low signal-to-noise ratio (SNR). Furthermore, the SR-DPD method can simultaneously locate multiple sources, thus avoiding the issue of complex data association. Using the SR-DPD method, the sparse signal containing the source position information can then be restored to achieve the positioning result. However, currently available recovery algorithms are constrained by the mutual coherence of the measurement matrix, and are therefore unable to locate adjacent position sources. Two scenarios of ideal and adjacent positions are investigated, and for the problem of adjacent sources, we propose an iterative local search (ILS)-based position method, which can update the source position according to the residual minimization criterion within a given search range and improve the resolution of positioning sources. The simulation results demonstrate the effectiveness of the proposed method.</p>