In classical TDOA/FDOA emitter location methods, pairs of sensors share the received data to compute the CAF and extract the ML estimates of TDOA/FDOA. The TDOA/FDOA estimates are then transmitted to a common site where they are used to estimate the emitter location. However, the two-stage method is not necessarily optimal because in the first stage of these methods, the TDOA and FDOA are estimated by ignoring the fact that all measurements should be consistent with a single emitter location. In this paper, we derive a one-stage localization method based on spatial sparsity of the grid plane. In this method, we directly estimate the location of the emitter without going through the intermediate stage of TDOA/FDOA estimation. The Monte Carlo simulation results show that the proposed method has better performance compared to two-stage classic method and also to another available one-stage method named Direct Position Determination (DPD). We will show that the proposed method is also a very effective and beneficial solution to deal with multipath scenarios.