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Indoor localization is one of the key topics in the area of wireless networks with increasing applications in assistive healthcare, where tracking the position and actions of the patient or elderly are required for medical observation or accident prevention. Most of the common indoor localization methods are based on estimating one or more location-dependent signal parameters like TOA, AOA or RSS. However, some difficulties and challenges caused by the complex scenarios within a closed space significantly limit the applicability of those existing approaches in an indoor assistive environment, such as the well-known multipath effect. In this paper, we develop a new one-stage localization method based on spatial sparsity of the x-y plane. In this method, we directly estimate the location of the emitter without going through the intermediate stage of TOA or signal strength estimation. We evaluate the performance of the proposed method using Monte Carlo simulation. The results show that the proposed method is (i) very accurate even with a small number of sensors and (ii) very effective in addressing the multi-path issues.