When using the compression sensing (CS) localization algorithm for large scene environments based on the wireless local area network (WLAN), there are two challenges: reduced positioning accuracy and increased computational complexity. To address them, this paper first introduces an improved clustering algorithm for coarse localization to reduce the search range. Specifically, for the singular value problem of wireless signals, we innovatively propose the adaptive intuitionistic fuzzy c-ordered mean clustering algorithm. Secondly, to overcome the high storage pressure brought by the high-dimensional observation matrix, a semi-tensor product compression sensing (STP-CS) technique is proposed. Compared with the traditional CS method, this method can accommodate more access points while maintaining the same dimensionality. Experimental results show that the algorithm proposed in this paper significantly reduces the storage space required by the observation matrix and the computational overhead under the premise of ensuring positioning accuracy. These advantages make it particularly well-suited for large-scale applications.