When using the compression sensing (CS) localization algorithm for large scene environments based on the wireless local area network (WLAN), two challenges arise: reduced positioning accuracy and increased computational complexity. To address these issues, this paper 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 proposed algorithm significantly reduces the storage space required by the observation matrix and decreases the computational overhead under the premise of ensuring positioning accuracy. These advantages make it particularly well-suited for large-scale applications.