###### Abstract  
The intelligent reflective surface (IRS) is a novel network node that consists of a large-scale passive reflective array to obtain a customized reflected wave direction by modulating the amplitude phase, which can be easily deployed to change the wireless signal propagation environment and enhance the communication performance under a non-line-of-sight (NLOS) environment, where location services cannot perform accurately. In this study, a low-rank matrix reconstruction-enabled fingerprint-based localization algorithm for IRS-assisted networks is proposed. Firstly, a 5G positioning system based on IRSs is constructed using multiple IRSs deployed to reflect signals. This enables the base station to overcome the influence of NLOS and receive the positioning signal of the point to be positioned. Then, the angular domain power expectation matrix of the received signal is extracted as a fingerprint to form a partial fingerprint database. Next, the complete fingerprint database is reconstructed using the low-rank matrix fitting algorithm, thereby considerably reducing the workload of building the fingerprint database. Finally, maximal ratio combining is used to increase the gap between the fingerprint data, and the Weighted K-Nearest Neighbor (WKNN) algorithm is used to match the fingerprint data and estimate the location of the points to be located. The simulation results demonstrate the feasibility of the proposed method to achieve sub-meter accuracy in an NLOS environment. 20241317431317431  
or triangulation-based localization methods [16; 17; 18; 19]. However, the measurement computation of this method requires the cooperation of multiple base stations, thus generating a large amount of information exchange overhead. To solve this problem, fingerprint-based localization methods [20] have been developed. The fingerprint localization method first constructs a fingerprint database required for localization in the offline phase. Subsequently, the fingerprint user data are matched to the localized signal received in real time with the data in the fingerprint database in the online phase to obtain the coordinates of the user to be localized. Traditional fingerprint data include the received signal strength (RSS) [21]; however, the RSS is susceptible to multipath effects, resulting in low localization accuracy. By contrast, channel state information (CSI)-based fingerprinting [22; 23; 24; 25] contains more multipath information than RSS, which can improve the accuracy of localization in multipath environments. In addition, the user can use MIMO technology to obtain high-resolution multipath characteristics in the angular domain of the channel, which improves the strength of the localization signal. In [26], an angle delay channel power matrix (ADCPM) was extracted from the MIMO channel as a fingerprint, and the fingerprint compression method and fingerprint clustering algorithm were combined to realize localization. Consequently, the numerical results verified the reduction in computational complexity and the ability to locate when using the proposed algorithm. In [27], a deep convolutional neural network (DCNN) localization algorithm combining an angular delay channel amplitude matrix (ADCAM) as the fingerprint was proposed, and the results confirmed the high localization accuracy of the algorithm. In [28], a noise reduction strategy was proposed to improve the accuracy of localization using the sparsity of ADCPM fingerprints. The above algorithms can solve the problem of low positioning accuracy caused by multipath signals to a certain extent; however, in the case of a non-line-of-sight (NLOS) path, where direct communication between the base station and the user is absent, the positioning accuracy of the above methods is very poor or even impossible. The intelligent reflective surface (IRS) [29; 30; 31; 32; 33], which has received significant attention in recent years, is expected to be the key to solving the problem of the inability to perform localization in an NLOS environment.