# DNCL: Hybrid DOA Estimation and NMDS Cooperative Multi-Target Localization for RFID
## 1 Introduction
The tag position was further triangulated by manipulating the shape of the radiation direction map of the reader-transmitting antenna array to estimate the tag direction in [27]. The DOA uses the phase difference between individual elements in an antenna array to estimate the directional angle of the signal arriving at the array reference element. However, the good accuracy of DOA estimation is connected with the number of elements in the antenna array, and, in practice, it is not very feasible to locate low-cost RFID tags by deploying bulky, costly, and multi-element antenna array. Inspired by synthetic aperture radar (SAR) high-resolution imaging [28; 29; 30; 31; 32], one can use a single antenna moving scan method to obtain phase information. Through the relative motion of the antenna and the objects, the signals received by the antenna at different sampling point positions during the motion were combined to construct a virtual antenna array for DOA estimation. This approach has considerable practical value, as it does not require hardware configuration changes or sophisticated antenna array hardware installations. In the last ten years, although a great number of passive UHF-RFID tag localization methods have been proposed, practical applications still face challenging problems that demand further research, notably for RFID-based automated inventory management in warehouses. 3 Dloc [33] utilizes a continuous mobile RFID antenna, and the scanning of marked objects in the 2D space in front of the marked objects can realize the three-dimensional localization of the tagged objects. RF-3 DScan [34] enables the 3D reconstruction of the tagged packages. Based on RSS and measured phase, ReLoc [35] proposes a hybrid relative passive RFID localization technique, which is a practical item-level inventory management solution. In order to better localize objects using RFID, several reference tag-based approaches have been proposed to improve accuracy. PinIt [36] compared and matched the multipath profile of the target tag with the reference tags deployed in the environment, based on identifying the nearest neighbors of the desired tag and then localizing it. The fingerprint localization technique and the NMDS algorithm are combined in [37] to achieve cooperative indoor RFID multi-tag localization. However, it chooses to use the RSS information received by the antennas, and this localization method has large errors in indoor scenarios where complex multipaths exist. In order to achieve RFID localization in the space, most of them need two antennas or two-dimensional scanning, which is more cumbersome to deploy. This paper proposes DNCL, a localization approach based on DOA directional angle information combined with the nonmetric multidimensional scaling algorithm (NMDS). Through the use of phase information obtained from a 1D scan with a single antenna, DNCL provides spatial coordinate localization of tagged objects on the shelves or racks, as depicted in Figure 1. The main contributions of this paper are as follows:  
1. Since different hardware characteristics of different antennas will introduce different phase errors in phase measurement, which are difficult to determine but hard to ignore, this paper is inspired by the principle idea of synthetic aperture radar and designs a phase correction method based on antenna moving scan to build a virtual antenna array, which can effectively eliminate the phase shift errors caused by hardware. 2. We propose a Toeplitz rank recovery method for the DOA estimation parameters RFID localization method, for the problem of the direction of arrival estimation rank deficit caused by a large number of coherent multipath signal interference in the environment, we use the Toeplitz method to rank recover the signal covariance matrix, which can effectively eliminate the direction of arrival estimation error caused by multipath signal interference. 3.