Abstract
This paper aims to overcome the drawbacks of the traditional object positioning algorithms. For this purpose, passives tags were adopted to position the objects, and the traditional radio frequency identification (RFID) positioning algorithm was optimized based on multi-hop neighbourhood positioning. The optimized algorithm only considers the basic function of the RFID system, excluding the signal transmission strength between the reader and tag. In this way, the positioning cost of the positioning system was significantly reduced, while its robustness and anti-interference property were greatly enhanced. Then, the author analysed the main influencing factors of the algorithm performance, and introduced the system construction and parameter selection. Finally, the simulation results of the optimized algorithm were contrasted with the test results. The comparison shows that the proposed positioning system enjoys high positioning accuracy and resistance to environment disturbances, and applies to the position estimation of moving objects. The research findings open up a new way to RFID positioning.
Introduction
With the continuous development of the Internet of Things (IoT), radio frequency identification (RFID) has emerged as a remote detection and recognition technique capable of acquiring the target information in a certain range via computer-controlled scanning of radio-frequency signals (Tanaka et al., 2007; Zhou and Shi, 2009; Salama and Mahmoud, 2009). This technique has been extensively applied in such fields as warehouse management, transport and freight tracking, thanks to its high efficiency, convenience and adaptability to various severe environments (Bouet and Pujolle, 2016; Liu et al., 2017; Hekimian-Williams et al., 2010).
Despite these advantages, the RFID fails to realize real-time positioning of numerous localized objects (e.g. vehicles and mails), as it cannot arrange a large amount of tag readers in a continuous manner (Li and Wang, 2014; Zhang, Amin and Kaushik, 2007; Zhou and Griffin, 2012). The tag reader is essential to the positioning accuracy of the RFID. If it is placed in the object, the reader can identify the tag barcode at its location, and send the information to the upper computer (Park and Hashimoto, 2009; Shi and Wong, 2011). However, the application range of the reader is constrained by its quality, size and tag cost. This calls for a low-cost, high-accuracy positioning algorithm (Ni et al., 2010; Wang et al., 2015; Zhi-Xiang and Zhang, 2016; Lee, Kim and Kim, 2011).
In the existing studies, object positioning mainly relies on various statistical algorithms, training samples, and the strength of radio frequency signals (Chon et al., 2004; Alghamdi et al., 2014). Nevertheless, all these methods share some common drawbacks: the reader has insufficient regulating power (Jing et al., 2011; Savochkin, 2014), the positioning accuracy is dampened as signal transmission is interfered by walls and other barriers (Scherhaufl et al., 2013), and the cost is pushed up by the adoption of active tags (Xu et al., 2017). One of the most viable options to overcome these drawbacks lies in the use of passive tags.
Passive tags are known for their low cost, simple fabrication, no maintenance and long service life. So far, there have been some preliminary discussions on passive tag-based positioning systems. For example, Chon et al. (2004) developed real-time vehicle positioning with passive tag-based positioning systems. Wilson et al. (2008) compared the number of passive tags identified under different signal attenuation levels with the empirical data in the existing database, and employed a weighting function to obtain the coordinates of the measured tags. Zhou et al. (2009) presented an empirical model of channel attenuation between passive tags and readers in an open environment. Choi et al. (2012) put forward a new passive tag-based intelligent shelf system. Although these studies are still in the initial stage, further research into passive tags may reduce the positioning cost, improve system coverage, optimize system performance, and realize real-time object tracking.
In light of the above, this paper adopts passive tags for object positioning, and optimizes the traditional RFID positioning algorithm based on multi-hop neighbourhood positioning. The optimized algorithm only considers the basic function of the RFID system, excluding the signal transmission strength between the reader and tag. In this way, the positioning cost of the positioning system was significantly reduced, while its robustness and anti-interference property were greatly enhanced (Park and Hashimoto, 2010; Nejad, Jiang and Kameyama, 2011; Kim and Lee, 2008; Digiampaolo and Martinelli, 2012). The research findings open up a new way to RFID positioning.
RFID-based neighbourhood location system and algorithm analysis
System structure
The RFID-based neighbourhood location system mainly consists of the reader, tag database, and algorithm library of tags arrangement. In this algorithm, the reader with transmission antenna is placed onto the measured object; the antenna is mainly used to transmit the collected signal to upper computer; for the tags, using the passive ones, the RFID-based tag library is built in the upper computer in order to store and real-time update the coordinate and surroundings of all tags. Figure 1 depicts the stored basic information of tags.

Basic information of tags.
Three tag arrangements were designed in this paper, including square net (Squ), triangular net (Tri), and random net (Rand). The related location algorithms of tags are shown as:
Square net (Squ)
Triangular net (Tri)
Random net (Rand)
It is specified that only 1 tag is allowed in the range of single reader, therefore, the interval between all tags should be within a certain range. In the three arrangements, the interval between max and min tag is expressed as:
Square net (Squ)
Triangular net (Tri)
Random net (Rand)
The related tag arrangements are shown in Fig. 2:

Tag arrangement modes of square net, triangular net, and random net.
In this section, based on traditional location algorithm, the VIRE algorithm was introduced and improved by replacing the tags outside the identification range of one certain reader with the virtual tag. To be specific, firstly the virtual tag set outside the range of reader was estimated, then by comparing the virtual tag set with the designed tag set, the interval between virtual tags was calculated as correction factor, and finally the optimal covering radius of reader was adjusted. The related concepts are defined as: Set the coordinate of one tag tagi as (xi, yi); with this coordinate as circle centre, draw one circle at the radius Rnei; then set all tags in the circle as one set, i.e. initial neighbour tag S1; Outside the circle, in the neighbour tags of this tag exists one hop neighbour tag; the set of these tags is 2 hop neighbour tag S2;
The RFID-based neighbourhood location algorithm is calculated in steps: Firstly, send the active order and the ID information to reader by CPU; then the reader feeds back the IP information of all tags to upper computer; One hop and two hop tag sets S1 and S2 are constructed by upper computer; Take the coordinates of all tags in S1, and calculate S1 central coordinate; draw a circle C_vir at the radius min (s, Rmax);
By taking the central coordinate in Formula (10) as criterion, insert the virtual tags vir_tag at the interval l in the x and y direction, then this virtual tag set is given as:
where p and q are non-negative real.
Construct one hop and two hop sets S1 and S2, and compare the distance of all tags between Sref and S1/S2; suppose the number of virtual tags in Sref as Num_T, then the average coordinate value of these virtual coordinates is calculated as:
By Formula (12), the coordinate location of reader can be calculated.
Figure 3 depicts the searching process for reader coordinate location by virtual tags

Searching process for reader coordinate location by virtual tags.
The simulation software is Matlab, the maximum center diameter is 10 m, and the simulation area is 100 m×100 m. Table 1 lists the calculation results between the numbers of tags in S2 and the estimated coordinates of the reader in a square grid, a triangular grid, and a random grid. It can be seen from the table that when Rnei is 0.2 s and 0.5 s respectively, the set of neighborhood tags are empty, and the algorithm presented in this study only gets the average value of tags. When Rnei >s, the distance between the neighborhood tag and the reader is greater and greater, and the intersection between the circle centered on the average coordinates of the set of distant neighborhood tags and S1 will be included in other circles, so that the distant neighborhood tags will not affect the position estimation of the reader.
Number of S2 tags and estimated coordinates of reader in the square net, triangular net, and random net
Number of S2 tags and estimated coordinates of reader in the square net, triangular net, and random net
For random uniform distribution, the distance between any two adjacent tags is floating in the range of (0, 2 s). In the first two cases, some neighborhood tags found at Rneigh = s may have moved out of range, so set Rneigh = 2 s.
Therefore, comprehensively considering the Rnei = s of square mesh and triangular mesh, in the random mesh, Rnei = 2 s. In this way, the influence of random tag distribution on calculation accuracy can be suppressed to the maximum extent.
Figure 4 depicts the distribution of estimated error mean in three distributions at the tag interval of s = 1 m and s = 5 m, where x-axis shows l = 0.05 s, 0.1 s, ... ,0.5 s. it can be found in Fig. 4 that with l value increasing gradually, the estimated error of reader also increases, but with the smaller l, there will be more virtual tags within a certain range, and also larger calculated quantity; besides, at l > 0.3 s, the three curves starts to slow down, thus, l can be set as l = 0.3 s.

Searching process for reader coordinate location by virtual tags.
Table 2 lists the estimated error and variance σ2 of square net, triangular net and random net in different tag intervals. It is seen in Table 2 that s is positively proportional to estimated error and σ2, and the setup of excessive interval between tags can result in zero tag in the identification range of one certain reader; besides, in the tag arrangement mode of triangular network, its maximum location error is only 3 m, obviously superior to the other two tag-arrangements.
Estimated error in different tag distances of square net, triangular net and random net in different tag intervals
Figure 5 shows the target estimated path in different tag intervals, and Fig. 5 (a) depicts the actual tracking of objects. In Figure, at the 3 m tag intervals, it is estimated that the object location by triangular net is basically the same as the actual location; as the tag interval increases gradually, the estimated error shall rise accordingly, but still can reflect the actual moving path of targets, indicating that the optimized algorithm in this paper is feasible for location estimation of moving object.

Target estimated path in different tag intervals.
Figure 6 depicts the test results and test errors in actual situation. The test was made for 20 times, including the parameters: 30 m×30 m test area, 2 m tag distance, (9.0 m, 10.5 m) location coordinate of reader. In Fig. 6, it is seen that the estimated error of actual test results is over the simulated results in the fluctuation state, because of actual complex environment and the directivity of the received signal for reader antenna; also, if the distance between tag and reader is too long, the identification angle of reader shall be less, causing the larger estimated error. What’s more, in the identification process, there exist the phenomena of mis-reading and reading-missing with the reader. Therefore, all these shall lead to certain errors for RFID location.

Error of actual measured results.
In this paper, to improve the object location algorithm, the passive tagging was adopted for object localization, and the traditional RFID location algorithm was optimized on the basis of multi-hop neighbourhood location thought; for the optimized algorithm, only the basic function of RFID system needs to be considered, excluding the signal transmission strength between the reader and tag, which can greatly simplify the cost of location and identification system as well as improve its robustness and anti-interference feature. The conclusions have been made as follows:
By calculation, it is concluded that Rnei = s for square net and triangular net, and Rnei = 2 s for random net; when l increases gradually, the estimated error for reader shall rise accordingly, and when l is too small, number of virtual tags in a certain range shall increase at higher computation quantity, so it can be set as l = 0.3 s;
s is positively proportional to estimated error and σ2, and the setup of excessive distances between tags can result in zero tag in the identification range of one certain reader; besides, in the tag arrangement mode of triangular network, its maximum location error is only 3 m, obviously superior to the other two tag-arrangements. The simulation results also show that the optimized algorithm in this paper is feasible for the location estimation of moving objects.
