The Indoor Positioning Method Time Difference of Arrival with Conic Curves Utilizing a Novel Networking RFID System

Abstract

At present, the demand for accurate indoor positioning at a low cost is increasing. Based on the architecture of networking passive radio frequency identification (RFID) systems, research into passive location algorithms is important for finding a location solution with ultra-low cost, easy implementation, and no required maintenance. In this paper, TDACC (time difference of arrival with conic curves) based on signal propagation time is proposed, which breaks down the positioning problem into solving the intersection of an ellipse and a hyperbola. The results indicate that this method has a positioning error of 0 m in the absence of signal interference. When the time delay fluctuates to 1 ns and 2 ns, the average errors of TDACC are 0.19 m and 0.33 m, respectively. Different from other time-based localization methods, the proposed method only requires two distribution nodes without time synchronization, which reduces the system cost. These results will help to promote the deeper semantic communication level fusion of passive RFID. By improving the coordinate positioning in the semantic prior knowledge base, this method will lead to more efficient and accurate industry applications.

1. Introduction

At this critical stage in the development of the digital economy, the Internet of Things (IoT) is an important part of the new generation of information technology. It plays an important role in connecting the physical world using digital twins and meta-universe development and promotes the coordinated development of digital industrialization and industrial digitization. Modern logistics and supply chain management are the foundation of industrial digitization. In the process of industrial digitization, the demands for indoor positioning services such as material finding, asset tracking, and shopping mall navigation are increasing. Especially in the field of warehouse management, enterprises hope to grasp the location information of materials in the storage and transportation chain and the operation of business lines in a timely manner, so as to ensure that accurate and timely supply of materials can be obtained in the production process. Therefore, how to achieve accurate and low-cost indoor positioning is an important research topic in the field of logistics and even industry-wide asset management. With the rapid spread of automated management methods based on smart devices, data interaction traffic is growing exponentially and rapidly. To avoid the impact of network capacity saturation on business, it becomes crucial to fuse and analyze data with actual scenes through semantic communication technology to mine the business and production information contained in the data, and to remove redundant transmission data.

In order to improve the accuracy of indoor positioning, researchers have proposed many positioning methods based on different IoT technologies, including Bluetooth, WiFi, ultrasonic, RFID, and other technologies. And, the location methods based on fusion techniques are also have been popular methods. Fen Liu et al. conducted a comprehensive comparison and analysis of WiFi-based active and passive indoor positioning techniques. Unlike most other surveys that focused on specific positioning algorithms, this survey was based on whether the target carried certain devices [1]. Zeynep Duygu Tekler et al. proposed a scalable and less intrusive occupancy detection method that leveraged existing BLE technologies found in smartphone devices to perform zone-level occupancy localization, without the need for a mobile application [2]. Salvatore A. Pullano et al. investigated a nonstandard cross-correlation method for TOF estimations to improve the accuracy of ultrasonic positioning. The procedure, based on the use of template signals, was implemented to improve the accuracy of recursive TOF evaluations [3]. Although the related techniques have been widely researched due to widespread availability and high applicability, there are still many difficult challenges to be solved in implementing the indoor positioning system. For example, ultrasonic, Bluetooth, and WiFi technologies have limited propagation distances and are not suitable for the localization of large-scale warehouses. Moreover, these technologies use active tags, which need to be charged regularly, causing inconvenience in use.

To achieve tag sensing and data transmission, passive RFID technology relies on the back scattering of radio waves, and it has become a representative technology in the field of through-sense integration. Passive RFID tags are low cost, and there is no battery or maintenance required. They can be easily deployed on all kinds of items and support batch reading. They can also be flexibly defined based on business needs; thus, they have been widely used in warehousing, logistics, industry, transportation, energy, and other fields and show great potential in the Internet of Things. Although the development in high-frequency RFID fields is relatively mature in China, there is still a large gap in ultra-high-frequency (UHF) RFID development compared with foreign countries.

Modern logistics and supply chain management are the foundation of industrial digitization. In the process of industrial digitization, the demands for indoor positioning services such as material finding, asset tracking, and shopping mall navigation are increasing. Especially in the field of warehouse management, enterprises hope to grasp the location information of materials in the storage and transportation chain and understand the operation of business lines in a timely manner to ensure the accurate and timely supply of materials in the production process. Therefore, how to achieve accurate and low-cost indoor positioning is an important research topic in the field of logistics and even industry-wide asset management. With the rapid spread of automated management methods based on smart devices, data interaction traffic is growing exponentially and rapidly. To avoid the impact of network capacity saturation on business, it becomes crucial to fuse and analyze data with actual scenes through semantic communication technology to mine the business and production information contained in the data and to remove redundant transmission data.

The traditional integrated UHF passive RFID system adopts a co-frequency transceiver architecture, as shown in Figure 1a. The reader simultaneously transmits the wireless signal to activate the tag and receives the reflected signal from the tag, presenting strong self-interference inside the system and mutual interference between several different systems. Due to this, the coverage of the traditional UHF passive RFID devices is greatly limited. In a normal outdoor environment, the traditional effective communication distance is around 10 m; this number can be dropped below 3 m with integrated sensors [4]. In addition, the traditional UHF passive RFID does not support large-scale networking, so it is difficult to form a continuous coverage Local Area Network (LAN) or Wide Area Network (WAN) with automated positioning functions, resulting in extra maintenance costs and decreases in the efficiency of implementation. The above problems have seriously hindered the application of UHF passive RFID in positioning scenarios.

In response to these problems, some scholars have proposed a networking passive RFID architecture in recent years [5]. The networking passive RFID system replaces the monostatic reader with a separated central node (referred to as R node) and distribution nodes (referred to as Q nodes), as shown in Figure 1b. The distribution nodes provide radio frequency (RF) energy to the tag, and the central node supervises multiple distribution nodes working together. Specifically, the central node sends an RF signal to the distribution node, and the distribution node is responsible for demodulation and transmitting a UHF signal to the tags. The passive RFID tag receives an RF signal from the distribution node and then backscatters the modulated signal to the central node. After receiving the signal from the RFID tag, the central node will demodulate and upload the data to the platform.

The networking passive RFID architecture has the following advantages: first, the communication distance is greatly improved, increasing the coverage from about 10 m to 100 m. As the tags use the distribution nodes to backscatter RF signal, the total transmission paths of the entire link can be significantly shortened. Additionally, the central node and distribution nodes are physically separated to avoid interference between the forward link and reverse link. Second, it can continuously group the network. The central node assigns different working time slots and frequency domains to different distribution nodes, so multiple distribution nodes can avoid mutual interference and work cooperatively.

Most prior studies with respect to indoor positioning have been based on integrated passive RFID systems; very few studies can be found in the literature that used networking passive RFID systems. According to the different features, the positioning methods can be divided into three categories: those based on the received signal strength indicator (RSSI) [6,7,8,9,10], the phase difference of arrival (PDoA) [11,12,13,14,15,16], or the angle of arrival (AoA) [17]. Among the RSSI-based localization methods, the fingerprint localization method is one of the most classic. It consists of two steps: offline deployment and online localization. During the offline period, a large number of reference tags are deployed in the environment, and the RSSIs of the reference tags are collected to establish an RSSI fingerprint database. For online positioning, the RSSI of the target tag is compared with the data in the fingerprint database, and the measuring coordinates are determined according to the most similar offline points [7]. In recent years, substantial research efforts have been dedicated to developing classical fingerprint positioning methods such as Landmarc [7]. Through using reference tags, the Landmarc method requires relatively low antenna numbers. Researchers in [18,19] combined the Landmarc method with a weight calculation algorithm, including KNN, to further improving the performance. Whereas, in [8], the authors proposed VIRE method implemented the idea of virtual reference tag to reduce the quantity of reference tag needed in Landmarc. However, the accuracy of all these fingerprint localization methods mainly depends on the quantify of data in the fingerprint database, which requires an abundance of time to deploy reference tags and collect offline data. Luoli et al. proposed an improved algorithm based on the strongest RSSI method [20]. The idea of this method is to find the reader with the strongest tested RSSI and use the reference tags that also has the strongest RSSI under that reader to locate. Alsinglawi B et al. proposed a localization system that utilized deep learning algorithms combined with RSSIs of passive RFID tags to improve the localization accuracy [21]. In addition, occlusion of the surrounding environment and movement of people could lead to significant changes in the RSSI of the tag, which could cause serious interference in the localization accuracy. To solve this problem, M. A. R. Mian et al. proposed the Frogeye algorithm [10] by building a hybrid Gaussian model, which determined whether the RSSI variation in a tag was caused by interference; however, it was still difficult to remove interference and restore effective data.

The PDoA-based localization method calculates the position of the tag by measuring the difference in the phase change produced by two signals of different frequencies after traveling the same distance. There are various methods to obtain the phase difference, among which, the method using a dual-frequency phase ratio is less complicated [11]. However, the selection of frequency difference in this method is a key factor affecting the ranging accuracy, and the positioning accuracy is affected when the frequency is selected randomly. To address this problem, Hongze Hu et al. proposed Frequency Domain Phase Difference Of Arrival (FD-PDOA) [12], which optimized the selection of frequency. However, in a networking RFID system, the distance between the central node and the tag may exceed 100 m, and the problem of phase rectification ambiguity may arise, resulting in inaccurate localization. For the AOA-based localization method, Rigall E et al. proposed a novel SAR tag positioning method based on an AoA hologram and hash tables for faster performance [22]. But, the requirement for antenna sequences is high, which increases the complexity of the system [17]. Therefore, this method is also not suitable for application in networking passive RFID. PinIt uses the arrival angle energy spectrum of the tag signal as the position dependent fingerprint of the tag in a multipath environment [23]. During localization, dynamic time planning algorithms can be used to find the reference node label that is most similar to the target label fingerprint, and then the fingerprint similarity is used as a weight weighting to obtain the position as the target position. However, this method requires relatively high algorithmic requirements and requires a lot of computation.

In order to achieve accurate and fast localization, TDACC method is proposed in this paper, offering great significance for practical application. First, the method can be integrated to the networking passive RFID architecture, making it suitable for wide-area positioning requirements. Second, compared with the traditional method, this method has higher positioning accuracy and maintains high accuracy under different device deployment methods. Finally, this method does not require the deployment of reference tags, which reduces the labor and time costs of deployment.

In Section 1, the passive RFID system architecture and positioning requirements are introduced, and, particularly, the problems of existing positioning methods applied to the networking passive RFID architecture are analyzed. In Section 2, the TDACC method proposed in this paper is illustrated in detail. It uses the signal time received by the central node to determine the hyperbola and ellipse where the tag to be measured is located and achieves positioning by solving the curve intersection. In Section 3, the proposed method is simulated and compared with the classical fingerprint localization method. In Section 4, the method is discussed based on the experimental results, which show that the method proposed in this paper is accurate in localization and low in complexity. Finally, Section 5 outlines the goals for future research.

2. System Model and TDACC Method

2.1. TDACC Method

This paper proposes a positioning method TDACC based on conic curves for the characteristics of the separation of transceivers in the networking passive RFID architecture. The system model consists of a central node R, two distribution nodes Q₁ and Q₂, and a computing platform. According to the data provided by the computing platform in the system, an elliptic equation and a hyperbolic equation are established to solve the position of each tag. The solution process of the equation is the TDACC method. The elliptic and hyperbolic equations are shown in Figure 2. Figure 2a is the curve of the standard elliptic equation:

$$\frac{{\mathrm{x}}^2}{a^2}+\frac{y^2}{b^2}=1$$

(1)

According to the definition of the ellipse equation, the sum of the distances from a moving point on the curve to the two foci of the ellipse is equal to a fixed length:

$$P{F}_1+P{F}_2=2\mathrm{a}$$

(2)

Figure 2b is the curve of the standard hyperbolic equation, given as follows:

$$\frac{{\mathrm{x}}^2}{a^2}-\frac{y^2}{b^2}=1$$

(3)

According to the definition of the hyperbolic equation, the difference between the distance of a moving point on the curve and the two foci of the hyperbola is equal to a fixed length:

$$\left|\left|P{F}_1\right|-\left|P{F}_2\right|\right|=2a,2a<\left|F_1\times F_2\right|$$

(4)

In Figure 3, the workflow of the entire system is as follows: first, the central node (R) sends an instruction signal to the distribution node (Q₁) at time $t_0$, and, when Q₁ receives the signal sent by R, it sends an excitation signal to the tag to be tested (T). Next, when T receives the signal from Q₁, it converts the electromagnetic wave signal into energy to activate itself and then feeds back the information to R through the antenna. Finally, R receives the radio frequency signal fed back by T at time $t_1$ and obtains the signal transmission time $\Delta t_1=t_1-t_0$. Similarly, the central node R sends instructions to the distributed node Q₂ and obtains the signal transmission time $\Delta t_2$. By utilizing $\Delta t_1$ and $\Delta t_2$, the distances in Formulas (5) and (6) can be calculated as follows:

$$d_{R-Q_1-T-R}={\mathrm{r}}_Q{}_{{}_1}+r_1+r_R=c\times \Delta t_1$$

(5)

$$d_{R-Q_2-T-R}={\mathrm{r}}_Q{}_{{}_2}+r_2+r_R=c\times \Delta t_2$$

(6)

where ${\mathrm{r}}_Q{}_{{}_1}$ and ${\mathrm{r}}_Q{}_{{}_2}$ are the distances from Q₁ and Q₂ to R, respectively; $r_1$ and $r_2$ are the distances from Q₁ and Q₂ to the tag, respectively; $r_R$ is the distance between the tag and Q; and c is the speed of light.

The deployment positions of Q₁ and R are known, which means ${\mathrm{r}}_Q{}_{{}_1}$ is a constant; therefore, $r_1+r_R$ is also a known constant that meets the condition for establishing an ellipse. Thus, an ellipse with Q₁ and R as foci can be established, such as c₁ in Figure 3 [24]. Similarly, $r_2+r_R$ can be obtained. There exists a common distance $r_R$ between the two paths of $r_1+r_R$ and $r_2+r_R$. Thus, subtracting the two path distances leads to the calculation of $\left|r_2-r_1\right|$. This means that the difference $\left|r_2-r_1\right|$ between the distances from the tag to Q₁ and Q₂ is constant, which meets the condition for establishing a hyperbola. Thus, a hyperbola with Q₁ and Q₂ as foci can be established. By comparing the sign of $r_2-r_1$, we can determine whether T is closer to Q₂ or Q₁ and thus determine on which branch of the hyperbola T is located, as shown in c₂ in Figure 3. By combining the equations of the ellipse and the hyperbola, a conic equation can be established to solve for the tag’s location. When the cone section method yields a unique solution, the solution corresponds to the coordinates of T. In the case of two solutions, depicted in Figure 3, where the ellipse and hyperbola intersect at two points p₁ and p₂, the power of Q₁ or Q₂ can be adjusted to modify the signal coverage range between the coordinates of p₁ and p₂. If, in this case, R receives feedback signals from T, it confirms that the closer solution represents the coordinates of T. Conversely, if R does not receive feedback signals from T, it indicates that the label is located at the position of the farther solution [25].

The procedural workflow for solving TDACC methods is delineated as follows:

$$\{\begin{array}{l}{r}_1^2={\left(x_1-x\right)}^2+{\left(y_1-y\right)}^2=K_1-2x_{1}x-2y_{1}y+x^2+y^2\\ r_R^2={\left(x_R-x\right)}^2+{\left(y_R-y\right)}^2=K_R-2x_{R}x-2y_{R}y+x^2+y^2\end{array}$$

(7)

In Equation (7), $r_1$ and $r_R$ denote the Euclidean distances from point T to Q₁ and point T to R, respectively. The notations $\left(x_1,y_1\right)$, $\left(x,y\right)$, and $\left(x_R,y_R\right)$ signify the Cartesian coordinates of Q₁, T, and R, respectively: $K_1=x_1^2+y_1^2$, $K_R=x_R^2+y_R^2$.

$$\{\begin{array}{l}{r}_R+r_1=d_{R1}\\ r_2-r_1=r_{21}\end{array}$$

(8)

In Equation (8), $r_2$ represents the distance from T to Q₂. $d_{R1}$ and $r_{21}$ denote the distance from a point on the ellipse to its focus and the difference in distance from a point on the hyperbola to its focus, respectively. By substituting Equation (8) into Equation (7), we obtain

$$\{\begin{array}{l}2\left(x_2-x_1\right)x+2\left(y_2-y_1\right)y=x_2^2+y_2^2-(x_1^2+y_1^2)-r_{21}{}^2-2r_{21}{r}_1\\ 2\left(x_{\mathrm{R}}-x_1\right)x+2\left(y_R-y_1\right)y=x_R^2+y_R^2-(x_1^2+y_1^2)-d_{R1}{}^2+2d_{R1}{r}_1\end{array}$$

(9)

By rearranging Equation (9) into matrix form, we obtain the following expression for Equation (10):

$$\left[\begin{array}{cc}{x}_{21}& y_{21}\\ x_{R1}& y_{R1}\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}-r_{21}\\ d_{R1}\end{array}\right]r_1+\frac{1}{2}\left[\begin{array}{c}{K}_2-K_1-r_{21}^2\\ K_R-K_1-d_{R1}^2\end{array}\right]$$

(10)

In Equation (10), $x_{21}=x_2-x_1$, $y_{21}=y_2-y_1$, $x_{R1}=x_R-x_1$, $y_{R1}=y_R-y_1$, $K_2=x_2^2+y_2^2$, and $K_R=x_R^2+y_R^2$.

By setting $P_1=-{\left[\begin{array}{cc}{x}_{21}& y_{21}\\ x_{R1}& y_{R1}\end{array}\right]}^{-1}$, $P_2=\left[\begin{array}{c}{r}_{21}\\ -d_{R1}\end{array}\right]$, $P_3=-\frac{1}{2}\left[\begin{array}{c}{K}_2-K_1-r_{21}^2\\ K_R-K_1-d_{R1}^2\end{array}\right]$, and $X_1=\left[\begin{array}{c}{x}_1\\ y_1\end{array}\right]$, the following is obtained:

$$\left[\begin{array}{c}x-x_1\\ y-y_1\end{array}\right]=P_1{P}_2{r}_1+P_1{P}_3-X_1$$

(11)

$$r_1^2={\left[\begin{array}{c}x-x_1\\ y-y_1\end{array}\right]}^T\left[\begin{array}{c}x-x_1\\ y-y_1\end{array}\right]={\left[P_1{P}_2{r}_1+P_1{P}_3-X_1\right]}^T\left[P_1{P}_2{r}_1+P_1{P}_3-X_1\right]$$

(12)

$$\left[\begin{array}{c}\\ {\left(P_1{P}_2\right)}^T{P}_1{P}_2-1\\ \end{array}\right]r_1^2+\left[\begin{array}{c}\\ {\left(P_1{P}_2\right)}^T\left(P_1{P}_3-X_1\right)+{\left(P_1{P}_3-X_1\right)}^T{P}_1{P}_2\\ \end{array}\right]r_1+{\left(P_1{P}_3-X_1\right)}^T\left(P_1{P}_3-X_1\right)=0$$

(13)

Equation (13) is a quadratic equation about r, where each component is known so the value of r can be solved. The coordinates of T can be solved as follows:

$$\left[\begin{array}{c}x\\ y\end{array}\right]=P_1{P}_2{r}_1+P_1{P}_3$$

(14)

By solving the aforementioned series of equations and adjusting the power of Q to eliminate invalid solutions, the final position of T can be determined. In the calculation of the algorithm, various matrix operations are involved, including multiplication, transpose, and inversion. Therefore, the overall computational complexity of the algorithm is O(${\mathrm{n}}^3$).

2.2. Comparison with Other Time-Based Positioning Methods

In Section 2.1, a TDACC positioning method was proposed that utilized signal propagation time to determine the ellipse and hyperbola for solving the location of a tag. In order to better understand the advantages of our proposed methodology, a comparative analysis of other time-based positioning methods, mainly the TOA (time of arrival) and TDOA (time difference of arrival) methods, is carried out in this section.

As shown in Figure 4, in a networking passive RFID system, the positioning process of the TOA method involves the distributed node Q₁ transmitting an excitation signal at time $t_Q$, which is received by the central node R at time $t_R$. Based on the calculation of $c\times (t_R-t_Q)$, the sum of the distances between the distributed node and the tag, and between the tag and the central node, can be computed, resulting in the determination of an ellipse. With the deployment of three distributed nodes, three ellipses can be determined, and the intersection of these ellipses serves as the position of the tag to be measured. However, as the distributed nodes and central node rely on their respective clocks to record time, the TOA method requires highly synchronized clocks between the distributed nodes and central node.

As shown in Figure 5, the positioning process of the TDOA method involves setting multiple central nodes R, and the distributed node Q transmitting an excitation signal. The time at which the reflected signal from the tag is received by the central node $R_i$ (i = 1, 2, 3) is denoted as $t_R{}_{{}_i}$. By computing $t_R{}_{{}_1}-t_R{}_{{}_2}$, a hyperbola with foci at $R_1$ and $R_2$ can be determined. Similarly, hyperbolas with foci at $R_2$ and $R_3$, as well as at $R_1$ and $R_3$, can be determined. The target position is determined by the intersection of these three hyperbolas. The TDOA method requires multiple central nodes that are time synchronized with each other. Due to the high cost of central nodes, the deployment cost of the system is significantly increased.

The positioning process of the proposed method in this paper involves setting one central node R and two distributed nodes Q₁ and Q₂, as shown in Figure 6. R sequentially controls the work of the distributed nodes and records the time when control instructions are issued and the time when the tag signal is received, respectively. Utilizing the TDACC method, the foci of the ellipses and hyperbolas are determined to pinpoint the target’s location. As shown in

Table 1. Requirements of TDACC and other time-based positioning methods.

Positioning Method	TOA	TDOA	TDACC
Device number in networking RFID systems	At least 3 distributed nodes and 1 central node	At least 3 base stations and 1 central node	At least 2 distributed nodes and 1 central node
Time synchronization	Requires time synchronization between distributed nodes and central nodes	Requires time synchronization between different central nodes	Dose not need time synchronization

, compared to traditional time-based ranging methods, the proposed method in this paper has the following significant advantages in summary: First, both TOA and TDOA require time synchronization between devices, whereas the proposed method uses the clock of the central node to calculate propagation time, eliminating the need for time synchronization. Second, in networking RFID systems, TOA and TDOA both require at least four nodes, whereas the method proposed in this paper can establish positioning with only three nodes, requiring fewer devices and reducing the system construction cost.

3. Simulation Results

3.1. TDACC Method

Based on the equations and methods presented in Section 2, a simulation validation of the entire process was performed. As shown in Figure 7, in the simulation scene, the positions of R, Q₁, and Q₂ were set as (10, 0), (0, 0), and (10, 10), respectively.

We randomly generated 25 tags within the range of 1–9 m in the horizontal and vertical coordinates, and the actual and calculated positions of T are shown in Figure 8. In the simulation process, we used time as the feature quantity for calculating the distance, and recorded the time spent in the whole process from the central node sending to receiving the signal in the system. The propagation delay and the time required for each node to process the signal could be corrected by software and methods, and, finally, the time error could be controlled within 1–2 ns. Figure 8a shows the actual and calculated positions of the T tags without considering the error. The actual and calculated positions of 25 randomly generated tags were completely coincident, which verified the feasibility of the TDACC method. In Figure 8b, the delay of the signal is 1 ns, and there is a deviation between the calculated and actual position of the tag, with an overall deviation range of 0.09–0.39 m. In Figure 8c, the delay of the signal is 2 ns. Compared to Figure 8b, there is a more severe deviation in the tag position, with an overall deviation range of 0.19–0.74 m.

After calculating the error distance between the actual and calculated positions of each tag, this paper calculated the data graph of error changes caused by signal fluctuations, as shown in Figure 9. The blue curve represents the trend in the maximum error generated during signal fluctuations. When the signal fluctuated to 0, 1 ns, and 2 ns, the maximum errors were 0, 0.39, and 0.74 m, respectively. The black curve shows the trend in the minimum error generated during signal fluctuations. When the signal fluctuations were 0, 1 ns, and 2 ns, the minimum errors were 0, 0.09, and 0.19 m, respectively. The red curve calculated the average error as the signal fluctuates. When the signal fluctuated to 0, 1 ns, and 2 ns, the average errors were 0, 0.19, and 0.33 m, respectively. In conclusion, the maximum error, minimum error, and average error all gradually increased with the enhancement of signal fluctuations, showing a positive correlation trend. Although the maximum error was relatively large, the maximum average error was 0.33 m when the sample size was sufficient. These data were very considerable, and the error was smaller than that of weighted fingerprint localization methods under the same conditions. This conclusion will be compared in detail in the next section.

3.2. Fingerprint Localization Method

After we calculated the tag position and error data using the TDACC method, we calculated the relevant data using the fingerprint localization method [26,27,28] and compared the results. Multiple fingerprint location databases were built with different densities of reference tags. Under completely identical configurations of R, Q₁, and Q₂ as in the TDACC method, the average errors of the NN algorithm (nearest neighbor algorithm) [29], the KNN algorithm (K-nearest neighbor algorithm) [30], and the WKNN algorithm (K-weighted K-neighbor algorithm) [31,32,33] were computed at reference tag intervals of 5 m, 2.5 m, 2 m, and 1 m.

To examine whether the quantity of the tags had an impact on the error, we conducted an analysis and plotted the curve graph, shown in Figure 10, under varying tag quantities. In Figure 10, we calculated the influence of signal fluctuations on the average error for tag quantities of 10, 50, 100, 500, and 1000. It can be observed from Figure 10 that the trend in the curve graphs remained consistent across different tag quantities, except for the case with a tag quantity of 10, where a different trend in average error was observed due to the smaller sample size. Therefore, based on Figure 10, it can be inferred that the error was not influenced by varying tag quantities in our algorithm as long as the sample size was sufficient.

Within an area of x and y ranges from 1 m to 9 m, randomly generated test tags were placed, and the positions of reference tags were set with different intervals. Specifically, the reference tag intervals were set at 5 m, 2.5 m, 2 m, and 1 m, with the total number of reference tags placed throughout the plane being 4, 16, 25, and 100, respectively. Figure 11 shows the average error of three different fingerprint localization algorithms (NN algorithm, KNN algorithm, and WKNN algorithm) at different reference label intervals. Although we calculated the average errors of the signal fluctuations ranging from 0 to 10 dB, the results showed that only when the signal fluctuation was 0 dB did the fingerprint positioning algorithm achieve accuracy comparable to that of the TDACC method. Therefore, we analyzed and discussed the average errors when the signal fluctuation was 0 dB in various fingerprint databases. As seen in Figure 11a, when the reference tag interval was set at 5 m, the lowest average error among the three algorithms was 2.75 m, which was not practically applicable. When the reference tag interval was adjusted to 2.5 m, as shown in Figure 11b, the average errors of the three algorithms were 1.08 m, 0.94 m, and 0.84 m, respectively. It could be observed that reducing the interval by half significantly improved the average error of the signals by more than 2.5 times. Further increasing the number of reference tags and decreasing the interval to 2 m, as shown in Figure 11c, improved the accuracy of all three algorithms, with average errors of 0.81 m, 0.69 m, and 0.58 m, respectively. When the tag interval was set to 1 m, as shown in Figure 11d, the three algorithms achieved average errors of 0.41 m, 0.28 m, and 0.23 m, respectively. In this scenario, with high reference tag density, the accuracy of all three algorithms improved by approximately twofold. Through calculation and analysis of the fingerprint positioning algorithm, it was shown that the average error was positively correlated with signal fluctuation under different reference tag densities and algorithms. Moreover, setting a higher reference tag density enabled the fingerprint positioning algorithm to achieve higher accuracy. However, in practical applications, more reference tags meant an increase in the overall cost of the system. Therefore, the number of reference tags needed to be set within an acceptable range of error. The TDACC method did not involve the setting of reference tags, and the method had an average error of 0.33 m when the maximum signal fluctuation was 2 ns. In the absence of signal fluctuations, the WKNN algorithm with the maximum number and highest accuracy of reference tags in the fingerprint positioning algorithm had an average error of 0.23 m, which was only 0.1 m less than the error of the TDACC method. This indicated that the TDACC method had a very high computational accuracy.

3.3. Comparison of TDACC Method and Fingerprint Location Method

Through the analysis of the TDACC method and fingerprint positioning method, the outstanding performance of the TDACC method was shown. Next, we will compare and analyze the stability of the two methods when calculating the same test tag.

As shown in Figure 12, for the same position of T, the TDACC method and the WKNN algorithm were used to compare the calculated position of each tag with the actual position, and the difference in error between the two different algorithms was analyzed. In Figure 12a, the distribution of tag position and calculated position is shown when the signal fluctuates by 1 ns; in Figure 12b, the distribution of tag position and calculated position is shown when the reference tag interval is 1 m, and there is no signal fluctuation. On the whole, the average errors obtained by the TDACC method and the WKNN algorithm were 0.22 m and 0.23 m, respectively. Although the difference was only 0.01 m, the TDACC method was closer to the real scene when considering the error. The result obtained by the WKNN algorithm ignored the signal fluctuation, which was a relatively ideal situation. Meanwhile, as can been seen in Figure 12a, the error between the actual position and calculated position of each tag using the TDACC method was not significant and oscillated between 0.11 and 0.39 m. However, as Figure 12b shows, the error when using the WKNN algorithm fluctuated between 0.05 and 0.54 m, indicating a larger range of variation. Through the calculation and analysis of Figure 12, it can be concluded that the TDACC method was more stable than the fingerprint positioning algorithm, and it required less equipment expenditure, making it a more practical method with significant value.

After confirming the outstanding performance of the TDACC method, we investigated the impacts of the different experiment scenarios of R and Q on the average errors of the two algorithms. As shown in Figure 13a, ten experiment scenarios for R, Q₁, and Q₂ were selected, and the average error for different locations was calculated using the TDACC algorithm and the WKNN algorithm. Figure 13b corresponds to Figure 13a and shows the histogram of the average error for the two algorithms under different deployment modes. Specifically, the average error obtained by the WKNN algorithm was under the conditions of no signal fluctuation and a reference tag interval of 1 m, whereas the average error obtained by the TDACC method was under a signal fluctuation condition of 1 ns. The results obtained in Figure 13 show that the average error of the TDACC method was consistently smaller than that of the WKNN algorithm for experiment scenarios. Furthermore, compared to the WKNN algorithm, the average error obtained by the TDACC method was more stable, with respect to changes in the experiment scenario, showing a fluctuation range of 0.08–0.16 m, whereas the average error of the WKNN algorithm varied from 0.24 to 0.64 m with changes in the experiment scenario. This suggests that the TDACC method not only exhibits excellent performance in terms of calculation accuracy but also outperforms the fingerprint localization algorithm when changes are made to the experiment scenario of the R and Q nodes.

Finally, we compared and analyzed the cumulative distribution functions (CDFs) of different algorithms. In order to better determine the performance of our method, we compared it with classic fingerprint algorithms and the outstanding PinIt algorithm, respectively. As shown in Figure 14, we selected 100 samples for each algorithm and calculated the probability distributions within different error ranges for the TDACC, NN, KNN, WKNN, and PinIt algorithms. From the graph, we can observe that the cumulative distributions for the TDACC, PinIt, WKNN, KNN, and NN algorithms were below 0.4, 0.9, 4.8, 5.9, and 8, respectively. The TDACC algorithm demonstrated excellent performance compared to the other algorithms.

4. Conclusions

This article presents the principle and derivation process of the TDACC method. This method is oriented toward networking RFID systems, which are suitable for wide-area positioning. Compared with the traditional TOA and TDOA methods, the method in this paper requires fewer devices and does not require time synchronization between devices, giving it a significant advantage. We designed the localization system model and conducted simulations of the algorithm under the condition of zero error, which proves the rationality and availability of the algorithm. Then, the TDACC method was simulated in the signal fluctuation range of 0–2 ns, and the variation trends in the average error, maximum error, and minimum error with the signal fluctuation were obtained. The results showed that the error increased with the increase in signal fluctuation, and the average error was 0.33 m under signal fluctuation of 2 ns. To demonstrate the superior properties of the TDACC method, the average error of the fingerprint localization algorithm was calculated under different densities of reference tags. Three commonly used algorithms, NN, KNN, and WKNN, were used for comparison. By comparing the average error of the TDACC method and the fingerprint localization algorithm, the computational accuracy and stability of the TDACC method were further demonstrated. Finally, by changing the deployment locations of R and Q, the generality of the TDACC method in computation was evaluated. The results showed that the error fluctuation range of the TDACC method was smaller under different deployment positions, and the average error at each location was lower than that obtained from the fingerprint localization algorithm. In summary, the TDACC method is an excellent algorithm with high computational accuracy and low volatility of calculation results. Moreover, it does not require the deployment of reference tags, which reduces the implementation and maintenance costs. This algorithm is of great significance to the actual positioning application.

5. Future Research and Outlook

Positioning technology based on passive RFID plays an increasingly important role in industry applications such as smart warehousing and smart logistics, improving both efficiency and accuracy. RFID technology enables real-time monitoring and location tracking of goods. Administrators can know the location and quantity of goods stored in real-time, which allows for easier logistics operations and management. According to the RFID standard protocol, passive RFID tags can feed back EPC codes and user-defined information. Label position combined with user-defined information enables fast and efficient parsing of asset information. The integration of RFID-based localization technology with semantic communication technology enables the development of a semantic prior knowledge base. This can then be decoded at the receiver to achieve a high-dimensional representation at the business layer, and more efficient information interaction and location awareness can be achieved. It needed to be pointed out that the proposed method TDACC is subject to several limitations that due to the intrinsic characteristics of RFID technology. These characteristics, including radio transmission and backscatter communication, etc., in a real-world scenario, will be more unexpected factors that could affect the performance of TDACC. For instance in [7], the authors discussed the effectiveness of varying indoor conditions to the wireless signal, such as signal absorption and shadowing caused by human mobility or placement of furniture. Similarly, in RFID-based positioning system, tag orientation and system sensitivity could also bring in uncertainties. These limitations would be addressed in future research with modifications of RFID tags or refining of system parameters. In addition, this team will be attempting to optimize the algorithm complexity to further improve the efficiency.

Our team will carry out further research in the combination of RFID-based localization and semantic communication.

The goal will be to obtain detailed business information and real-time statistics on boredom status in the material cart handling scenario, including warehouse location number, material information, cart information, inbound time, etc. The identification process includes the following:

Construction of a semantic knowledge base: There are three methods for constructing a semantic knowledge base in semantic communication technology: (1) based on a knowledge graph, (2) based on a training set with labels, and (3) based on a deep learning feature map/feature vector. As the construction of both (2) and (3) requires a large amount of high-quality, labeled data, this study plans to extract the set of semantic triples (entities, attributes, values) using knowledge graphs in source dimension and channel dimension.

Source knowledge base: Passive RFID labels are placed on the material carts and materials, and the EPC code is bound with the storage number, material details, and other information to extract the semantic triples.

Channel knowledge base: As the environment in the warehouse logistics scene is dynamic, channel characteristics such as shading are irregularly dynamic. It is necessary to build a channel knowledge base based on environmental characteristics. A static channel knowledge map includes the R and Q nodes’ power coordinates, obstacle location collection in the warehouse, channel gain, channel path, etc. A dynamic channel knowledge map includes the material carts’ coordinates and materials, etc.

Semantic transmission: RFID labels transmit data to the central node R by responding to the node Q. Node R can obtain EPC coding and semantic information encoded using knowledge graphs.

Semantic parsing: When the material carriage is out/in, the semantic information of the material carriage and material is decoded to determine the correspondence of material, warehouse, material cart, out/in, time, and business.

Semantic communication technology can process the information obtained by RFID to build a semantic knowledge base and achieve more intelligent warehouse management. For example, the system can automatically plan the optimal storage location and outgoing time for goods based on the type, quantity, location, and maintenance time of the goods. The team will continue to carry out research on semantic applications based on RFID positioning and semantic communication technology for smart storage yards, such as material location planning and prediction and material cart path planning, to bring more efficient, convenient, and accurate technology applications to the warehousing and logistics industry.

In the future, the team will also research wide-area passive RFID technology for positioning, by combining passive RFID with cellular mobile communication technology to further exploit the advantages of 5G high speed, low latency, large capacity, high bandwidth, and large-scale antennas.

By using existing base station resources, we can make base station antenna that have passive RFID transmission capability in order to increase the communication distance. Then, we can realize unified scheduling of base stations to cope with larger and more complex scenarios of network and application requirements.

6. Patents

Object positioning methods, devices, equipment, systems, and storage media, 202211223300.7