Efficient localization in warehouse logistics: a comparison of LMS approaches for 3D multilateration of passive UHF RFID tags

Nowadays, many industries employ mobile robots to move goods and products efficiently from storage areas to the production lines within the warehouses. This kind of machine serves as an alternative to the customary belt-based transportation system. The increase of global export activity has led to a transformation from human performed activities to machine activities and the demand for quick delivery due to increasing e-commerce volumes and online trade. The Fourth Industrial Revolution, or Industry 4.0, aims at automating traditional manufacturing and industrial practices using modern smart technologies. Some of the pillars are machine-to-machine communication (M2M) or Internet of Things (IoT) to improve communication and self-monitoring, technologies enabling remote operations [1], or autonomous and intelligent systems for automatizing some human tasks like bin picking [2, 3] and quality inspection [4, 5] that make use of computer vision or artificial intelligence techniques even though a lot of industries perceive them as black-boxes [6].

Complex and dynamic industrial environments need to move and locate goods from storage units in warehouses passing through production facilities for manufacturing to arrive in retail stores. The localization and tracking of both autonomous systems and products in the whole production chain demands accurate estimations of the full pose of machines and production items.

Logistics robots can be used to carry heavy payloads, increasing the safety of human workers and reducing possible product damages. The introduction of autonomous robots in the production line led to a reduction in the cost of labor and an increase in efficiency compared to manual work. The use of novel sensing technologies along with intelligent machines enables further interesting applications that, for instance, allow human personnel or robots to identify and localize items and products easily [7] or update retail store inventory in real time [8].

The localization problem in industries could be categorized in outdoor localization [9, 10] considering logistics applications between plants and within plant facilities, or in indoor localization [11‐13] that considers more common applications regarding the motion and storage of items within production plants. In the last decades, many approaches employing different sensing elements have been presented in the literature. Machine vision is probably the most used technology for the navigation of autonomous systems and recognition of objects [14‐16]. Such approaches detect and identify features in the environment and therefore need stable and uniform lighting conditions. However, in real scenarios, such methods suffer from the presence of light interferences such as shadows or changing illumination characteristics if considering outdoor environments or the traversal of different locations or facilities. An additional issue comes from object similarities that pose difficulty in distinguishing between objects of the same type easily. The most promising solutions based on light detection are based on laser imaging detection and ranging (LIDAR) due to their flexibility and robustness. These approaches make use of the LIDAR to perceive and produce accurate maps of the environments and localize the robot motion as a consequence [17‐19]. The same technology has been applied to identify and localize objects in applications that require considerable computing power and under specific environment setups [20, 21]. Lately, wireless techniques fostered the adoption of effective IoT solutions leveraging on different sources of information like Wi-Fi or Bluetooth signal strength indicator of radio frequency communications [22, 23], time of flight measurements [24], ultrasonic [25], or ultra wide band (UWB) communications [26]. Radio frequency identification (RFID) is one of the most promising technologies of the Internet of Things, and it has been widely applied in industry and retail applications due to its low cost. Moreover, compared to machine vision approaches, it is not affected by lighting conditions allowing its usage even in dark environments, and it has the advantage of uniquely identifying each tag by its associated ID.

In the following, multilateration techniques that employ time-of-arrival measurements will be applied to RFID phase signals to obtain estimations of the localization of passive RFID tags. The novel contribution of this research is to explore the possibility offered by multilateration and phase unwrapping for RFID tags 3D localization employing least-squares optimization methods and mobile robot navigation. Precise localization and ad hoc motion of a mobile robot allow reconstructing without discontinuities an unwrapped phase distance to be used as a pseudo range in the multilateration problem. Four methods are proposed, and their performance is assessed using three different datasets. The first two datasets contain virtual data that has been generated by simulation. The third one comes from an indoor experimental setup. According to the latest trends in RFID localization, the proposed algorithms show competitive performances concerning recent solutions in the literature.

Section 2 will discuss in detail recent findings in radio frequency communication applications for the localization and tracking of goods in warehouses and retail stores. Section 3 will introduce four different methods employing the least mean square optimization to solve the multilateration problem. Section 4 will present and discuss the experimental tests performed to assess the accuracy of the methods. Finally, Sect. 5 will conclude this manuscript.

A first consideration could emerge by analyzing the worldwide interest in radio frequency technologies in the latest years. Fig. 1 shows the comparison in the occurrence of some research terms in recent years obtained by Google trends. The search acronyms taken into account in the comparison are RFID, UWB, BLE (Bluetooth Low Energy), and IoT. As can be seen, RFID technology founds a large audience, and its results are comparable with the more general IoT term, especially in the last year.

Passive RFID tags require few electronic elements and no power source and thus are the preferred solutions for their reduced costs that allow their employment in applications requiring a large number of them. Each time a reader antenna interrogates a passive tag, it generates a backscatter signal at a certain strength in dBm referred to as received signal strength (RSS). The signal can be modeled with a standard radio frequency propagation model in free space [27]. The strength can be employed to obtain a rough estimation of the distance between the tag and the reader antenna. It is known as received signal strength indicator (RSSI), and its value is related to RSS but can differ depending on the specific radio chip manufacturer. However, this signal is affected by reflection, interference (constructive and destructive), and absorption. Anyway, it is possible to describe the signal attenuation as a function of the distance by considering uniform radiation patterns typical of omnidirectional antennas. Unfortunately, antennas of tags and readers are directional in practice introducing another source of disturbance that, along with the multipath effects, may invalidate the distance estimation. For such a reason, this kind of solution is limited to open space environments with low reflections. In order to efficiently estimate distances based on RSS only, there is the need to properly characterize several parameters like the antenna gains of both the reader and the tag, the alignment of the antennas, and others. As a consequence, the use of the RSS measurement has been limited to an extra source of information in the recent literature approaches [28].

RFID phase-based distance methods exploit consecutive measurements of the RFID signal phase over a short time. The method used to measure the distance can be either the phase difference of arrival (PDOA), the angle of arrival (AOA), or the time difference of arrival (TDOA). AOA techniques require specific setups to obtain good accuracy, and they are useful to determine the direction of traveling of tags. However, the need to have specific setups and knowledge of the antenna characteristics reduce their usage in industrial applications. TDOA methods need synchronization between the tags and the reader, and the backscattered signal lacks proper synchronization. On the contrary, PDOA allows having measurements that are less sensitive to reflections and multipath and could be obtained from equipment already adopted in industries for logging items.

Phase measurements could be achieved employing time domain, frequency domain, or spatial domain techniques [29]. The frequency-domain technique can be efficiently used for estimating the distance of tags and sampling the phase at different frequencies [30]. The spatial domain technique allows the computation of accurate directions of travel of tags and requires multiple antennas [31]. The time-domain approach allows both the computation of tags velocities and their direction of travel, enabling not only the localization but also the tracking of tags’ motion [32].

To avoid the need for multiple antenna systems and to increase the accuracy of localization, strategies in which a single antenna is moved in the environment to emulate a synthetic aperture radar (SAR) have been presented in the last years [33]. Given the grid-based structure of such algorithms, SAR approaches require large computation steps and were initially meant for offline reconstruction [34], but lately, online estimation results have been obtained employing optimization algorithms [35]. The antenna can be moved in the environment by means of a mobile robot allowing the sorting of RFID tags in libraries, manufacturing lines, or offices [36] or enabling robot localization strategies [37].

An approach to RFID tags localization by combining both the RSSI and the phase signals acquired by two moving antennas with different orientations has been proposed in [38]. The signal strength values are used to estimate the heights of the tags in the environment and also to compensate for the orientations and the materials on which the tags are attached. The lateral location of the tag is obtained from the phase information employing a matching function that considers the signal-to-noise ratio of each phase sample. An alternative SAR model based on multiple baseline synthetic arrays has been proposed in [39], where phase samples are evaluated in couples, comparing them with a baseline to understand which samples are mostly affected by multipath interference. This method showed an advantage compared to traditional SAR in an indoor experiment. A different multi-granularity SAR-based approach has been presented in [40] to obtain the high-probability region of the tag position by estimating the reflection coefficient. This method reduces the computational effort and has been proven in real experiments showing a centimeter-level localization accuracy.

Whether the tag motion is greater than half of the wavelength between two subsequent measurements, the computed phase difference exceeds \(2\pi\), and the antenna is unaware of how this can be determined. In order to efficiently use the phase difference measurement, the phase angle signal should be conveniently wrapped to become continuous in cases where the reader value presents jumps. The unwrapping technique has been recently introduced in RFID localization to eliminate the phase cycle ambiguity obtaining promising results [41]. Another approach to RFID localization is to exploit geometrical properties by computing hyperbolic intersections [42, 43]. A hyperbola is the locus of points where the difference of the distance to the two foci is constant. Therefore, placing the antennas on the foci, the target tag lies on the hyperbola curve, and the hyperbolic intersection may solve the localization problem.

Many RFID localization techniques focus on bidimensional localization since, given the knowledge of the warehouse environments and where the goods are stored, 2D solutions provide an efficient way to localize the products on shelves or boxes. However, lately, some approaches to 3D localization for warehouse logistics can be found in the literature. Motroni et al. [44], for instance, employ two RFID reader antennas on a mobile robot to estimate the 3D location of passive RFID tags exploiting synthetic apertures and the backscattered signal phase. The method does not require any reference tags or large phased array antennas. Real-time 3D positioning has been obtained on SAR-based methods with the application of the particle swarm optimization with a two-antenna setup [45]. Tzitzis et al. [46] recently proposed a novel method for 3D RFID tags localization by moving an antenna attached to a mobile robot and forcing a non-straight path motion. Results present a mean error of 35 cm in a scenario involving tags placed on different vertical planes. An optimized interferometric SAR-based 3D localization has been presented by Liang et al. [47] allowing fast estimations with a median accuracy of 18.4 cm on a moving single-antenna setup. All these recent findings confirm the RFID technology as one of the most promising solutions for warehouse logistics and goods tracking that will enable new scenarios in the upcoming industry of the future.

This manuscript focuses on the application of multilateration algorithms for RFID tag localization.

Given a mobile robot equipped with a reader antenna and a tag positioned in the surrounding environment, at any robot motion, the relative distance r between the tag and the antenna varies along the path. A phase observation sequence can be acquired as the tag is interrogated multiple times by the moving reader antenna, and a relative phase history of the complex signal is obtained from the signal phase variation. The equation that relates the phase difference to the distance is given by:where the \(\Delta\) operator represents the difference of the values at two consecutive time steps, \(\phi _n\) is the phase signal at time instant n, and \(\lambda\) is the free-space wavelength of the radiated field. It has to be noted that, by using a differential reading, there is no need to estimate the phase offset \(\phi _0\) that depends upon tags and antenna electronic circuits characteristics (see Fig. 2).

Solving a multilateration problem is equivalent to computing the intersection of two-sheeted hyperboloids (quadric surfaces) in the 3D space. The tag location can be found on the hyperboloid surface by knowing the pose of the robot at two different time instants and the phase difference between the two measurements. Figure 3 shows a two-sheet hyperboloid in classic form, while Fig. 4 shows the locus of the possible tag positions (one sheet of the hyperboloid) generated by moving the antenna from position 1 to position 2. The tag position can be found at the intersection between two hyperboloids by adding a third measurement. With a fourth reading, it is possible to determine the precise location of the tag. Furthermore, it is possible to increase the estimation accuracy of the localization procedure by using additional measurements.

Naming \(P = [ x , y, z]\) the position and coordinates of a tag, and \(P_i = [ x_i , y_i, z_i]\) the i-th position of the moving antenna, the distance ranges can be computed as:

Without losing generality, it is possible to consider the measurements referred to the first reading \(r_1\) and define:

In the TDOA literature, \(m_i\) are pseudo ranges representing the time difference of a traveling wavefront touching each antenna position.

It is worth noticing that the ambiguity generated by the phase cycle has been addressed by using an unwrapping algorithm to efficiently use the presented method. This method adjusts the phase angles by adding multiple cycles when absolute jumps between consecutive phase samples are greater than or equal to the jump tolerance \(\pi\). Naming the unwrapped phase \(\phi ^u\), the procedure is equivalent to:

Three different datasets have been employed to analyze the performances of the proposed methods. The first two datasets contain virtual data that has been generated by simulation. The third dataset comes from an indoor experimental setup. All the datasets provide positions and respective phase signals of two moving antennas and fixed tags.

Synthetic datasets allowed the executions of multiple Monte Carlo simulations over different noise conditions considering signal reflections, multipath, electrical, and thermal noises. The real dataset shows the correspondence of the estimated performance with actual data. The measured 2D and 3D errors on each experiment are defined as:with (x, y, z) the exact location of a tag and \((\hat{x},\hat{y}, \hat{z})\) its estimated position.

The ongoing industrial revolution demands efficient logistics and inventory management in warehouses. The mobile robotics sector is growing more and more, intending to satisfy such demands. Efficient robot motion and planning depend on precise localization, mapping, and awareness of the environment. The overall efficiency mainly relies on specialized sensing technologies to track the robot’s motion and measure the positions of the items with accuracy. Recent attempts employing radio frequency identification (RFID) in a 3D environment have been made to localize the items properly. This manuscript addresses the problem of RFID tag localization by using multilateration techniques that employ time-of-arrival measurements on RFID phase signals to obtain estimations of the localization of passive RFID tags. Given a mobile robot equipped with a reader antenna and a tag positioned in the surrounding environment, the motion of the antenna generates a synthetic aperture. The system receives the phase measurements from the RFID tags and generates a distance model through phase unwrapping. Solving a multilateration problem is equivalent to computing the intersection of two-sheeted hyperboloids in the 3D space. By knowing the pose of the robot at two different time instants and the phase difference between the two measurements, the tag location can be found on the hyperboloid surface. The tag position can be found at the intersection between two hyperboloids by adding a third measurement. With a fourth reading, it is possible to determine the precise location of the tag. Furthermore, it is possible to increase the estimation accuracy of the localization procedure by using additional measurements.

Formulating the system of equations that represent the squares of the ranges between the tag coordinates and the varying position of the moving antennas, the least-squares optimization method is applied to explore four methods. Three approaches are based on single-antenna reading, while the other one leverages multiple antenna readings to estimate the position of passive RFID tags. Such methods are tested using three different datasets. The first two datasets contain virtual data that has been generated by simulation. The third one comes from an indoor experimental setup. Synthetic datasets allowed the executions of multiple Monte Carlo simulations over different noise conditions considering signal reflections, multipath, electrical, and thermal noises.

It has to be noticed that the motions that involve a synthetic aperture on all the 3D coordinates improve the methods estimations. Additionally, in the case of environmental noises, like multipath, reflections, unmodelled antenna properties, and thermal disturbances, the use of multiple antennas shows better accuracy. Limitation to the usability of the proposed techniques comes from the maximum feasible motion between two antenna readings that depends on the lambda parameter and should be satisfied to obtain smooth unwrapped phase distances. If this constraint is not guaranteed, the reconstructed phase distance could show holes compromising the accuracy of the reconstruction. It is recommendable to design the antenna motion accordingly, and, if a mobile robot is used for the antenna motion as in the experimental tests, the robot localization and navigation algorithm should satisfy such constraints.