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Abstract

In many logistics applications, densely placed objects on high-speed conveyor belts are attached with passive tags for automatic identification and sorting to work more efficiently. Traditional localization or sorting methods cannot effectively work in such scenarios due to complex environments. In this article, we propose a new passive radio frequency identification sorting system for dense mobile tags on high-speed conveyor belts by utilizing the output phase. At first, a relative motion model is utilized to get the zero point time when the object passes the radio frequency identification portal. Then, the coarse-grained time and the corresponding speed of the conveyor belt are obtained by the phase curve fitting. Finally, the inverse synthetic aperture radio frequency identification is used to get the fine-grained zero point time, which is realized based on the holographic image reconstruction. And the particle filter is utilized to get a significant reduction of computational burden. The proposed method is implemented with commercial-off-the-shelf devices, and the evaluation results in various scenarios show our system can achieve an average accuracy of 97% with the tag density of 10/m and at a speed of 4 m/s.

Keywords

Radio frequency identification sorting inverse synthetic aperture high-speed conveyor belt dense objects

Introduction

The Internet of Things (IoT) is the key to industrial upgrading, which has been attracting increasing attention in both academia and industry recently. At the same time, as an important component of industrial automation, radio frequency identification (RFID)-based conveyor belts are widely deployed in many applications to identify objects quickly and improve work efficiency, such as postal sorting offices and airport baggage handling systems.

Moreover, sorting of the objects in conveyor belt systems is an important problem. Item-level processes can only be done correctly after knowing the order or the location of each object. The operation that the RFID-based conveyor belt systems distinguish objects and then deliver them to the proper destinations is usually called sorting. In these systems, the RFID reader antennas are fixed on a gate above the conveyor belt, which is called the RFID portal. Furthermore, in order to work more efficiently, objects are usually densely placed on high-speed conveyor belts which makes sorting more difficult. Both the increasing number of tags in the RFID interrogation zone and the reduction of the dwell time that a tag stays in the interrogation zone make sorting challenging.

For example, in some high-speed conveyor belts of liquor factories, RFID sorting system is used to check whether the RFID tag attached on each bottle of liquor is initialized successfully. Due to the dense and high-speed bottles on conveyor belts, special devices like near-field antennas or shielding devices are used. In these practical industrial fields, the core idea of accurately sorting objects on RFID-based conveyor belts is to limit the RFID interrogation zone to ensure that there is only one tag at a time. There are still some incorrect operations and it works better for sparse object placement. Researchers^1,2 utilize the time when the tag enters the interrogation zone or received signal strength indication (RSSI) to estimate the order of the objects. However, these techniques cannot work for dense objects. The RFID interrogation is based on a probabilistic algorithm,³ which means tags’ replies are random. And RSSI is seriously affected by noise and multi-path effect in industrial environment.

In recent years, other low-level data like phase provided by commercial-off-the-shelf (COTS) RFID readers have been exploited by the state-of-the-art systems to serve the needs of sorting on conveyor belts. Tagoram⁴ and Buffi et al.⁵ leverage synthetic aperture radar (SAR) concept to locate RFID tags on a conveyor belt with a centimeter-level accuracy. However, they require the prior knowledge about the speed of the conveyor belt, which may not be measured accurately. Besides, they do not consider the angle-dependent phase response of the antenna and have a heavy computational burden. STPP⁶ analyzes the spatial–temporal dynamics of phase for sorting, but it requires a strong consistency among RFID tags and suffers from low read rate on account of high-speed conveyor belt.

As dense tags move fast on conveyor belts, the measurements may be sparse and thus require intelligent processing of the tag measurement results, while previous methods cannot provide sufficient accuracy to differentiate and track each tag. Therefore, we present a lightweight passive RFID sorting system (PRSS) for dense objects on high-speed conveyor belts based on COTS RFID devices. The contributions of this article are as follows.

First, a relative motion model and a phase curve fitting method are proposed to get the coarse-grained time when the object passes the RFID portal and the corresponding speed of the conveyor belt. In this step, PRSS filters out those objects which are not on the conveyor belt.

Second, inspired by other synthetic aperture RFID localization systems, we utilize the obtained coarse-grained time and matched filter for holographic image reconstruction to get the fine-grained time and the location of each tag with a light computational burden, which is further reduced by particle filter. We also analyze the theoretical −3 dB width of ambiguity for the hologram.

Finally, a prototype system is built and extensive experiment results show that it achieves up to 97% sorting accuracy on average. It has a high tolerance for the interference, multi-path, and other noise.

The rest of the article is organized as follows: the related works are presented in section “Related works.” In section “Background,” the background is introduced. The research methodology and algorithm design are illustrated in section “Research methodology and system design.” In section “Evaluation,” the performance evaluation of the system is analyzed. And finally, this article is concluded in section “Conclusion.”

Related works

The sorting problem is also a localization problem, and a great number of systems utilize RFID to identify and track objects. Our work is standing on the shoulders of previous works.

In theory, the RSSI value is inversely proportional to distance between the RFID reader antenna and the tag.⁷ Early indoor localization systems like SpotON⁸ and Landmarc⁹ usually utilize RSSI with the radio propagation model or fingerprint map for location estimation. Some device-free systems^10–12 monitor the activities of target objects by the changes of the signals from the reference tag array, but the reference tag array is almost impossible to be deployed on the conveyor belt.

RSSI is also regarded as a basis of RFID sorting system. Combined with hidden Markov model^1,13 or response reception ratio,² RFID tags are sorted with a 0.5 m luggage distance. However, RSSI is sensitive to the environment noise, so it is still hard to get a satisfying precision of dense tags in a high-speed scenario.

Phase-based RFID localization is proposed by many research communities based on its proportional relationship to the propagation distance.¹⁴ Some special devices are applied for phase or phase difference measurement, such as the special two-antenna array,¹⁵ the rotating antenna,¹⁶ software defined radio,¹⁷ near-field cascaded shelf antennas,¹⁸ and multiple receivers with one transmitter.¹⁹ A joint iterative phase reconstruction with weighted localization algorithm²⁰ or hyperbolic localization algorithm²¹ is also utilized for the localization of static tags. Tadar²² tracks one mobile object by extracting reflections off the moving object with a learning phase. RF-scanner²³ uses the super V-zone of the phase profile to pinpoint the tag position. These systems are hardly used for the dense objects sorting on the high-speed conveyor belt.

Then, RFID-based localization is incorporating with SAR²⁴ in recent years to accurately locate stationary tag with a known trajectory of a reader antenna.²⁵ This method is called synthetic aperture RFID localization, and the known trajectory is the synthetic aperture. In contrast, a mobile RFID tag with a known trajectory is located based on the inverse synthetic aperture RFID in one dimension,²⁶ two dimensions,²⁷ and three dimensions.²⁸ MobiTagbot²⁹ excludes sample points where multi-path is likely prevalent to improve the accuracy. And it also can be utilized to capture multi-path profiles³⁰ for localization. The coherent reconstruction in synthetic aperture RFID localization leads to an effective multi-path distortion suppression. However, it is a pity that they all have a high computational complexity.

The output phase values are also utilized for sorting systems. STPP⁶ utilizes the change of RFID phase and the change sequence to calculate the order of tags. But it suffers from the consistency among RFID tags and low read rate in dense tags with a high-speed scenario. Similar to other synthetic aperture RFID localization systems, normal coherent reconstruction⁵ or differential augmented coherent reconstruction in Tagoram⁴ is utilized to locate RFID tags on a conveyor belt with a centimeter-level accuracy. But they demand accurate prior knowledge about the speed of the conveyor belt, and do not consider the angle-dependent phase response of the antenna. These existing sorting systems can hardly sort the dense objects with a high speed due to the heavy computational burden and the interference from those tags not on conveyor belt in the industrial scenario.

Background

In this section, the sorting problem of dense tags on high-speed conveyor belts is described. And the output phase of RFID reader is introduced.

Problem specification

As shown in Figure 1, a sequence of objects attached with RFID tags moves along the conveyor belt at a velocity of $v$ . A reader antenna $(m)$ of the RFID portal is fixed over the belt. Suppose that the tag spacing is $Δ s_{t}$ , and let the direction from the tag to the antenna be positive. The reading range of the RFID portal is called interrogation zone. Due to the dense placement, there are many tags in the interrogation zone in the same time. When the tags move along the conveyor belt, they will be interrogated a few times with RSSI and output phase.

Figure 1.

Dense tags on a high-speed conveyor belt.

For each tag, the trajectory from its first interrogation to the last interrogation is its aperture. Meanwhile, each point where the antenna interrogates the tag is known as aperture point. For convenience, the point where the tag is directly under the RFID portal is defined as zero point (the line connecting the tag and the reader is perpendicular to the x-axis). The time when the tag is at the zero point is defined as zero point time, and the distance between the antenna and the tag at the zero point is called zero point distance.

Suppose that the conveyor belt speed is $v$ , a tag on it will be interrogated at $n$ different aperture points by the antenna $m$ , and the output phase is $φ_{m, n}$ at time $t_{n}$ . So, the sorting problem is how to accurately estimate the tag’s zero point time $t_{0}$ . Meanwhile, its trajectory function $l (t)$ can be calculated based on $t_{0}$ and the conveyor belt velocity $v$ .

Output phase

Modern COTS RFID readers like Impinj 420 in PRSS can report the phase value $φ$ , which is the phase difference between the transmitted signal and the received one, consisting of three parts¹⁴

φ = (φ_{p r o p} + φ_{r} + φ_{t}) \mod 2 π, where φ_{p r o p} = \frac{4 π f d}{c}

(1)

$φ_{prop}$ is the phase variation due to the signal propagation in space, while $φ_{r}$ and $φ_{t}$ are the phase offsets caused by the reader antenna and the tag, respectively. $d$ is the distance between the antenna and the tag, and $c$ is the velocity of light. For the fixed carrier frequency, $φ_{r}$ and $φ_{t}$ are both constant for one tag and one antenna. The radial velocity $v_{r}$ between the antenna and the tag can be estimated according to equation (2)

v_{r} = \frac{\partial d}{\partial t} = - \frac{c}{4 π f} \frac{\partial φ}{\partial t}

(2)

Research methodology and system design

In this section, major methodology and the system design are introduced. The system contains three stages: first, radial velocity is calculated to get the initial zero point time and filter out those tags which are not on the conveyor belt. Second, the curve fitting is used to obtain the coarse-grained zero point time and the corresponding speed of the conveyor belt. Finally, the more accurate zero point time is estimated by advanced holography-based sorting. The detailed relationship of three stages is shown next.

Radial velocity-based sorting

When a tag crosses the RFID portal, the change of phase value is regular: two consecutive phase values are decreasing before the zero point while increasing after the zero point. To find the zero point time, the radial velocity $v_{r}$ between two consecutive interrogations is estimated using equation (2). As depicted in Figure 1, if the angle between the direction of tag movement and the direction from the tag to the antenna is $θ$ , the radial velocity $v_{r}$ is $v \cos θ$ .

Along the conveyor belt, $θ$ gradually increases to $π / 2$ (at zero point) and then continues to increase. So, $v_{r}$ is monotonically decreasing from positive to negative. In one experiment, tags move along the conveyor belt at a velocity of 4 m/s, and the radial velocity $v_{r}$ of a certain tag is illustrated by the green line in Figure 2(a), which is obtained from the output phase (the blue points).

Figure 2.

The effectiveness of radial velocity estimation: (a) the output phase values and the radial velocity (v = 4 m/s, the zero point time is 252 ms), (b) the CDF of the time needed to identify one tag twice, and (c) the maximum interval along the conveyor belt (v = 4 m/s and h = 0.5 m).

It is noticed that the phase values are discontinuous and the phase points are sparse. That is because the reader takes a modulo $2 π$ operation on the output phase. If the prior output phase and the current phase are in different cycles, the phase difference may be positive or negative due to modulo operation, which will cause a wrong estimated direction of velocity. Furthermore, once the distance of relative motion between two consecutive interrogations exceeds half a wavelength, the phase difference will exceed $2 π$ .

Then, we explore the time needed to identify one tag twice. Different numbers of static tags are placed in the interrogation zone of the reader and each experiment lasts 5 min. As illustrated in Figure 2(b), when the number of tags is 15, in over 80% cases, the time needed to identify one tag twice is less than 40 ms. And the maximum time needed to identify one tag twice is about 70 ms when the number of tags is 20. Is this interval long enough for the radial velocity estimation?

If a tag moves $Δ s$ along the conveyor belt between two consecutive interrogations ( $t_{1}$ to $t_{2}$ ), at time $t_{1}$ , the distance between the tag and the zero point is $s$ and the distance from the tag to the antenna is $d_{1} = \sqrt{s^{2} + h^{2}}$ , while at time $t_{2}$ , these distances change to $s + Δ s$ and $d_{2} = \sqrt{{(s + Δ s)}^{2} + h^{2}}$ , respectively. When the radial motion distance is less than half a wavelength $(d_{2} - d_{1} < λ / 2)$ , the radial velocity can be estimated correctly (phase difference smaller than $2 π$ ). Then, we can get the maximum movement distance between two consecutive interrogations as $Δ s_{MAX} = \sqrt{{(λ / 2 + \sqrt{h^{2} + s^{2}})}^{2} - h^{2}} - s$ . The interval between two consecutive interrogations must satisfy $Δ t = t_{2} - t_{1} < Δ s_{MAX} / v$ to get the unambiguous and effective velocity. If the velocity of the conveyor belt is 4 m/s and the zero point distance $h$ is 0.5 m, the upper bound of the intervals $Δ s_{MAX} / v$ is illustrated in Figure 2(c) (the blue solid line; and 0 m in the conveyor belt represents the zero point). And at the beginning, $v$ is pre-estimated by experience for the first 20 tags. The closer a tag is to the zero point, the larger the maximum interval is. Near the zero point, the maximum interval is about 100 ms, while it approaches 40 ms far away from the zero point. To estimate the radial velocity effectively, the interval time between two consecutive interrogations should be less than $Δ s_{MAX} / v$ , which could be set to 40 ms. However, the threshold can be larger near the zero point.

As mentioned before, it is hard to recognize whether the phase is increasing or decreasing because of the modulo operation. Fortunately, the conveyor belt is a special situation: the phase monotonically decreases before zero point and then monotonically increases. The time that a tag needs to move $λ / 4$ on the relative distance is shown in Figure 2(c) (the green dashed line). If the time difference is less than $Δ t'_{th} = Δ s_{MAX} / (2 v)$ , the phase difference must satisfy $| Δ φ | < π$ . The algorithm for estimating the radial velocity with strong constraint based on phase is shown in Algorithm 1. A sliding window consisting of two consecutive interrogations data is founded and the threshold is used to filter it before the velocity estimation.

Algorithm 1 Radial velocity with strong constraint
Input: the time of the ith tag interrogated $t_{i}$ ; the phase of the ith tag interrogated $φ_{i}$ ; Output: the ith velocity of tag $v_{i}$ ; the maximum time of the positive velocity $t_{p}$ ; the minimum time of the negative velocity $t_{n}$ ; 1: $Flag = 0$ 2: while $i \geq 2$ do 3: $Δ t_{i} = t_{i} - t_{i - 1}$ 4: if $Δ t < Δ t'_{th}$ then 5: $Δ φ_{i} = φ_{i} - φ_{i - 1}$ 6: if $\| Δ φ_{i} \| > π$ then 7: $δ = Δ φ_{i} > 0 ? (- 2 π) : 2 π$ 8: $Δ φ_{i} = Δ φ_{i} + δ$ 9: end if 10: $v_{i} = (λ^{} Δ φ_{i}) / (Δ t_{i} 4 π)$ 11: if $v_{i} > 0$ and $Flag = 0$ then 12: $t_{p} = (t_{i} + t_{i - 1}) / 2$ 13: else if $v_{i} < 0$ and $Flag = 0$ then 14: $t_{n} = (t_{i} + t_{i - 1}) / 2$ 15: $Flag = 1$ 16: end if 17: end if 18: end while 19: return $v_{i}$ , $t_{p}$ , and $t_{n}$ .

Algorithm 1 Radial velocity with strong constraint

Input:
the time of the ith tag interrogated

t_{i}

;
the phase of the ith tag interrogated

φ_{i}

;
Output:
the ith velocity of tag

v_{i}

;
the maximum time of the positive velocity

t_{p}

;
the minimum time of the negative velocity

t_{n}

;
1:

Flag = 0

2: while

i \geq 2

do
3:

Δ t_{i} = t_{i} - t_{i - 1}

4: if

Δ t < Δ t'_{th}

then
5:

Δ φ_{i} = φ_{i} - φ_{i - 1}

6: if

| Δ φ_{i} | > π

then
7:

δ = Δ φ_{i} > 0 ? (- 2 π) : 2 π

Δ φ_{i} = Δ φ_{i} + δ

9: end if
10:

v_{i} = (λ^{*} Δ φ_{i}) / (Δ t_{i} * 4 π)

11: if

v_{i} > 0

and

Flag = 0

then
12:

t_{p} = (t_{i} + t_{i - 1}) / 2

13: else if

v_{i} < 0

and

Flag = 0

then
14:

t_{n} = (t_{i} + t_{i - 1}) / 2

15:

Flag = 1

16: end if
17: end if
18: end while
19: return

v_{i}

t_{p}

, and

t_{n}

For the consecutive points which satisfy $λ / 4 v < Δ t < λ / 2 v$ , if both the prior and next velocity points are positive or negative, this velocity should be positive or negative. If the prior velocity point is negative and the next point is positive, this point is around the zero point: the change of the phase values is slow $(| Δ φ | < π)$ . So, the data are processed again based on the critical time $t_{p}$ and $t_{n}$ . When the velocity changes from positive to negative steadily, the initial zero point time is approximated as the mean value of two opposite interrogations data.

As discussed above, the radial velocity can be estimated effectively with small interval between two consecutive aperture points. As illustrated in Figure 2(b), over 60% of time differences between two consecutive interrogations are less than 40 ms, making velocity estimation practical. So, the radial velocity can be effectively estimated by Algorithm 1. After getting the maximum time of the positive velocity $t_{p}$ and the minimum time of the negative velocity $t_{n}$ , the simple linear interpolation is utilized for the zero point time $t_{0}$ estimation.

In one experiment, 10 tags with a 10 cm spacing move along a conveyor belt at a speed of 4 m/s, and most of them are interrogated about 20 times in the interrogation zone. Then their radial velocity in one experiment is shown in Figure 3. The changes of radial velocity of every tag can be conveniently taken and the zero point of each tag can also be easily recognized. Only the order of tag 5 and tag 6 is nearly incorrect. The calculated velocity fluctuates wildly especially away from the zero point because the tag in the edge of the interrogation zone cannot be interrogated stably. But near the zero point, radial velocity is accurate. The values that do not satisfy the threshold criteria are ignored. Although the velocity values may be inaccurate, the change trend of velocity values is correct and really matters, which can be used to estimate the zero point time correctly. Furthermore, some more accurate methods are employed next.

Figure 3.

Velocity-based tag sorting ( $v = 4 m / s$ , 10 tags with a 10 cm spacing).

The curves in Figure 3 also show a uniform linear motion with the conveyor belt speed, which can be utilized to detect whether the tags are on conveyor belt or not. If the interrogated tag is not on the conveyor belt, its radial velocity will be different. Due to the noise, the radial velocity of static tags fluctuates around zero. The mobile tags with different directions can also be easily filtered out due to monotonically increasing. For the mobile tags with same direction, the slope of the velocity curve around the zero point may be different from that of normal tags. In addition, according to OTrack,² the read rate of the tag on the conveyor belt stabilizes at a certain high value around the zero point. After getting the zero point time, the read rate within 200 ms range of the zero point time is also calculated for detecting tags not on conveyor belt. From Figure 4 (an experiment with 10 interference tags), we can easily search for a threshold to filter out these tags. The threshold depends on the conveyor belt speed and the tag spacing, and it can be learned by simple classification method like logistic regression.

Figure 4.

Detect those tags not on conveyor belt (red circles represent tags on conveyor belt, while blue crosses denote those tags not on conveyor belt).

Phase curve fitting-based sorting

The radial velocity-based tag sorting method treats the average velocity in short time as an instantaneous velocity. When the density of tags increases, the sampling interval will increase due to the reduction in read rate. This will result in an offset of the zero point estimation.

For a linear conveyor belt, if the conveyor belt speed is $v$ and at the zero point time $t_{0}$ the tag is at $(0, y_{0}, z_{0})$ , the trajectory of the tag can be represented by a function of the time t: $l (t) = ((t - t_{0}) v, y_{0}, z_{0})$ . The zero point distance $h_{0}$ with antenna $m$ can also be estimated. Then, the distance between the tag and the antenna at time $t$ is $h_{t, m} = \sqrt{{((t - t_{0}) v)}^{2} + {h_{0}}^{2}}$ . To sort these tags, the zero point time $t_{0}$ of each tag is more important than its other coordinates. If there is only one antenna and $φ_{t_{0}}$ is the phase at the zero point, the output phase at time $t$ can be calculated by equation (3)

f (t) = φ_{t_{0}} + \frac{2 (\sqrt{{(v (t - t_{0}))}^{2} + {h_{0}}^{2}} - h_{0})}{λ} 2 π

(3)

The curve fitting technique can be used to estimate the zero point time $t_{0}$ . The main problem is the modulo operation. In the ideal situation, the phase difference of two interrogation points satisfies $Δ φ < 0$ when a tag moves toward the antenna, and $Δ φ > 0$ when moves away. So, we use the zero point time from the radial velocity-based method to correct the sign of phase difference and then integrate the phase values together, which is illustrated by red points in Figure 5.

Figure 5.

Phase curve fitting-based sorting ( $v = 4 m / s$ and $t_{0} = 269 ms$ ).

As shown in Figure 2(a), there is a “V-zone” from 160 to 350 ms, where the tag moves through the zero point in this cycle. In PRSS, only the points near the zero point are selected for integration to avoid the phase difference over $2 π$ and improve the accuracy. The interrogation rate is high around the zero point, and each cycle usually has more than one aperture point. Unlike the “V-zone”⁶ or “super V-zone”²³ for book ordering, sorting for dense objects on high-speed conveyor belt is quite different. For each tag, the aperture points are very sparse due to the dense tags and short dwell time in the interrogation zone. If only the data in “V-zone” are leveraged for curve fitting, the lack of phase data will decrease the accuracy. On the other hand, if “super V-zone” is obtained with all data, there may be no aperture in some cycle (after modulo operation) due to sparse aperture points, which will also decrease the accuracy.

So, PRSS only integrates (unwraps) the phase data around the zero point for curve fitting. If the interrogation point closest to the zero point is $t_{0, init}$ , PRSS selects the aperture points around the zero point: $t \in (t_{0, init} - \sqrt{{(λ + h)}^{2} - h^{2}} / v, t_{0, init} + \sqrt{{(λ + h)}^{2} - h^{2}} / v)$ .

The integrated phase values are substituted into equation (3). Then, the problem can be easily converted to find $X = [φ_{t_{0}}, t_{0}, h_{0}, v]^{T}$ to minimize equation (4)

F (X) = \sum_{t} {[φ_{r} (t) - f (t, X)]}^{2}

(4)

where $φ_{r} (t)$ is the measured phase of the reader, $f (t, X) = φ_{t_{0}} + 4 π [\sqrt{{(v (t - t_{0}))}^{2} + {h_{0}}^{2}} - h_{0}] / λ$ .

Then, Levenberg–Marquardt algorithm is used. $f (t, X)$ can be approximated by first-order Taylor series expansion with a given initialization value $X' = [φ', t', h', v']^{T}$ , and t′ is the zero point from the previous method

f (t, X^{'} + Δ) \approx f (t, X^{'}) + J_{t} Δ

(5)

where $J_{t} = δ f (t, X') / δ X$ and $Δ = [Δ φ, Δ t, Δ h, Δ v]^{T}$ . So, $F$ can be expressed as $\sum_{t} [φ_{r} - f (t, X') - J_{t} Δ]^{2}$ . At the minimum of the sum of squares $F$ , the gradient of $F$ with respect to $Δ$ will be zero. $Δ$ and $F$ can be calculated. X′ is adjusted for the next iteration until the minimum $F (X)$ is achieved. Then, the zero point time $t_{0}$ is achieved, which is shown by green curve in Figure 5.

Obviously, $t_{0}$ decides the sorting result, while $φ_{t_{0}}$ and $h_{0}$ do not affect the result. We only focus on $t_{0}$ , so this method can be further simplified. Equation (3) can be approximated as a quadratic polynomial near t₀: $f (t) = a (t - t_{0})^{2} + b$ , which can be used for quadratic fitting to get $t_{0}$ . As shown by blue curve in Figure 5, it is the same as the curve based on equation (3). But not all the zero point times are estimated based on the simplified equation in PRSS. For the first few tags, their zero point times are estimated based on equation (4) to obtain the possible conveyor belt speed $v$ .

Normal holography-based sorting

The noise will weaken the performance of previous method. As aforementioned, synthetic aperture RFID localization can get accurate results. For simplicity, it is assumed that there is only one antenna at first.

PRSS focuses on the zero point time and the zero point distance, which also simplifies the three-dimensional (3D) space location. Suppose the zero point time is $t_{0}$ and the zero point distance is $h_{0}$ , at time $t$ , the distance between the tag and the antenna is $h_{t, m} = \sqrt{{((t - t_{0}) v)}^{2} + {h_{0}}^{2}}$ . So, for each pair of assumed zero point time $t_{0}$ and the zero point distance $h_{0}$ , a trajectory $l (t)$ can be determined. And at its each aperture point, the phase offset due to space propagation is $φ_{prop} = 4 π h_{t, m} / λ$ .

From equation (1), if an assumed pair $(t_{0}, h_{0})$ is right, the phase difference between the measurement phase $φ_{m}$ and the calculated one should be constant along the aperture: $Δ φ = φ_{prop} - φ_{m} = - (φ_{r} + φ_{t})$ . Then, we can reconstruct a holographic image based on matched filter.

The phase difference $Δ φ$ is used to form a special signal $A e^{j Δ φ}$ , where $A$ is the measured RSSI. If the tag is interrogated $n$ times at $n$ different aperture points $(x_{i}, y_{i}, z_{i}), i = 1, . . ., n$ , the vector sum of $n$ special signals represents the likelihood of the assumption about the zero point time $t_{0}$ and the zero point distance $h_{0}$

χ (t_{0}, h_{0}) = | \frac{1}{K} \sum_{i = 1}^{n} A_{i} e^{j ((4 π h_{t, m} / λ) - φ_{i, m})} |

(6)

where $K$ is a normalizing factor and $(t_{0}, h_{0})$ denotes a pair of assumption, while $t_{i}$ and $φ_{i, m}$ denote the time and output phase at ith aperture point by antenna $m$ , respectively.

At a point near the assumption, the value of $χ (t_{0}, h_{0})$ grows as the signals superimpose constructively. So, the assumed point with the maximum vector sum is the real zero point. Because noise and multi-path distortions are different among different aperture points, the superimposition in equation (6) leads to an effective distortion suppression. The longer the aperture is, the better suppression effect is achieved.

This vector sum is also called the coherent reconstruction of a holographic image, and the output of the matched filter can be regarded as the amplitude of a holographic image, which is shown in Figure 6 with the same data used in Figures 2(a) and 5. This method can get an accurate zero point time.

Figure 6.

Holographic image calculated with test data $(267 ms, 0.5 m)$ .

The likelihood function $χ (t_{0}, h_{0})$ is also an ambiguity function. If the actual value is $(t'_{0}, h'_{0})$ , the assumed point in the holographic image is $(t'_{0} + Δ t, h'_{0} + Δ h)$ . If the tag is interrogated from $(- D / 2, 0, 0)$ to $(D / 2, 0, 0)$ and the conveyor belt is linear, $χ (t_{0}, h_{0})$ in equation (6) can be written as ambiguity function $χ (Δ t, Δ h)$ and the sum is replaced by an integral. The time length of the synthetic aperture is D/v. If $t'_{0}$ is $0$ , then the synthetic aperture time point changes from $(- D / 2 v)$ to $(D / 2 v)$

χ (Δ t, Δ h) = | \frac{1}{K} \int_{- D / 2 v}^{D / 2 v} A_{t} e^{j Δ φ} d t |

(7)

$Δ φ$ can be approximated based on the first-order Taylor series expansion

Δ φ \approx \frac{4 π}{λ d} [- Δ t v^{2} \cdot t + Δ h \cdot h_{0}]

(8)

where the distance between the aperture and the reader antenna $d$ is seen as a constant approximately when $d$ is much longer than aperture length $D$ .

To get the lateral resolution, $Δ h$ is set to zero, A_t is set to 1, and $χ$ can be written as a sinc function $χ (Δ t) \approx | sinc (2 π D \cdot Δ tv / (λ d)) |$ . So, the −3 dB width of the ambiguity function in lateral direction is $0.88 λ d / (2 Dv)$ . However, sometimes the antenna position is not close to the bisector of the aperture. If the angle from the aperture to the antenna is $θ$ , the aperture length $D$ should be replaced by an equivalent aperture length $D \sin θ$ . Then, the −3 dB width in lateral direction is

δ_{lat} \approx 0.88 \frac{λ d}{2 Dv \sin θ}

(9)

Similarly, the 20% loss in intensity width in radial direction can be calculated based on the Fresnel integral

δ_{rad} \approx λ {(\frac{d}{D \sin θ})}^{2}

(10)

It is obvious that $δ_{lat}$ is seriously smaller than $δ_{rad}$ , which is also shown in Figure 6. In the holographic reconstruction, different directions will have divergent accuracy. But as mentioned before, the zero point time $t_{0}$ is the most important in a sorting system, so this difference is acceptable. In fact, the real resolution is much better due to the approximation in equation (8) and the successful response from only one tag.

Equation (6) can be simplified if the trajectories of all tags are in the same line because the zero point distance $h_{0}$ of different tags is the same. If there are $m$ antennas, due to their different zero point distances, it cannot be simplified to a two-dimensional (2D) condition. And what is worse is different antennas usually have different $φ_{r}$ . This means the direction of the special signal $A e^{j Δ φ}$ may be different even with the right assumption. To deal with this diversity, the relative phase method is used. The phase differences for each antenna $j$ are all subtracted by the first phase difference of this antenna. At the same time, if the exact speed of the conveyor belt is unknown, the assumption should also contain the conveyor belt speed $v$

χ (t_{0}, y_{0}, z_{0}, v) = | \frac{1}{K} \sum_{j = 2}^{m} \sum_{i = 1}^{n} A_{i, j} e^{j [((4 π (d_{i, j} - d_{1, j})) / λ) - Δ φ_{i, j}]} |

(11)

where $Δ φ_{i, j} = φ_{i, j} - φ_{1, j}$ , $d_{i, j}$ is the distance between the jth antenna and the tag at time $t_{i}$ . Similarly, different carrier frequencies have different $(φ_{r} + φ_{t})$ . If the tag is interrogated in several carrier frequencies, the relative phase method is also used for each frequency.

Phase value calibration

The error of the measured phase, especially the regular error, would result in the performance degradation of PRSS. In the coherent reconstruction, the antenna is abstracted as a point. However, the actual antenna cannot be abstracted as a static point simply. Its phase center moves on the evolute of the equiphase wave front and can only be seen as a constant for small changes of the angle of arrival.²⁵ The phase response of the antenna is angle-dependent.

If the antenna at $(0, 0)$ rotates around its vertical axis from $0$ to $π$ , and there is a static tag at $(0, 1.5 m)$ , the measured phase value changes with the angle of arrival as illustrated in Figure 7. The angle-dependent phase response has a broad range of nearly 2 rad. Therefore, all measured phase values are corrected with the angle-dependent curve $p_{m} (θ)$ of the antenna $m$ in holography-based method. This method assumes the possible zero point time $t_{0}$ and distance $h_{0}$ , and each pair of assumption represents a possible trajectory. Therefore, the angle of arrival $θ$ is calculated with any assumed trajectory. Then, the measured phase $φ_{m}$ is calibrated by $φ_{m} + [p_{m} (π / 2) - p_{m} (θ)]$ .

Figure 7.

The phase response changes along with the angle-of-arrival (the blue point is the measured data while the red curve is the fitting curve $p_{m} (θ)$ ).

In most scenarios, if there is a long aperture, the main localization error stems from the phase center drift, rather than the multi-path or noise which is suppressed during the reconstruction. With phase calibration, a better accuracy can be achieved.

Advanced holography-based sorting

The computational burden of the normal holography-based sorting is heavy. Even for a 2D holographic image with NM pixels and $K$ aperture points, the algorithm complexity is $O (MNK)$ , which makes it difficult for real-time application. The computational burden can be reduced by tuning the proper scope of variables and step size of the holographic image reconstruction, which can be estimated by phase curve fitting-based method.

In fact, most of the assumed points have a low likelihood value, so a simplified version of particle filter can be used. If a set of weighted particles is utilized to represent the pixels, the computational burden can be effectively reduced. Enough particles can get the accurate zero point time. And the particle number is subsequently reduced with a resample algorithm after iterations.

The zero point $(t, h)$ is described by a set of particles $p$ . The whole aperture is divided into $L$ pieces. After the lth aperture, update and resample occur. The particle $p_{l, k}$ means an assumption that a possible zero point of the lth aperture is at the point $p_{l, k}$ . And the holographic image is replaced by $χ (p_{l, k})$ .

At first, all pixels in the holographic image are set as particles $p_{0, k}$ , which obey uniform distribution with the same initial weight $w_{0, k} (\sum_{k = 1}^{M} w_{0, k} = 1)$ . Then, in lth iteration, half of the particles are ignored according to their weight $w_{l}^{k}$

w_{l}^{k} = \frac{χ (p_{l, k})}{\sum_{k = 1}^{M} χ (p_{l, k})}

(12)

The positions of these son particles are the same as their fathers’. After $L$ iterations, particles are fewer and fewer, and the zero point is the weighted sum of all remaining particles $(\sum w_{k} t_{k}, \sum w_{k} h_{k})$ .

Moreover, not all phase values from aperture points are used for sorting in this stage. The aperture points far away from the zero point are more likely to have bigger measured error. And when the tag is far away from the antenna, it can be interrogated usually due to complex multi-path. With the help of the first two stages, aperture points are selected around the zero point at the range of 1 s.

PRSS design

Radial velocity-based sorting uses the average velocity during a short time to approximate the instantaneous velocity. This approximation will result in inaccuracy due to the long interval between two consecutive aperture points, especially when the tag is around the zero point, caused by dense tags and high speed. But it has the minimum computational burden. Phase curve fitting-based sorting needs to unwrap the phase values. This unwrapping seriously suffers from the sparse aperture points, especially when there are no interrogation points in some cycle. These two methods need enough aperture points to ensure the accuracy. Holography-based sorting achieves the highest accuracy with the maximum computational burden.

Putting things together, we get PRSS, the quick and correct passive RFID sorting method for dense objects on high-speed conveyor belt, which is illustrated in Figure 8.

Figure 8.

The PRSS architecture.

First, PRSS utilizes radial velocity-based method implemented with minimum computational burden to get the zero point time $t_{0_{i}}$ for every tag $i$ and filter out tags not on conveyor belt. The zero point $t_{0_{i}}$ is estimated by the point where the velocity changes from positive to negative. For the tags on the conveyor belt, their velocities change from positive to negative, and have similar slope around the zero point. So, those tags with different change trends of velocity are filtered out.

Second, according to $t_{0_{i}}$ , the tag $i$ is inserted to a sequence. The time difference between the zero point time of tag $i$ and tag $i - 1$ or tag $i + 1$ is used as the judgment by comparing with threshold $Δ t$ . $Δ t$ is determined by the mean spacing $Δ s_{t}$ of tags, which is half the ideal time difference $Δ t = Δ s_{t} / 2 v$ . If the time difference is smaller than the threshold, and in other words, it is too close to its neighbor, the phase values around the zero point are unwrapped and the phase curve fitting is used to update the zero point time $t_{0_{i}}$ and get the speed of the conveyor belt $v$ . Otherwise, the advanced holography-based method is directly used. Due to the same speed of different tags on the same conveyor belt, the mean of the conveyor belt speed $v$ is utilized for the trajectory in holography-based method next.

Finally, the advanced holography-based method is used. The search scope of the assumption zero point time and zero point distance is determined by the coarse-grained results from previous methods. Then, the fine-grained results are estimated in real time and the sequence is updated according to the fine-grained zero point time.

As noted above, the exact speed of the conveyor belt is significant. Due to the stability and the consistency of the conveyor belt’s speed with RFID tags, the Levenberg–Marquardt algorithm and the speed search in holography-based method are used to get the speed of the conveyor belt for the first 20 tags. And the average value is utilized for the holography-based method next.

In addition, RFID portal is usually equipped with more than one antenna. It will take extra time for antenna switching, which means a lower read rate. On the other hand, the advanced holography-based method achieves higher accuracy than other two methods. As shown in equations (9) and (10), its lateral accuracy (x-direction in Figure 1) is much better than others (perpendicular to x-direction). More importantly, the sorting system mainly focuses on the lateral positions of the dense objects on conveyor belts, especially for the linear conveyor belt, which is the most common. So, PRSS employs one antenna for sorting, while it is convenient to extend to multi antennas.

Evaluation

In this section, we present the implementation of PRSS and conduct its performance evaluation.

Implementation

We adopt a COTS RFID reader Impinj 420 with a Larid S9028PCR antenna and UPM tags without any modification for PRSS. The RFID reader operates at about 920 MHz, whose wavelength is about 0.32 m. The reader mode is set as “Dense Mode (M=4)” for the practical industrial settings and the transmit power is 20 dBm. The experiment environment is depicted in Figure 9. The maximum speed of the conveyor belt is 240 m/min, which can meet the demand of most applications. And we place the antenna on a RFID portal at a height of 1.5 m over the conveyor belt. Some tags are regularly or irregularly attached to the boxes. Low-level reader protocol (LLRP)³¹ extended by Impinj is regarded as a communication approach between the computer and the reader. We implement PRSS using C# on a computer equipped with an Intel Core i7-4790 CPU 3.6 GHz and a 16 GByte memory.

Figure 9.

Dense tags on conveyor belt across the RFID portal.

There are two parameters that dramatically affect the system performance.

The speed of the conveyor belt determines the dwell time of a tag in the interrogation zone. A longer time length means more interrogation times and smaller phase difference between two consecutive interrogations.

The tag spacing affects the number of tags in the interrogation zone and the interrogation times of a tag. Due to the RFID air interface protocols C1G2,³ a shorter spacing brings more collisions, which means less effective data. Densely placed tags also cause the threshold of effective velocity to be small.

The performance of PRSS

We compare PRSS with other three sorting systems, Tagoram,⁴ STPP,⁶ and OTrack.² For evaluation, the accuracy ratio is calculated by dividing the length of the longest subsequence with the correct order by the total number of tags on the conveyor belt.

At first, the tag spacing is fixed at 10 cm and the speed of the conveyor belt changes from 0.5 to 4 m/s. The interrogation zone is about 0.5 m long. Only one antenna is used, while there are 15 tags across the RFID portal in one experiment. As shown in Figure 10(a), OTrack and STPP suffer a lot from the high-speed conveyor belt, high density of tags, and short dwell time in the interrogation zone for each tag. Tagoram is also a synthetic aperture RFID localization system, which has similar performance to PRSS (both over 95% and even the speed is 4 m/s).

Figure 10.

Performance comparisons of different sorting systems: (a) different speeds of conveyor belt, (b) different tag spacings, and (c) with unknown conveyor belt speed.

Then, we fix the speed of the conveyor belt at 4 m/s and change the tag spacing from 7 to 20 cm. As illustrated in Figure 10(b), STPP and OTrack have some improvement with the increasing spacing. But due to less samples, they are unsuitable for sorting objects on high-speed conveyor belts. PRSS and Tagoram have similar performance. On account of the phase calibration and the aperture points screening, PRSS is a little better.

The performance of holography-based sorting (PRSS and Tagoram) also depends on the accuracy of the aperture position, which is determined by the conveyor belt speed. The aperture length is about 0.5 m and the tag spacing is 10 cm. If the speed (3.9 m/s) of the conveyor belt is unknown or known incorrectly (known as 4 m/s), the sorting accuracy is depicted in Figure 10(c). Without the exact speed of the conveyor belt, the performance of Tagoram decreases a lot. If the speed is wrong, the longer the aperture is, the lower sorting accuracy ratio is achieved. So, the speed search is necessary, which can be obtained by equation (11). At the same time, although STPP and OTrack are insensitive to the prior speed knowledge, they are unsuitable for sorting dense objects on high-speed conveyor belts.

The number of aperture points $M$ has a positive correlation with the computation overhead. Although the computational complexities of PRSS and Tagoram are all $O (MN)$ with $N$ grids, PRSS has a much smaller $N$ due to the simplified particle filter (we assume they have the same search scope, but it is restricted for PRSS in practice). After $l$ times iterations, the computational complexity of PRSS is $O (2 MN / l)$ because each iteration eliminates half of grids/particles. Without simplified particle filter, the average run time of PRSS is about 500 ms, while it is about 34 ms after the first iteration. The whole run time of five iterations is no more than 60 ms, which is much smaller than $5 \times 25 ms = 125 ms$ in Tagoram.

So, PRSS is adaptive for the unknown high speed of the conveyor belt and the dense objects with a small delay. And the tags sorting with 97% accuracy on average is achieved, when there are 10 tags/m and the speed is 4 m/s. PRSS achieves high accuracy with good robustness. Its first two methods can narrow down the search scope and reduce the computation burden, while the holography-based method improves the accuracy.

Detection of tags not on conveyor belt

PRSS filters out those tags not on conveyor belt. Five static tags are placed near the conveyor belt and there are three people attached with five tags walking (about 1.5 m/s) around. After 50 experiments ( $v = 14 m / s$ , 10 tags on the conveyor belt with a 10 cm spacing), the filtering result is shown in Table 1. As mentioned before, the slope of the velocity curve and the read rate within 200 ms range of the zero point are utilized for detection. With the radial velocity-based method, almost all tags not on conveyor belt are filtered out by the slope of the radial velocity curve and the tag read rate near the zero point, while the detection accuracy in SARFID³² is 95% with 1 s observation.

Table 1.

Filtering out tags not on conveyor belt.

	Classified as
	On conveyor belt	Not on conveyor belt
On	100%	0%
Not on	0.8%	99.2%

Benchmarks

To further analyze the performance of PRSS, we perform several benchmarks. Usually, the aperture is 0.5 m length, the tag spacing is set as 10 cm, and the speed is 4 m/s.

The performance of three subsystems

The accuracy ratio of radial velocity-based sorting is shown in Figure 11(a). The speed of the conveyor belt and the tag spacing have great influence on the performance of radial velocity-based sorting. The descent of the tag spacing and the ascent of the speed both cause the decrease of interrogation times for a tag, that is, there are fewer velocity points to estimate the zero point time. Then, the phase curve fitting method is used to get a coarse-grained time $t_{0}$ and a corresponding conveyor belt’s speed. As shown in Figure 11(b), the result is similar to the radial velocity-based method. Due to a good tolerance to the measurement error, this method achieves higher precision. It achieves 95% average accuracy when the density of tags is 10/m and the speed is 4 m/s. Unlike the previous methods, the holography-based method is not affected by the modulo operation. The sorting accuracy of holography-based sorting is depicted in Figure 11(c), which is much better than previous methods.

Figure 11.

The performance of three subsystems (the horizontal axis shows the tag spacing, all tags are regularly placed): (a) the radial velocity-based method, (b) the phase curve fitting-based method, and (c) the advanced holography-based method.

Moreover, as aforementioned, the aperture points far away from the zero point are more likely to have more error. In an experiment, the zero point time is about 5800 ms, while there are some outliers of phase values as illustrated in Figure 12(a) (the tag is interrogated when it is static). Without the first two methods, these outliers cannot be filtered and the search scope is huge. From Figure 12(b), it is obvious that the single holography-based method cannot get the right result and the advanced holography-based method may not get global optimization. In PRSS, the noise caused by outliers is removed, and the accurate result is achieved with a small search scope, which is illustrated in Figure 12(c).

Figure 12.

Holography-based method: (a) some outliers (<4000 ms), (b) with all data points (2567 ms), and (c) the holographic image of PRSS (5716 ms).

Different iterations

The simplified particle filter in the advanced holography-based sorting can decrease the computational burden effectively. The sorting result of the first iteration (0.1 m aperture) is inaccurate, while after five times iteration (0.5 m aperture), the accuracy is very high. The relative error is the difference between tag spacing 10 cm and the distance estimated by zero point times of two neighboring tags and the conveyor belt speed. As illustrated in Figure 13(a), after five iterations, the advanced holography-based method gets accurate results because this probabilistic method coherently utilizes all measurement phase values.

Figure 13.

The accuracy of PRSS: (a) the CDF of advanced holography-based method after the first and the fifth iteration, (b) the CDF of advanced holography with different aperture length, and (c) different noise, multi-path, and material.

Aperture length

Different aperture lengths have different ambiguity in holography-based sorting. A longer aperture usually means more obvious difference in noise of different aperture points, which can be weakened by each other in coherent reconstruction. On the conveyor belt with the RFID portal, the aperture length is hard to be accurately adjusted. So, we change the transmission power of the RFID reader to adjust its interrogation zone. The sorting system with high transmission power will have longer aperture. As shown in Figure 13(b), a longer aperture length has a more accurate result. At the same time, due to much longer aperture, the read time for one tag with 30 dBm is almost double than that with 20 dBm. So is the computational burden. What is worse is the reader with 30 dBm has a large interrogation zone which contains a lot of tags not on the conveyor belt and will interfere other radio devices. So, our system sets the transmission power at 20 dBm and then the aperture is about 0.5 m long to achieve satisfying sorting results.

Different noise, multi-path, and material

Tag positions determine their trajectories. Irregular positions mean different tags have different zero point distances $h$ in equation (6). Thus, to get the accurate zero point, the computational complexity will increase due to a large search scope for zero point distance. In addition, the received signal consists of the signals reflected by the tag and other reflectors known as multi-path propagation. Only the signal directly reflected by the tag includes useful location information. As aforementioned, multi-path and noise profiles can be weakened by each other in coherent reconstruction, as the direct signal is the strongest one. Because each aperture point has various interference, noise, and multi-path profiles, these distortions will be summed up incoherently, and thereby weakened as well. It is difficult to carry out a quantitative analysis on their impact. So, we utilize an extra reader to produce interference and some metal reflectors to enhance multi-path distortion. As depicted in Figure 13(c), their accuracies are almost the same as before. PRSS is robust to the regularity of tags’ positions, noise, and multi-path. The material such as water will result in the reduction of the interrogation rate, and then the accuracy decreases a lot because much UHF RF power is absorbed by water molecules. The counts of one tag interrogated decrease a lot.

Conclusion

In this article, we present a RFID-based sorting system PRSS for dense objects on high-speed conveyor belts with high accuracy. We take advantage of the output phase to calculate radial velocity and the phase curve fitting to estimate coarse-grained zero point time. Then, we reconstruct a holographic image to get fine-grained locations. The final process achieves a significant reduction of computational burden by a small search scope and particle filter. The algorithm parameters and performance are mathematically discussed. We implement PRSS and conduct extensive experiments to validate its effectiveness with COTS RFID devices. The experimental results show that PRSS achieves up to 97% accuracy on average in less than 60 ms delay when the tag spacing is 10 cm. Our future work will further improve the accuracy and real-time performance.

Footnotes

Handling Editor: Qi Han

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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Passive radio frequency identification sorting for dense objects on high-speed conveyor belts

Abstract

Keywords

Introduction

Related works

Background

Problem specification

Output phase

Research methodology and system design

Radial velocity-based sorting

Phase curve fitting-based sorting

Normal holography-based sorting

Phase value calibration

Advanced holography-based sorting

PRSS design

Evaluation

Implementation

The performance of PRSS

Detection of tags not on conveyor belt

Benchmarks

The performance of three subsystems

Different iterations

Aperture length

Different noise, multi-path, and material

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References