The key for a movement behavior-based smoothing filter lies in how to establish the conversion relationship between read rate sequences and kinematic parameters of tags to assist in RFID data cleaning. To do so, we proposed a movement behavior detection model.

The process of tag passing through the reader's read range follows the laws of kinematics. The change of kinematic parameters such as displacement and velocity which possess an important feature is continuous, not transitional, so if the location (which mainly refers to the distance between tag and reader) and the relative velocity of tag at the time can be obtained through the original data, we can speculate the parameters of the tag at the missed reading time by these parameters and their trends, and further assist in data cleaning and improve its accuracy. BBS uses this approach, for example, using existing tag data to analyze and get the location p₁ and the velocity v₁ of the tag at the time t₁, which can help approximately inferring to the relative location of the tag at the time t₁ + T (T refers to a short period of time). Finally, by mapping the location information back to the RFID data, we can fill the missed RFID data. Therefore, through these kinematic parameters BBS can obtain whether the tag is in the detection range at the time, and further give its specific location.

Adopting the statistical methods similar to SMURF, each epoch is viewed as an independent Bernoulli trial with success probability p_i [12]. An epoch may be specified as a number of interrogation cycles or a unit of time. A typical epoch range is 0.2–0.25 seconds [5]. For each epoch, the reader keeps track of all the tags that have been identified, and additional information such as the number of interrogation responses for each tag and the last time the tag was read. Assuming, there are n interrogation cycles in an epoch, the number that tag_i is monitored is m_i. We can get the read rate of tag_i at the moment by p_i = m_i/n. In the process of passing through the reader's read range, tags will be continuously scanned. Also in the whole process, the read rate of tag is not constant but constantly changing with the distance between the tag and reader. Besides, some researchers have proved by experiments that in the reader's detection region there is a linear relationship between read rate p and distance s [12]. For specific readers, the detection range S is a constant. To confirm this conclusion, we have carried out similar experiments and the conclusion is shown in Figure 1. The quiet condition means an ideal working environment of RFID devices with only a few interferences, while the noisy condition means a work environment with more interferences.

By further abstraction of the conclusions above we get the relationship between read rate p and distance s in Figure 2. Obviously, the distance s between tag and reader and the read rate p follow the relation as: (1) p = { 0 k s + b < 0 k s + b 0 ≤ k s + b ≤ 1 1 k s + b > 1where, b = −kS, and k is the slope of the line, so above equation can be further written as: (2) p = { 0 s > S k ( s − S ) 0 ≤ k ( s − S ) ≤ 1 1 k ( s − S ) > 1

In this section, how to use the model to fill the missed RFID data will be discussed. In our model, epoch is the basic unit of RFID data streams. Our mission is to fill in the missed epoch information. The information of RFID data stream that we get includes tag ID, the number of interrogation responses for each tag in an epoch and the time of the epoch, in the form of (tag ID, Response number, time). Let us analyze Equation (2). The read rate p can be calculated through Response number, and the detection range S is a constant, but the distance s can't be calculated directly. In practice, the detection region of each reader is generally not very large, ranging from a few meters to tens of meters. Therefore, the movement through the detection region for persons, vehicles and goods on the conveyor belt and other tagged items can be approximately considered as uniform linear motion or a combination of several successive uniform linear motions. In addition, even if the velocity and direction of the objects has obviously changed in this process, we can also break down their movement, and approximately consider each short process as uniform linear motion. Well known, the speed v of uniform linear motion satisfies the equation Δs = vΔt. And if we consider s₀ is the original distance of the tag, and Equation (2) can be further written as: (3) p = { 0 K Δ t + B < 0 K Δ t + B 0 ≤ K Δ t + B ≤ 1 1 K Δ t + B > 1where K = ± kv (It take the negative sign when the value of p increases, otherwise take the positive sign), and B = k(s₀−S).

In practice, readers are usually interfered by the surroundings including the signal reflection and obstruction or sudden current gain, etc., so the read rate that is calculated by Response number will be unstable. The results from directly treating the raw data may differ from the actual movement characteristics, so we use a weighted moving average of order n to smooth the initial read rate sequences. The process of replacing the read rate sequences by its moving average eliminates unwanted fluctuations. Furthermore, the influence of extreme values can be reduced by employing a weighted moving average with appropriate weights to get more realistic movement features of items to be monitored. The calculation is as follows: (4) p i = w 0 p i − n − 1 2 ′ + w 0 p i − n − 1 2 + 1 ′ + ⋯ + w 1 p i ′ + ⋯ + w 0 p i + n − 1 2 ′ ( ∑ j = i − n − 1 2 i + n − 1 2 ⌈ p j ′ ⌉ − 1 ) w 0 + w 1where w₁ and w₀ are the weights of read rate of current epoch and other epochs respectively.

In the above treatment, we only discuss such epoch whose read rate p i ′ ≠ 0. When the read rate of the epoch is p i ′ = 0, there are two possibilities: the tag is indeed outside the detection range or miss reading occurs to the tag, i.e., the tag is in the detection range but not captured for interference factors. It is necessary for accurate data cleaning to distinguish these two cases clearly. We should analyze its movement feature in the adjacent time. The movement of tags is approximately uniform linear motion and satisfies Equation (3), so we can calculate the read rate p_i of the tag by the value of K and the read rate p_ia in the adjacent time, to further determine it is a true value or a missed reading. In order to solve the coefficient K, we denote epoch_j = {t_j, p_j}, where t_j and p_j are the time and read rate of epoch_j respectively, and a training set TS = {epoch_i+l | p_i-l ≠ 0, −m ≤ l ≤ m}, where the upper limit of |TS| is 2m + 1. So the coefficient K can be solved by the method of least squares on the trainings set of TS, which estimates the best-fitting straight line as the one that minimizes the error between the actual data and the estimate of the line: (5) K i = ∑ epoch j ∈ T S ( p j − p ¯ ) ( t j − t ¯ ) ∑ epoch j ∈ T S ( p j − p ¯ ) 2 (6) B i = t ¯ − K i p ¯where, p ¯ = ∑ epoch j ∈ T S p j | T S | , t ¯ = ∑ epoch j ∈ T S t j | T S |.

In the data stream processing, data are normally processed in order. However, if the RFID data stream corresponding to a tag is filled in chronological order by the above-mentioned method, it is easy to bring the problem of miss filling, as shown in Figure 3(a). We analyze the read rate of a tag in one time period in detail in Figure 3. Figure 3(c) indicates the read rate of the tag without miss readings and Figure 3(b) shows the raw read rate that the reader actually read. For an epoch_p in Figure 3(a), if the corresponding coefficient K_p > 0 and the data before the time t_p has been miss read for a long period of time, the data before a period of t_p will not be filled because the RFID data stream are processed in order. A simple solution is to process the RFID data stream twice, forward and backward. However, this will add a lot of computational overhead. To solve this problem, we introduce a Reverse Order Filling Mechanism. As soon as we detect the situation mentioned above occurs, the read rate of the corresponding data stream is to be refilled in the reverse direction from epoch_p+T. Until the original read rate p_i ≠ 0 or the filling value of read rate p_f = 0 the reverse filling mechanism will not be terminated. And the rest of data will be processed after that. So we only need a twice process to the corresponding data rather than all data, which ensures the completeness of RFID data cleaning, but also does not add too much computational overhead. Algorithm 1 shows a pseudo-code description of BBS cleaning algorithm.

In the experiment, we compare the accuracy of data filled by BBS (with n = 3, n = 7 and n = 11, respectively), SMURF, and sliding-windows methods (with different window size: 5 epoch, 20 epoch and 35 epoch) under different missing rate (from 10% to 80%). The other experimental parameters of BBS are set as follows: m = 7, w₀ = 1 and w₁ = 2. We clean the same raw data with different methods. Comparing the corresponding cleaning result with real data, we can get the error rate of each method. As shown in Figure 4, the error rate of BBS is lower than that of sliding windows methods in all cases. We found that the choice of the parameter n will have some impact on the experimental results when the missing rate is greater than 70%. Therefore, in practical applications, for optimal cleaning results we should set parameters n, m, w₀ and w₁ with appropriate values in accordance with the actual needs. Usually, the more unstable the read rate sequence, the larger the value of n should be set; the higher the missing rate, the larger the value of m should be set.

We compare the accuracy of data filled by different methods under different tag speeds. The error rates obtained are used to compare the accuracy of methods where lower error rate means higher accuracy. As shown in Figure 5, the results of BBS are obviously superior to all other methods, especially when the speeds of tags are higher than 1.0 m/s.

Furthermore, we analyze the case in one time period in detail (missing rate = 50%, and the length of time is 1,000 epochs). As shown in Figure 6, Reality refers to readings that would have been produced by a perfect reader without missreadings. Raw means the raw data that the reader actually read and while the others refer to the data filled with four kinds of data cleaning methods (BBS, SMURF, 5 epoch sliding-window, and 35 epoch sliding-window). The bold horizontal lines indicate the tag is present/read, and vice versa. The line at the bottom of Figure 6 is the real data of read rate without miss reading, and another line above it is the estimate of read rate by BBS (n = 7, w₀ = 1 and w₁ = 2). Obviously, compared with sliding window methods, BBS greatly improved the accuracy of RFID data cleaning. In particular, our BBS method not only accurately draws whether the tag is in the read range of the reader, but also can give the read rate of each epoch. So BBS make it possible to get a more exact position of the tag.

To verify the validity and necessity of Reverse Order Filling Mechanism, we design the following experiment. We focus on readings produced from a single tag with different missing rates from 10% to 80% in 10,000 epochs. We process 8 sets of data by two different methods, the Reverse Order Filling Mechanism method and the Twice Scanning Method, and determine their performance by comparing the response times. As show in Figure 7, the Reverse Order Filling Mechanism only needs a twice cleaning process to the corresponding data while the Twice Scanning Method needs the process to all data. Therefore, the former is obviously superior to the latter in the efficiency of processing data.