CN111178100A - Radio frequency identification RFID tag quantity estimation method - Google Patents
Radio frequency identification RFID tag quantity estimation method Download PDFInfo
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Abstract
A method for estimating the number of RFID tags for radio frequency identification belongs to the field of radio frequency identification, and aims at solving the problem of large error of the existing tag estimation scheme, firstly, an adjustment factor is determined according to the number relation between the number of tags and the frame length; secondly, researching the proportion of the successful time slot to the total time slot in the tag identification process to obtain the relation between the regulating factor and the proportion; and finally, solving by using a Newton iteration method to obtain the accurate label quantity. Simulation results show that the NIATE algorithm has better self-adaptive capacity and smaller average error of tag estimation compared with the existing mainstream algorithm under the condition of different tag quantities.
Description
Technical Field
The invention belongs to the field of radio frequency identification, and relates to a Radio Frequency Identification (RFID) tag quantity estimation method.
Background
Radio Frequency Identification (RFID) technology is widely used in many fields, such as warehouse management, logistics control, intelligent shelves, product tracking[1,2]And the like. Electronic tags have the advantages of small size, low cost, easy handling, etc., and are generally very large in number in the above application fields. When two or more tags communicate with the reader at the same time, signals will interfere with each other, and the problem of tag collision inevitably occurs, resulting in the failure of reading information of the reader.
Currently, there are mainly two types of tag identification algorithms: tree-based algorithm and Aloha protocol-based algorithm[3～7]. In the application of a large RFID system, the tag population is large, the complexity of a binary tree algorithm is high, the delay is long, and the requirement of real-time identification in an identification environment cannot be met[8]. Therefore, based on Aloha protocol is widely used, and the algorithm is simple and low in use cost. Based on Aloha's algorithm, document [9]]The identification efficiency is highest when the number of the tags is equal to the frame length, so that the selection of the communication time slot plays a key role in the tag identification performance, too many time slots exist, too many idle time slots exist, too few idle time slots exist, and the actual number of the tags needs to be estimated for determining the frame length. The number of the rapidly and accurately identified tags can be set to be the best Aloha algorithm frame size to accelerate the tag ID information collection speed, and can also be used for inventory monitoring to facilitate the management of goods[10]。
Schoute[11]The number of tags is estimated according to the number of collision time slots, and the number of tags in each collision time slot is assumed to be a fixed value and cannot be adjusted along with the increase of the size of the tags, so that the estimation error can increase along with the increase of the number of the tags. Vogt[12]The maximum likelihood estimation method is applied to estimate the number of the labels, the accuracy of label estimation is improved at the cost of the frame length larger than the number of the labels, the search process and calculation are too complex, and the label estimation method is rarely used. Document [13 ]]The maximum posterior probability method is provided for estimating the number of the labels, the algorithm estimates the number of the labels based on polynomial distribution and the maximum posterior probability, the accuracy of label estimation is further improved, but if the number range of the labels is large, the problem of overlarge operation amount also exists. Document [14]A method for roughly and finely estimating the number of labels for the second time is provided, whether fine estimation is needed or not is determined through an evaluation standard obtained through analysis, the fine estimation adopts a maximum posterior probability algorithm based on priori knowledge, the roughly estimated number of labels is used as a starting point value of the fine estimation, the fine estimation search range is reduced by 90%, and the average estimation error is larger. Document [15 ]]And [16 ]]The method is similar to the maximum posterior probability method, but the calculation complexity is lower than that of the maximum posterior probability method, the defects are that the Bayesian estimation observation value requirement is higher, and a reader-writer only acquires information from one frame and cannot acquire enough observation results. Document [17]]Based on the linear relation between the mean square Bayes method and the lower limit value estimation method, the two methods are carried outThe number of the labels estimated by the two algorithms is provided by fusion, the estimation accuracy is higher, but the errors of the two algorithms are different, which algorithm is selected under different conditions is not explained, and the defect that the Bayesian estimation observation value requirement is higher is still not solved. Document [18]The other scheme for estimating the number of the labels is provided, only the relation between the number of the successful time slots in a frame under theoretical and actual conditions needs to be analyzed, and the accurate number of the estimated labels can be obtained by applying a cut-line iteration method, but in the estimation process, an extra detection frame needs to be sent to remove a pseudo solution generated by label estimation, so that the time overhead and the algorithm estimation complexity of a system are increased, and in addition, when the frame length is small and the number of the labels cannot be estimated, a frame length adjusting scheme capable of estimating the number of the labels is not provided in the text.
Disclosure of Invention
In order to solve the problems that additional detection frames need to be sent to remove pseudo solutions generated by label estimation and the time overhead of a system and the algorithm estimation complexity are increased, the invention provides the following technical scheme: a method for estimating the number of RFID tags based on Radio Frequency Identification (RFID) is characterized in that an estimation model of the number of tags is obtained by a Newton iteration method according to the ratio of the number of successful time slots in a frame to the total time slots under theoretical and actual conditions, and the number of the tags is estimated.
Furthermore, when the Newton iteration method is used for calculation, a proper iteration initial value is analyzed and selected according to the relation between the successful time slot number and the actual successful time slot number, and the number of the labels is estimated through finite iterations.
Further, the method for obtaining the estimation model of the number of the tags by using the newton iteration method is as follows: the frame length is set to F, and assuming that the number of tags to be identified is n, each tag randomly generates a random number RiN, wherein m is 0,1, F-1;
the probability that each tag selects a certain time slot is 1/F, and then the probability that r tags select the same time slot is as follows:
where r is 0,1 or greater than 1, and obviously, r is the probability of a successful timeslot when r is 1:
the expected number of successful slots in a frame is:
the ratio of the number of successful timeslots to the total number of timeslots is:
assuming that the initial frame length F is n/b, where b is an adjustment factor, the F is n/b is substituted into equation (4):
number of successful time slots N in tag identificationsThe statistic result is obtained according to the identification result after one frame is finished, and the proportion of the number of the successful time slots is assumed to be PSAAnd then:
ideally, after one frame identification is finished, the relationship between the number of successful timeslots in practical and theoretical situations is: e [ P (F, n,1)]＝NsThen, the following formula (5) and formula (6) are obtained:
as can be seen from equation (6), one frame recognition ends, PSAThe value of the adjustment factor b can be obtained by the ratio of the number of successful time slots to the frame length, and the estimated value of the number of the labels is determined by the formula (7):
order:
f(x)＝x·e-x-PSA,x＞0\*MERGEFORMAT (9)
the estimation model of the label number according to the Newton iteration formula is expressed as follows:
further, the selection method of the iteration initial value is as follows: according to the relation b between the number of the tags and the frame length, x ∈ (0, + ∞)]. From the formula (7), it is found that f (x) falls within the interval x ∈ (0,1)]Is monotonically increased, and is increased in the interval x ∈ [1, + ∞]Monotonically decreasing upward, so 0 < f (x)max＝f(1)≈0.3679-PSA＜0.3679，0＞f(x)min＝f(∞)≈-PSA> -0.3678, so that f (x) is in the interval x ∈ [0, + ∞]The number of solutions is 1 or 2;
the second derivative is obtained by calculating f (x) in equation (7):
f”(x)＝e-x(x-2)\*MERGEFORMAT (11)
from the formula (10), it is understood that the pattern of f (x) is convex in the interval x ∈ (0, 2), and concave in the interval x ∈ [2, + ∞ ];
x is the interval of the equation root, x0For the initial value of the iteration:
in the first case:
when the solution of the equation f (x) is in the interval x ∈ (0,1)]When f (x) has constant unevenness, the initial value of iteration is x according to the principle of Newton's iteration method0E (0,1) can be solved;
in the second case:
when the solution of the equation f (x) is in the interval x ∈ [1, + ∞ ], as can be known from the formula (10), f (x) is convex when x ∈ [1,2 ]; x ∈ [2, + ∞ ], f (x) is concave, and f (x) has a unique inflection point x ═ 2 in the interval x ∈ [1, + ∞ ];
when the equation root is in x ∈ [1,2]]F (x) in the interval x ∈ [1,2]]The concave-convex property of the material is unchanged, and the initial value of iteration can be x according to the principle of a Newton iteration method0∈(1,2]Any number of (a), (b), (c) of fig. 2; if the initial value of iteration is x0∈(2,+∞]Any number of (2) cannot solve the equation solution;
let the root of f (x) be xkWhen the root of the equation is in x ∈ [2, + ∞ ∈]The initial value of iteration may be x0∈[2,xk]When the initial value of the iteration is x0E (1,2) or x0∈[xk,+∞]The root of the equation is not obtained.
Further, when the successful time slot number is 0, the length F of the second frame is adjusted2＝F1And x 2, then estimating the number of the labels of the second frame, and so on until the proportion of the successful time slot to the total time slot is not 0.
Further, small-range adjustment of estimation error: the relative error is defined as:
wherein the content of the first and second substances,
setting the number of estimated labels after adjustment for the estimated number of labels and n is the actual number of labels
Wherein the content of the first and second substances,
to adjust the estimated number of tags, a is an adjustment factor.
Has the advantages that: the Newton iteration-based RFID label quantity estimation algorithm provided by the invention provides an automatic adjustment scheme for the frame length required by label quantity estimation when the label quantity is different, solves the problem of large time slot quantity required during label estimation, and realizes accurate estimation of the label quantity. Through experimental comparison and analysis, the label estimation error is small, the total time slot number required when the label is identified is small, and the system throughput rate is high. Therefore, the algorithm provided by the invention improves the accuracy of the RFID system label quantity estimation, and can be used for the application of different label quantity environments.
Drawings
FIG. 1 is a flow chart of a dynamic frame time slot Aloha protocol anti-collision algorithm
FIG. 2 different initial values x of iteration0Influence on the results
Fig. 3 relative error before and after adjustment (F128)
Relative error in fig. 4 (initial frame length F64, 128, 256, respectively)
Total number of slots in FIG. 5
FIG. 6 System throughput
Detailed Description
The Aloha algorithm is a widely adopted Radio Frequency Identification (RFID) tag anti-collision algorithm, and to improve the Identification efficiency, the algorithm frame length must be adaptively adjusted according to the number of tags, so the accuracy of tag number estimation is very important. Aiming at the problem of large error of the existing label estimation scheme, a label quantity estimation algorithm (NIATE) based on a Newton iteration method is provided. Firstly, determining an adjusting factor according to the quantity relation between the number of labels and the frame length; secondly, researching the proportion of the successful time slot to the total time slot in the tag identification process to obtain the relation between the regulating factor and the proportion; and finally, solving by using a Newton iteration method to obtain the accurate label quantity. Simulation results show that the NIATE algorithm has better self-adaptive capacity and smaller average error of tag estimation compared with the existing mainstream algorithm under the condition of different tag quantities, so that the total time slot number required by identifying all tags is reduced, and the system throughput rate is improved.
The invention provides a label quantity estimation scheme (NIATE) based on a Newton iteration method. According to the optimal identification rate under the theoretical condition proved by the literature [9], assuming the quantity relationship between the number of the tags and the frame length, analyzing a relational expression of the successful time slot number in one frame in the proportion of the total time slot number, and solving the obtained relational expression by using a Newton iteration method to obtain the estimated tag number; based on the analysis research of iterative initial value selection in the relation, the time overhead and algorithm complexity of removing consumption due to pseudo-solution are solved; according to the obtained distribution condition of the number of the estimated labels, the number of the estimated labels is adjusted in a small range; meanwhile, for different numbers of labels, the invention provides a scheme for automatically adjusting the frame length. Simulation results show that the error of the number of the labels estimated by the algorithm is small, the self-adaptive capacity of label estimation is strong, when the estimated number of the labels is used for label identification, the total time slot number is small, and the system throughput rate is high.
1 dynamic frame time slot Aloha algorithm
Referring to fig. 1, a dynamic frame timeslot Aloha anti-collision algorithm workflow in an RFID system. Where F is the frame length, NCNumber of collision slots, NSFor the number of successful timeslots, SN is the communication timeslot selected by the tag. The invention counts the number of successful time slots by the algorithm shown in fig. 1, and is used for estimating the number of tags.
2 tag number estimation scheme
According to the invention, the estimated label number is calculated by utilizing a Newton iteration method according to the ratio of the successful time slot number in one frame in the total time slot, and the number of the empty time slot and the collision time slot does not need to be calculated. In order to reduce the calculation complexity of an estimation algorithm, according to the relationship between the successful time slot number and the actual successful time slot number under the theoretical condition, analyzing and selecting a proper iteration initial value, and estimating the number of labels through finite iteration; in order to make the algorithm adapt to the estimation of different label quantities, the algorithm provides a scheme for adjusting the initial frame length according to the number of successful time slots; in order to further improve the accuracy of label estimation, the label quantity distribution is adjusted in a small range according to the preliminary estimation.
2.1 tag quantity estimation model
The frame length is first set to F and the number of tags to be identified is assumed to be n. Each label randomly generates a random number RiM, (i ═ 1,2.. n) as its own communication slot, where m ═ 0,1.., F-1.
Theoretically, the probability that each tag selects a certain time slot is 1/F, and then the probability that r tags select the same time slot is:
wherein r is 0,1 or greater than 1. Obviously, the probability of a successful slot is when r is 1:
therefore, the expected value of the number of successful slots in one frame[19]Comprises the following steps:
if the frame length F, i.e. the number of timeslots is F, and the formula (3) is an expected value of the number of successful timeslots, the ratio of the number of successful timeslots to the total number of timeslots is:
assuming that the initial frame length F is n/b, where b is an adjustment factor, substituting F into n/b into equation (4) yields:
in practical application, when the label is identified, the number N of successful time slotssCan be obtained by statistics according to the identification result after one frame is finished, and the ratio of the number of the successful time slots is assumed to be PSAAnd then:
ideally, after one frame identification is finished, the relationship between the number of successful timeslots in practical and theoretical situations is: e [ P (F, n,1)]＝Ns. Then, from equation (5) and equation (6):
as can be seen from equation (6), one frame recognition ends, PSAThe adjustment factor b can be found by the ratio of the number of successful slots to the frame length, and is determined by equation (7), so that the tag number estimate is:
to facilitate the solution of the adjustment factor b in equation (7), let:
f(x)＝x·e-x-PSA,x＞0\*MERGEFORMAT (9)
f(x)＝x·e-x-PSAwhen x > 0\ MergeEFORMAT (10) indicates that the label number is equal to the selected frame length, 0.3679 can be obtained with the highest system identification efficiency, so PSA∈[0,0.3679]。
The transcendental equation root finding method generally includes a dichotomy, a secant method, a Newton iteration method and the like. The dichotomy solving speed is low, two initial points are needed for the secant method solving, and pseudo-solutions are easy to occur in the solving. The Newton iteration method has the property of second-order convergence, is quick in solving process, and meets the actual requirements of engineering, so that the method adopts the Newton iteration method to solve the transcendental equation (9).
Thus, the estimation model of the number of labels according to the newton iteration formula can be expressed as:
it should be noted that, when the adjustment factor b is calculated by using the newton iteration method, the selection of the initial iteration value, the number of iterations, and the frame length value all affect the estimation of the number of tags. The selection of the initial iteration value generally has obvious influence on the iteration result, the initial iteration value is not well selected, the result may be diverged or oscillated, and an accurate result cannot be obtained; the more the iteration times, the smaller the estimation error of the number of the labels, however, the algorithm complexity is higher and the algorithm time is prolonged; if the frame length is too small and the number of tags is large, the number of successful time slots may be 0, and equation (9) will not solve the number of tags. The constraints over the solution of equation (9) are analyzed in detail below.
2.2 selection of initial values for the iterations
According to the relation b between the number of the tags and the frame length, x ∈ (0, + ∞)]. From the formula (7), it is found that f (x) falls within the interval x ∈ (0,1)]Last but not lastIncreasing, in the interval x ∈ [1, + ∞]Monotonically decreasing upward, so 0 < f (x)max＝f(1)≈0.3679-PSA＜0.3679，0＞f(x)min＝f(∞)≈-PSA> -0.3678, so that f (x) is in the interval x ∈ [0, + ∞]The number of solutions is 1 or 2.
The second derivative is obtained by calculating f (x) in equation (7):
f”(x)＝e-x(x-2)\*MERGEFORMAT (12)
from the formula (10), it is understood that the pattern of f (x) is convex in the interval x ∈ (0, 2), and concave in the interval x ∈ [ 2] + ∞ ].
FIG. 2 is a diagram illustrating the influence of different iteration initial values on the equation root when the equation root is solved by the Newton iteration method, where x is the interval where the equation root is located, and x is0Is an iteration initial value.
In the first case:
when the solution of the equation f (x) is in the interval x ∈ (0,1)]When f (x) has constant unevenness, the initial value of iteration is x according to the principle of Newton's iteration method0E (0,1), the equation solution can be solved. As shown in fig. 2 (a).
In the second case:
when the solution of the equation f (x) is in the interval x ∈ [1, + ∞ ], as can be seen from the equation (10), f (x) is convex when x ∈ [1,2 ]; x ∈ [2, + ∞ ], f (x) is concave. And f (x) has a unique inflection point x ═ 2 in the interval x ∈ [1, + ∞ ].
When the equation root is in x ∈ [1,2]]F (x) in the interval x ∈ [1,2]]The concave-convex property of the material is unchanged, and the initial value of iteration can be x according to the principle of a Newton iteration method0∈(1,2]Any number of (a), (b), (c) of fig. 2; if the initial value of iteration is x0∈(2,+∞]Cannot solve the equation, as shown in fig. 2 (d).
Similarly, assume the root of f (x) is xkWhen the root of the equation is in x ∈ [2, + ∞ ∈]The initial value of iteration may be x0∈[2,xk]Any number of (a), as shown in (e) of fig. 2; when the initial value of iteration is x0E (1,2) or x0∈[xk,+∞]The equation root is not obtained, as shown in (f), (g) of fig. 2.
The key point of the algorithm is to determine an initial iteration value x0From the above analysis, the initial iteration value is selected to be any value less than 1 or 2. The number of successful slots generated theoretically is shown in equation 3, and as the frame length increases, the number of successful slots increases. The actual number of successful time slots generated is NSWhen E [ P (F, n,1)]＞NSThen, the initial frame length is larger than the number of labels, and an iteration initial value x is selected02; when E [ P (F, n,1)]＜NSWhen the length of the initial frame is less than the number of labels, selecting any number with the initial iteration value less than 1, and selecting x in the invention0＝0.5。
2.3 iteration number and error analysis
Considering the simplicity of the algorithm, the present invention uses | nk-nk-1Controlling iteration precision, namely the error of the number of labels obtained by two iterations is less than 1, the set iteration upper limit is 10, and the relation between the observed estimation error and the iteration times is shown in table 1. As can be seen from Table 1, the requirement of the accuracy of the estimation of the number of tags can be completely met by applying 10 iterations of the Newton iteration method.
TABLE 1 iteration number and error analysis
2.4 tag number vs. frame size
According to the formula (7), when the ratio of the successful timeslot to the total timeslot is 0, it indicates that the length of the selected frame is too small to estimate the number of tags, and the frame length needs to be adjusted. For example, according to equation (3), the initial frame length F1When the number of tags n is 870 at 128, the ratio of successful timeslots to total timeslots is 0, and the number of tags cannot be estimated using the newton iteration method.
Based on the above analysis, when the successful number of timeslots is 0, the second frame length F is adjusted2＝F1And x 2, then estimating the number of the labels of the second frame, and so on until the proportion of the successful time slot to the total time slot is not 0. Table 2 shows the frame length and the maximum range of the number of labels that can be estimated.
TABLE 2 frame Length and range of number of labels that can be estimated
2.5 Small Range adjustment of estimation error
In the invention, a passive tag intelligent warehousing environment which is generally regarded as good is taken as an example, in practical application, a warehousing shelf is generally 1-2m, and the induction range of passive RFID is about 60cm, so that the number of tags existing in the effective identification range of a reader is limited (< 2000), and the maximum value of the number of tags estimated by an estimation algorithm is assumed to be 2000.
The relative error is defined as:
wherein the content of the first and second substances,
for the estimated number of tags, n is the actual number of tags. Fig. 3 (a) shows the relative error relationship between the number of tags and the tag estimation algorithm of the present invention when the frame length F is 128. The estimated number of tags in (a) of fig. 3 can be adjusted to a small extent to be closer to the actual number of tags.
Setting the adjusted estimated tag number
Wherein the content of the first and second substances,
for the estimated number of labels before adjustment, a is the adjustment factor, and the relationship between the number of labels and the adjustment factor is shown in table 3. In the relation between the adjusted label number and the relative error in fig. 3 (b), the stability and accuracy of the estimation of the adjusted label number are obviously improved. The error ratio before and after parameter adjustment is shown in table 4, and taking F as an example of 128, the maximum relative error and the average error after adjustment are reduced by 66.2% and 74%, respectively.
TABLE 3 tag number vs. adjustment factor relationship
TABLE 4 comparison of error before and after parameter adjustment
3 simulation results
In order to verify the performance of the label quantity estimation algorithm provided by the invention, MATLAB simulation software is utilized to carry out simulation experiment comparison on Schoute [11], Vogt [12], Ding [14], Cooperative [17], SIADA [18] algorithm and the estimation algorithm (NIATE) provided by the invention from the aspects of estimation error, total time slot number required by label identification and system throughput, the number of label samples is 2000 at most, 50 times of simulation result average value is measured by each sample number at intervals of 50 times.
3.1 error Performance comparison
The tag number estimation accuracy is the most important performance index. FIG. 4 is a graph showing the relationship between the number of estimated tags and the relative error for different initial frame lengths.
The estimation error of Schoute and Vogt algorithm is obviously higher than that of the other four estimation algorithms, because the influence of the frame length on the estimation result is not considered. In the Ding algorithm, when the number of tags is greater than 1000, the tag number estimation error gradually increases. When the number of tags is less than 100, the Cooperation calculation has a large estimation error and is not suitable for estimation of a small number of tag environments. The estimation accuracy of the SIADA algorithm is obviously affected by the frame length, and when the frame length F with a larger frame length is selected to be 256, the estimation accuracy of the label within 1200 can be ensured. The algorithm provided by the invention fully considers the influence of the frame length in the label estimation process, provides an adjustment scheme, has smaller estimation errors in different frame lengths, and reduces the average estimation error by 63% and 60% respectively compared with Cooperative and SIADA algorithms in the range of ensuring a certain number of estimation error labels.
3.2 Total number of time slots
Fig. 5 shows the total number of time slots required to identify a tag in relation to the number of tags. The initial frame length F is 128, as is apparent from fig. 5, the algorithm and Cooperative algorithm provided by the present invention are obviously better than other algorithms. The SIADA algorithm requires a large number of slots when estimating the number of tags since the spurious removal requires additional transmission of the sounding frame. The Cooperative algorithm can realize the estimation of the number of the labels only by a small frame length, and the total time slot is less than that of other algorithms. The algorithm of the invention needs to adjust the frame length to estimate the number of the labels again when the initial frame length is selected to be smaller and the number of the labels is larger, but the accuracy of the estimation of the number of the labels makes the selection of the frame length for identifying the labels closer to the actual number of the labels, and the total time slot number is reduced by 24 percent compared with the total time slot number of the SIADA algorithm.
3.3 System throughput
In an ideal state, the number of tags is known, and the system throughput rate calculation formula is as follows:
wherein N isSFor successful slot number, T is the total number of slots used to identify all tags, and when F ═ n (frame length equals tag number), the system is most efficient[9]And was 36.79%. However, when a label estimation algorithm is added, the throughput rate calculation formula is as follows:
FinitialThe total number of slots needed to estimate the number of tags and the tag number estimation has errors, so the actual system throughput is lower than 36.79%.
Fig. 6 is a graph of system throughput versus number of tags. And selecting an initial frame length F of 128, Vogt and Schoute algorithm, wherein the label estimation error is large, and the system throughput rate is low. The SIADA algorithm requires a large number of time slots in the tag number estimation, and the system throughput rate is low. The Cooperative algorithm can estimate the number of the labels in one frame, the throughput rate of the system is high, but when the number of the labels is less than 300 and more than 1500, the estimation accuracy of the labels is reduced, and the throughput rate of the system is reduced. In the algorithm, the maximum estimable tag number is 862 when the initial frame length is 128; when the number of the tags is larger than 862, the frame length needs to be adjusted to estimate the number of the tags, and the number of the slots for estimating the number of the tags is increased, so that the throughput rate of the system is reduced, but the accuracy for estimating the number of the tags is higher, and the throughput rate of the system can still be kept above 32%, which is improved by 33% compared with the throughput rate of a system adopting the SIADA algorithm.
4 conclusion
The Newton iteration-based RFID label quantity estimation algorithm provided by the invention provides an automatic adjustment scheme for the frame length required by label quantity estimation when the label quantity is different, solves the problem of large time slot quantity required during label estimation, and realizes accurate estimation of the label quantity. Through experimental comparison and analysis, the label estimation error is small, the total time slot number required when the label is identified is small, and the system throughput rate is high. Therefore, the algorithm provided by the invention improves the accuracy of the estimation of the number of the tags in the RFID system, and can be applied to the environment with different numbers of tags.
Reference documents:
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Claims (6)
1. A method for estimating the number of RFID tags for radio frequency identification is characterized in that an estimation model of the number of the tags is obtained by utilizing a Newton iteration method according to the ratio of the number of successful time slots in a frame in the total time slots under theoretical and actual conditions, and the number of the tags is estimated.
2. The method of claim 1, wherein when the number of RFID tags for RFID is calculated by using the newton iteration method, an appropriate initial iteration value is selected according to a relationship between a successful time slot number and an actual successful time slot number, and the number of tags is estimated through a limited number of iterations.
3. The method for estimating the number of RFID tags for radio frequency identification according to claim 1, wherein the method for obtaining the estimation model of the number of tags using the newton iteration method is: the frame length is set to F, and assuming that the number of tags to be identified is n, each tag randomly generates a random number RiN is used as its own communication time slot, i is 1,2Wherein m is 0,1, F-1;
the probability that each tag selects a certain time slot is 1/F, and then the probability that r tags select the same time slot is as follows:
where r is 0,1 or greater than 1, and obviously, r is the probability of a successful timeslot when r is 1:
the expected number of successful slots in a frame is:
the ratio of the number of successful timeslots to the total number of timeslots is:
assuming that the initial frame length F is n/b, where b is an adjustment factor, the F is n/b is substituted into equation (4):
number of successful time slots N in tag identificationsThe statistic result is obtained according to the identification result after one frame is finished, and the proportion of the number of the successful time slots is assumed to be PSAAnd then:
ideally, after one frame identification is finished, the relationship between the number of successful timeslots in practical and theoretical situations is: e [ P (F, n,1)]＝NsThen, the following formula (5) and formula (6) are obtained:
as can be seen from equation (6), one frame recognition ends, PSAThe value of the adjustment factor b can be obtained by the ratio of the number of successful time slots to the frame length, and the estimated value of the number of the labels is determined by the formula (7):
order:
f(x)＝x·e-x-PSA,x＞0\*MERGEFORMAT (9)
the estimation model of the label number according to the Newton iteration formula is expressed as follows:
4. the method of estimating the number of RFID tags for radio frequency identification according to claim 3, wherein the iterative initial value is selected by: according to the relation b between the number of the tags and the frame length, x ∈ (0, + ∞)]. From the formula (7), it is found that f (x) falls within the interval x ∈ (0,1)]Is monotonically increased, and is increased in the interval x ∈ [1, + ∞]Monotonically decreasing upward, so 0 < f (x)max＝f(1)≈0.3679-PSA＜0.3679，0＞f(x)min＝f(∞)≈-PSA> -0.3678, so that f (x) is in the interval x ∈ [0, + ∞]The number of solutions is 1 or 2;
the second derivative is obtained by calculating f (x) in equation (7):
f”(x)＝e-x(x-2)\*MERGEFORMAT (11)
from the formula (10), it is understood that the pattern of f (x) is convex in the interval x ∈ (0, 2), and concave in the interval x ∈ [2, + ∞ ];
x is the interval of the equation root, x0For the initial value of the iteration:
in the first case:
when the solution of the equation f (x) is in the interval x ∈ (0,1)]When f (x) is not changed, the degree of unevenness is determined byNewton's principle of iterative method, the initial value of iteration is x0E (0,1) can be solved;
in the second case:
when the solution of the equation f (x) is in the interval x ∈ [1, + ∞ ], as can be known from the formula (10), f (x) is convex when x ∈ [1,2 ]; x ∈ [2, + ∞ ], f (x) is concave, and f (x) has a unique inflection point x ═ 2 in the interval x ∈ [1, + ∞ ];
when the equation root is in x ∈ [1,2]]F (x) in the interval x ∈ [1,2]]The concave-convex property of the material is unchanged, and the initial value of iteration can be x according to the principle of a Newton iteration method0∈(1,2]Any number of (a), (b), (c) of fig. 2; if the initial value of iteration is x0∈(2,+∞]Any number of (2) cannot solve the equation solution;
let the root of f (x) be xkWhen the root of the equation is in x ∈ [2, + ∞ ∈]The initial value of iteration may be x0∈[2,xk]When the initial value of the iteration is x0E (1,2) or x0∈[xk,+∞]The root of the equation is not obtained.
5. The method of estimating the number of RFID tags for radio frequency identification according to claim 3, wherein the second frame length F is adjusted when the number of successful slots is 02＝F1And x 2, then estimating the number of the labels of the second frame, and so on until the proportion of the successful time slot to the total time slot is not 0.
6. The method of estimating the number of RFID tags for radio frequency identification according to claim 3, wherein the small-range adjustment of the estimation error: the relative error is defined as:
wherein the content of the first and second substances,
setting the number of estimated labels after adjustment for the estimated number of labels and n is the actual number of labels
Wherein the content of the first and second substances,
to adjust the estimated number of tags, a is an adjustment factor.
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