CN111178100B - Radio Frequency Identification (RFID) tag number estimation method - Google Patents
Radio Frequency Identification (RFID) tag number estimation method Download PDFInfo
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Abstract
The method for estimating the number of RFID tags of Radio Frequency Identification (RFID) belongs to the field of radio frequency identification, and aims at solving the problem of large error existing in the existing tag estimation scheme, firstly, determining an adjusting factor according to the number relation between the number of tags and the frame length; secondly, researching the proportion of successful time slots to total time slots in the label identification process, and obtaining the relation between the regulating factors and the proportion; and finally solving by utilizing a Newton iteration method to obtain the accurate label number. Simulation results show that the NIATE algorithm has better self-adaptive capacity and smaller average error of label estimation compared with the existing mainstream algorithm under the condition of different label numbers.
Description
Technical Field
The invention belongs to the field of radio frequency identification, and relates to a method for estimating the number of RFID tags of radio frequency identification.
Background
Radio Frequency Identification (RFID) technology is widely used in many fields such as warehouse management, logistics control, intelligent shelves, product tracking [1,2] Etc. The electronic tag has the advantages of small volume, low cost, easy processing and the like, and the number of the electronic tags is large in the application field. When two or more tags communicate with the reader at the same time, signals will interfere with each other, and a tag collision problem inevitably occurs, resulting in failure of reading information from 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, an Aloha protocol-based algorithm is widely adopted, and the algorithm is simple and low in use cost. Based on Aloha algorithm, literature [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 slots plays a key role in the tag identification performance, the number of the time slots is too large, the number of the idle time slots is too large, and too many collision time slots can occur if too few idle time slots are too small, and therefore, the determination of the frame length needs to estimate the actual number of the tags. The number of the labels which are rapidly and accurately identified can be used for setting the frame size of the optimal Aloha algorithm to accelerate the collection of the label ID information, can also be used for inventory monitoring, and is convenient for the management of goods [10] 。
Schoute [11] The number of tags is estimated based on the number of collision slots, and the number of tags in each collision slot is assumed to be a fixed value, and cannot be adjusted with the increase of the tag size, so that the estimation error increases with the increase of the number of tags. Vogt [12] Using maximum likelihood estimation methodsTo estimate the number of tags, the accuracy of tag estimation is improved at the cost of a frame length greater than the number of tags, the search process and calculation are too cumbersome, and little use has been made. 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, and the accuracy of label estimation is further improved, but if the range of the number of the labels is large, the problem of overlarge operand is also caused. Document [14]The method for estimating the number of the labels in the coarse and fine secondary mode is provided, whether the fine estimation is needed or not is determined according to an estimation standard obtained through analysis, the fine estimation adopts a maximum posterior probability algorithm based on priori knowledge, the number of the labels in the coarse estimation is used as a starting point value of the fine estimation, the searching range of the fine estimation is reduced by 90%, and the average estimation error is larger. Document [15]And [16 ]]Another tag estimation algorithm is provided, the number of tags is estimated by using a bayesian rule, the estimation accuracy is superior to that of a Vogt method, the method is similar to a maximum posterior probability method, but the calculation complexity is smaller than that of the method, the defect is that the requirement on the observed value of the bayesian estimation is larger, and a reader-writer only acquires information from one frame and cannot acquire enough observed results. Document [17]Based on the linear relation between the mean square Bayesian method and the lower limit value estimation method, the two methods are fused to provide the number of the estimated labels of the two algorithms, so that the method has higher estimation accuracy, but the two algorithms have different errors, which algorithm is selected under different conditions is not described, and the defect that the Bayesian estimation observation value has larger requirement is not solved yet. Document [18]The method is characterized in that a scheme for estimating the number of the tags is provided, the number of the tags can be accurately estimated by only analyzing the relation between the theory in one frame and the number of successful time slots in the actual situation and applying a secant iteration method, but an additional detection frame is required to be transmitted in the estimation process to remove a pseudo solution generated by tag estimation, so that the time overhead of a system and the complexity of algorithm estimation are increased, and in addition, when the frame length is smaller and the number of the tags cannot be estimated, a frame length adjustment scheme capable of estimating the number of the tags is not provided.
Disclosure of Invention
The invention provides the following technical scheme for solving the problems that the time cost and the algorithm estimation complexity of a system are increased because additional detection frames are required to be sent to remove the false solution generated by label estimation: according to the theory and the actual situation, the ratio of the successful time slot number in a frame in the total time slot is utilized to obtain an estimation model of the number of the tags by utilizing a Newton iteration method, and the number of the tags is estimated.
Further, when the Newton iteration method is used for calculation, according to the relation between the number of successful time slots and the number of actual successful time slots, proper iteration initial values are analyzed and selected, and the number of labels is estimated through limited iterations.
Further, the method for obtaining the estimation model of the label number by utilizing the Newton iteration method comprises the following steps: setting the frame length to F and assuming that the number of tags to be identified is n, each tag randomly generates a random number R i =m, i=1, 2..n as own communication slot, where m=0, 1., F-1;
the probability that each tag selects a certain time slot is 1/F, and the probability that r tags select the same time slot is:
where r takes a value of 0,1 or greater than 1, it is apparent that r=1 is the probability of a successful slot:
the expected value of the number of successful slots in a frame is:
the ratio of the number of successful time slots to the total number of time slots is:
assuming an initial frame length f=n/b, where b is an adjustment factor, bringing f=n/b into equation (4):
number of successful time slots N during tag identification s According to the statistics of the recognition result after one frame is finished, the proportion of the number of the successful time slots is assumed to be P SA Then:
ideally, after one frame identification is finished, the relation between the number of successful time slots in actual and theoretical conditions is as follows:then it is derived from equation (5) and equation (6):
as can be seen from equation (6), one frame identification ends, P SA 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 tags is determined by a formula (7):
and (3) making:
the estimation model according to the number of labels of the Newton iteration formula is expressed as:
further, the selection method of the iteration initial value is as follows: according to the relation between the number of labels and the frame length, it can be seen that x epsilon (0, ++ infinity]. From equation (7), it can be seen that f (x) falls within interval x ε (0, 1)]The number of the steps is increased monotonously, in interval x epsilon [1, + ] infinity]Monotonically decreasing in magnitude, so 0 < f (x) max ＝f(1)≈0.3679-P SA ＜0.3679，0＞f(x) min ＝f(∞)≈-P SA > -0.3678, so that f (x) is equal to x.epsilon.0, +.infinity]The number of solutions is 1 or 2;
obtaining a second derivative of f (x) in the formula (7):
f”(x)＝e -x (x-2) (11)
from equation (10), it can be seen that the pattern of f (x) is convex over the interval x e (0, 2); on the interval x e 2, ++ infinity, the pattern of f (x) is concave;
x is the interval where the equation root is located, x 0 For the initial iteration value:
first case:
when the solution of equation f (x) is within the interval xE (0, 1)]When f (x) is concave-convex, according to Newton iteration principle, the iteration initial value is x 0 Any number of e (0, 1) can be solved for the equation;
second case:
when the solution of equation f (x) is within the interval x e 1, + -infinity, as can be seen from equation (10), when x ε [1,2], f (x) is convex; when x is 2 and + -infinity, f (x) is concave, and f (x) has a unique inflection point x=2 in the interval x is 1 and + -infinity;
when the equation root is x epsilon 1,2]F (x) is within the interval x E [1,2]]The convexity of (a) is unchanged, and according to the principle of Newton's iterative method, the iterative initial value can be x 0 ∈(1,2]Any number of (a) as in fig. 2 (b), (c); if the iteration initial value is x 0 ∈(2,+∞]No equation solution can be found;
let the root of f (x) be x k When the root of the equation is x epsilon 2, ++ infinity]The iteration initial value may be x 0 ∈[2,x k ]When the iteration initial value is x 0 E (1, 2) or x 0 ∈[x k ,+∞]No root of the equation is available.
Further, when the number of the obtained successful time slots is 0, the first time slot is adjustedTwo frame length F 2 ＝F 1 X 2, then performing label number estimation of the second frame, and so on until the proportion of successful time slots to total time slots is not 0.
Further, small-range adjustment of estimation errors: the relative error is defined as:wherein (1)>For the estimated number of tags, n is the actual number of tags, let the adjusted estimated number of tags +.>Wherein (1)>For the number of tags estimated before adjustment, a is the adjustment factor.
The beneficial effects are that: the RFID label number estimation algorithm based on Newton iteration provided by the invention provides an automatic adjustment scheme for frame length required by label number estimation when the label number is different, solves the problem of larger time slot required by label number estimation, and realizes accurate label number estimation. Through experimental comparison analysis, the label estimation error is smaller, the total time slot number required when the label is identified is smaller, and the system throughput rate is higher. Thus, the algorithm presented herein improves the accuracy of the RFID system tag count estimation, and can be used for applications in different tag count environments.
Drawings
FIG. 1 is a flow chart of an Aloha protocol anti-collision algorithm for dynamic frame time slots
FIG. 2 different iteration initial values x 0 Effect of the results
Fig. 3 adjusts the relative error before and after adjustment (f=128)
Fig. 4 relative error (initial frame length f=64, 128, 256, respectively)
FIG. 5 total number of timeslots
FIG. 6 System throughput Rate
Detailed Description
The Aloha algorithm is a widely adopted radio frequency identification (Radio Frequency Identification, RFID) tag anti-collision algorithm, and to improve its 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 existing in the existing label estimation scheme, a label number estimation algorithm (NIATE) based on Newton iteration method is provided. Firstly, determining an adjusting factor according to the number relation between the number of labels and the frame length; secondly, researching the proportion of successful time slots to total time slots in the label identification process, and obtaining the relation between the regulating factors and the proportion; and finally solving by utilizing a Newton iteration method to obtain the accurate label number. Simulation results show that the NIATE algorithm has better self-adaptive capacity and smaller average error of label estimation under the condition of different label numbers compared with the existing mainstream algorithm, so that the total time slot number required by identifying all labels is reduced, and the throughput rate of the system is improved.
The invention provides a label number estimation scheme (NIATE) based on Newton iteration method. According to the optimal recognition rate under the theoretical condition proved by the literature [9], assuming the number relation between the number of labels and the frame length, analyzing a relation formula of the proportion of the number of successful time slots in one frame to the total time slots, and solving the obtained relation formula by using a Newton iteration method to obtain the estimated number of labels; based on analysis research on iterative initial value selection in the relation, the time cost and algorithm complexity consumed by pseudo-resolution are solved; according to the obtained distribution condition of the estimated label quantity, small-range adjustment is carried out on the estimated label quantity; meanwhile, for different numbers of labels, the invention provides a scheme for automatically adjusting the frame length. The simulation result shows that the number of tags estimated by the algorithm is smaller in error, the self-adaptive capacity of tag estimation is stronger, and when the estimated number of tags is used for tag identification, fewer total time slots are needed, and the throughput rate of the system is higher.
Aloha algorithm for 1 dynamic frame time slot
Referring to fig. 1, the dynamic frame slot Aloha anti-collision algorithm workflow in an rfid system. Wherein F is the frame length, N C N is the number of collision time slots S For successful slot number, SN is the labelAnd signing the selected communication time slot. The book is provided with
The invention counts the number of successful time slots through the algorithm shown in fig. 1 and is used for estimating the number of tags.
2 tag quantity estimation scheme
According to the invention, the estimated label number is calculated by Newton iteration method according to the duty ratio of the successful time slot number in a frame in the total time slot, and the number of empty time slots and collision time slots does not need to be calculated. In order to reduce the calculation complexity of the estimation algorithm, according to the relation between the number of successful time slots and the number of actual successful time slots under the theoretical condition, analyzing and selecting proper iteration initial values, and estimating the number of labels through limited iterations; in order to adapt the algorithm to the estimation of different label numbers, the algorithm provides a scheme for adjusting the initial frame length according to the successful time slot number; in order to further improve the accuracy of label estimation, small-range adjustment is performed on the initial estimated label quantity distribution condition.
2.1 Label 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 tag randomly generates a random number R i =m, (i=1, 2..n) as own communication slot, where m=0, 1..f-1.
Theoretically, the probability that each tag selects a certain time slot is 1/F, and the probability that r tags select the same time slot is:
wherein r is 0,1 or more than 1. Obviously r=1 is the probability of a successful slot:
thus, the expected value of the number of successful slots in a frame [19] The method comprises the following steps:
the frame length F, i.e. the number of slots is F, and equation (3) is an expected value of the number of successful slots, then the ratio of the number of successful slots to the total number of slots is:
assuming an initial frame length f=n/b, where b is an adjustment factor, it is possible to bring f=n/b into equation (4):
in practical application, when the tag is identified, the number N of successful time slots s Can be obtained according to the statistics of the recognition result after one frame is finished, and the ratio of the number of successful time slots is assumed to be P SA Then:
ideally, after one frame identification is finished, the relation between the number of successful time slots in actual and theoretical conditions is as follows: e [ P (F, n, 1)]＝N s . Then it is available from equation (5) and equation (6):
as can be seen from equation (6), one frame identification ends, P SA The adjustment factor b can be obtained by the ratio of the number of successful time slots to the frame length, and is determined by the formula (7), so that the estimated value of the number of tags is:
to facilitate the solution of the adjustment factor b in equation (7), let:
f(x)＝x·e -x -P SA ,x＞0 (9)
f(x)＝x·e -x -P SA when x is more than 0 (10), the highest system identification efficiency of 0.3679 can be obtained when the number of labels is equal to the selected frame length value, so P SA ∈[0,0.3679]。
The transcendental equation root-finding method generally comprises a dichotomy method, a secant method, a Newton iteration method and the like. The dichotomy solution is slow, the secant solution requires two initial points, and the solution is easy to generate pseudo solutions. The Newton iteration method has the second-order convergence property, the solving process is faster, and the actual engineering needs are met, so that the invention adopts the Newton iteration method to solve the overrunning equation (9).
Thus, an estimation model based on the number of labels of the newton's iterative formula can be expressed as:
it should be noted that, when the newton iteration method is used to calculate the adjustment factor b, the iteration initial value, the iteration number and the frame length value are all selected to affect the label number estimation. The iteration initial value is selected with obvious influence on the iteration result, the iteration initial value is not selected well, the result is possibly scattered or oscillated, and an accurate result cannot be obtained; the more the iteration times are, the smaller the label number estimation error is, however, the algorithm complexity is higher, and the algorithm time is prolonged; when the frame length value is selected to be too small and the number of tags is large, the number of successful time slots may be 0, and equation (9) cannot solve the number of tags. The constraints beyond the solution of equation (9) are analyzed in detail below.
2.2 selection of iteration initial values
According to the relation between the number of labels and the frame length, it can be seen that x epsilon (0, ++ infinity]. From equation (7), it can be seen that f (x) falls within interval x ε (0, 1)]The number of the steps is increased monotonously, in interval x epsilon [1, + ] infinity]Monotonically decreasing in magnitude, so 0 < f (x) max ＝f(1)≈0.3679-P SA ＜0.3679，0＞f(x) min ＝f(∞)≈-P SA > -0.3678, so that f (x) is equal to x.epsilon.0, +.infinity]The number of solutions is 1 or 2.
Obtaining a second derivative of f (x) in the formula (7):
f”(x)＝e -x (x-2) (12)
from equation (10), it can be seen that the pattern of f (x) is convex over the interval x e (0, 2); on the interval x e 2, ++ infinity, the pattern of f (x) is concave.
FIG. 2 is a graph showing the influence of different iteration initial values on the equation root when solving the equation root by Newton's iteration method, wherein x is the interval in which the equation root is located, and x 0 Is an iteration initial value.
First case:
when the solution of equation f (x) is within the interval xE (0, 1)]When f (x) is concave-convex, according to Newton iteration principle, the iteration initial value is x 0 Any number of e (0, 1) can be used to solve the equation. As shown in fig. 2 (a).
Second case:
when the solution of equation f (x) is within the interval x e 1, + -infinity, as can be seen from formula (10), when x ε [1,2], f (x) is convex; x.epsilon.2, +.infinity ], f (x) is concave. And f (x) has a unique inflection point x=2 in the interval x e 1, + -infinity.
When the equation root is x epsilon 1,2]F (x) is within the interval x E [1,2]]The convexity of (a) is unchanged, and according to the principle of Newton's iterative method, the iterative initial value can be x 0 ∈(1,2]Any number of (a) as in (b), (c) of fig. 2; if the iteration initial value is x 0 ∈(2,+∞]No equation solution can be found, as shown in fig. 2 (d).
Similarly, assume that the root of f (x) is x k When the root of the equation is x epsilon 2, ++ infinity]The iteration initial value may be x 0 ∈[2,x k ]As shown in fig. 2 (e); when the iteration initial value is x 0 E (1, 2) or x 0 ∈[x k ,+∞]No root of the equation is obtained, as shown in fig. 2 (f) and (g).
The key point of the algorithm is to determine the iteration initial value x 0 From the above analysis, the iteration initial value is selected as any value less than 1 or 2. The number of successful slots generated in the theoretical case is shown in formula 3, and increases with the increase of the frame length. The number of actually generated successful time slots is N S When E [ P (F, n, 1)]＞N S At the time, the initial frame length is largeSelecting iteration initial value x from the number of labels 0 =2; when E [ P (F, n, 1)]＜N S When the initial frame length is smaller than the label number, the iteration initial value is selected to be any number smaller than 1, and the invention selects x 0 ＝0.5。
2.3 iteration number and error analysis
In view of algorithm simplicity, the present invention uses |n k -n k-1 And (3) controlling iteration accuracy, namely controlling the error of the label number obtained by two iterations to be smaller than 1, setting the upper limit of iteration to be 10, and observing the relation between the estimated error and the iteration number as shown in table 1. As can be seen from table 1, the number of tags estimation accuracy requirement can be completely satisfied by using the newton iteration method for 10 iterations.
TABLE 1 iteration number and error analysis
2.4 tag number and frame size relationship
According to the formula (7), when the proportion of the successful time slot to the total time slot is 0, the selected frame length 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 F 1 When the number of labels n=870 is=128, the ratio of successful time slots to total time slots is 0, and newton's iteration method cannot be used to estimate the number of labels.
Based on the above analysis, when the number of successful slots is 0, the second frame length F is adjusted 2 ＝F 1 X 2, then performing label number estimation of the second frame, and so on until the proportion of successful time slots to total time slots is not 0. Table 2 is the frame length and maximum number of label estimatable range.
Table 2 frame length and range of number of tags that can be estimated
2.5 small-Range adjustment of estimation errors
In the invention, a widely-seen intelligent storage environment with passive tags is taken as an example, in practical application, storage shelves are 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 (1)>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 labels and the label estimation algorithm of the present invention when the frame length f=128. A small adjustment to the estimated tag number of fig. 3 (a) can be made to more closely approximate the actual tag number.
Estimating the number of tags after setting adjustmentWherein (1)>For the number of tags estimated before adjustment, a is an adjustment factor, and the relationship between the number of tags and the adjustment factor is shown in table 3. The relationship between the number of labels after adjustment and the relative error in fig. 3 (b) is obviously improved, and the stability and accuracy of the label number estimation after adjustment are obviously improved. The error pair before and after parameter adjustment is shown in table 4, and taking f=128 as an example, the maximum relative error and the average error after adjustment are reduced by 66.2% and 74%, respectively.
TABLE 3 relationship between the number of tags and the adjustment factor
Table 4 comparison of errors before and after parameter adjustment
3 simulation results
In order to verify the performance of the label number estimation algorithm provided by the invention, the invention utilizes MATLAB simulation software to compare Schoute [11], vogt [12], ding [14], cooperating [17], SIADA [18] algorithm and the estimation algorithm (NIATE) provided by the invention in a simulation experiment manner from three aspects of estimation errors, total time slot number required by label identification and system throughput rate, the number of label samples is 2000 at maximum, 50 is taken as an interval, and 50 simulation result averages are measured for each sample number.
3.1 error Performance comparison
Tag quantity estimation accuracy is the most important performance indicator. FIG. 4 is a graph showing the relationship between the number of estimated labels and the relative error when selecting different initial frame lengths.
The estimation error of Schoute and Vogt algorithms is significantly higher than the other four estimation algorithms because it does not take into account the effect of frame length on the estimation results. 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 Coopertive algorithm has larger estimation error and is not suitable for the estimation of the small number of tag environments. The estimation accuracy of the SIADA algorithm is obviously influenced by the frame length, and when a large frame length F=256 is selected, the estimation accuracy of the label within 1200 can be ensured only. The algorithm fully considers the influence of the frame length in the label estimation process, gives an adjustment scheme, has smaller estimation errors in different frame lengths, and reduces the average estimation errors by 63% and 60% respectively compared with Cooperating and SIADA algorithms within a certain estimation error label quantity range.
3.2 total number of timeslots
Fig. 5 shows the relationship between the total number of time slots required for identifying a tag and the number of tags. As is evident from fig. 5, the algorithm and the Cooperative algorithm provided by the present invention are significantly better than the other algorithms by selecting the initial frame length f=128. The SIADA algorithm requires a large number of slots when estimating the number of tags because additional transmission of a sounding frame is required for the spurious resolution. The Cooperative algorithm can realize the label number estimation with only a small frame length, and the total time slot number is less than that of other algorithms. When the initial frame length is selected to be smaller and the number of labels is larger, the algorithm needs to adjust the frame length to re-estimate the number of labels, and the number of time slots required for estimating the labels may be larger, but the accuracy of estimating the number of labels ensures that the frame length selection when identifying the labels is closer to the number of actual labels, and the total time slot number is reduced by 24% compared with the total time slot number of the SIADA algorithm.
3.3 System throughput Rate
In an ideal state, the number of tags is known, and a system throughput rate calculation formula is as follows:wherein N is S For the number of successful slots, T is the total number of slots used to identify all tags, and when f=n (frame length equals the number of tags), the system is most efficient [9] 36.79%. However, when a label estimation algorithm is added, the throughput rate calculation formula is as follows: />F Initial initiation The total number of slots needed to estimate the number of tags and there is an error in the tag number estimation, so the actual system throughput is below 36.79%.
Fig. 6 is a graph of system throughput versus number of tags. And an initial frame length F=128, vogt and Schoute algorithm is selected, the label estimation error is larger, and the system throughput rate is lower. The SIADA algorithm requires a large number of time slots when estimating the number of tags, and the system throughput rate is low. The number of labels can be estimated by the Coopertive algorithm in one frame, the throughput rate of the system is high, but when the number of labels is smaller than 300 and larger than 1500, the accuracy of label estimation is reduced, and the throughput rate of the system is reduced. In the algorithm of the invention, the number of the most estimated labels is 862 when the initial frame length is 128; when the number of the labels is larger than 862, the number of the estimated labels needs to be adjusted, and the number of time slots of the estimated labels increases, so that the throughput rate of the system is reduced, but the accuracy of the estimated number of the labels is higher, the throughput rate of the system can still be kept above 32%, and is improved by 33% compared with the throughput rate of a SIADA algorithm system.
Conclusion 4
The RFID label number estimation algorithm based on Newton iteration provided by the invention provides an automatic adjustment scheme for frame length required by label number estimation when the label number is different, solves the problem of larger time slot required by label number estimation, and realizes accurate label number estimation. Through experimental comparison analysis, the label estimation error is smaller, the total time slot number required when the label is identified is smaller, and the system throughput rate is higher. Therefore, the algorithm provided by the invention improves the accuracy of the label number estimation of the RFID system, and can be used for the application of different label environments.
Reference is made to:
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Claims (5)
1. The radio frequency identification RFID label number estimation method is characterized in that according to the theoretical and actual conditions, the ratio of the successful time slot number in a frame to the total time slot is utilized to obtain an estimation model of the label number by utilizing a Newton iteration method, and the label number is estimated;
the method for obtaining the estimation model of the label number by utilizing the Newton iteration method comprises the following steps: setting the frame length to F and assuming that the number of tags to be identified is n, each tag randomly generates a random number R i =m, i=1, 2..n as own communication slot, where m=0, 1., F-1;
the probability that each tag selects a certain time slot is 1/F, and the probability that r tags select the same time slot is:
where r takes a value of 0,1 or greater than 1, it is apparent that r=1 is the probability of a successful slot:
the expected value of the number of successful slots in a frame is:
the ratio of the number of successful time slots to the total number of time slots is:
assuming an initial frame length f=n/b, where b is an adjustment factor, bringing f=n/b into equation (4):
number of successful time slots N during tag identification s According to the statistics of the recognition result after one frame is finished, the proportion of the number of the successful time slots is assumed to be P SA Then:
ideally, after one frame identification is finished, the relation between the number of successful time slots in actual and theoretical conditions is as follows: e [ P (F, n, 1)]＝N s Then the formula (5) and the formula (6) are used for obtaining:
as can be seen from equation (6), one frame identification ends, P SA 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 tags is determined by a formula (7):
and (3) making:
f(x)＝x·e -x -P SA ,x＞0 (9)
the estimation model according to the number of labels of the Newton iteration formula is expressed as:
2. the method for estimating the number of RFID tags according to claim 1, wherein the number of tags is estimated by analyzing and selecting an appropriate iteration initial value according to the relation between the number of successful time slots and the number of actual successful time slots and by performing a limited number of iterations when the number of RFID tags is calculated by Newton iteration.
3. The method for estimating the number of RFID tags for radio frequency identification according to claim 1, wherein the method for selecting the iteration initial value is: according to the relation between the number of labels and the frame length, it can be seen that x epsilon (0, ++ infinity]. From equation (7), it can be seen that f (x) falls within interval x ε (0, 1)]The number of the steps is increased monotonously, in interval x epsilon [1, + ] infinity]Monotonically decreasing in magnitude, so 0 < f (x) max ＝f(1)≈0.3679-P SA ＜0.3679，0＞f(x) min ＝f(∞)≈-P SA > -0.3678, so that f (x) is equal to x.epsilon.0, +.infinity]The number of solutions is 1 or 2;
obtaining a second derivative of f (x) in the formula (7):
f”(x)＝e -x (x-2) (11)
from equation (10), it can be seen that the pattern of f (x) is convex over the interval x e (0, 2); on the interval x e 2, ++ infinity, the pattern of f (x) is concave;
x is the interval where the equation root is located, x 0 For the initial iteration value:
first case:
when the solution of equation f (x) is within the interval xE (0, 1)]When f (x) is concave-convex, according to Newton iteration principle, the iteration initial value isx 0 Any number of e (0, 1) can be solved for the equation;
second case:
when the solution of equation f (x) is within the interval x e 1, + -infinity, as can be seen from equation (10), when x ε [1,2], f (x) is convex; when x is 2 and + -infinity, f (x) is concave, and f (x) has a unique inflection point x=2 in the interval x is 1 and + -infinity;
when the equation root is x epsilon 1,2]F (x) is within the interval x E [1,2]]The convexity of (a) is unchanged, and according to the principle of Newton's iterative method, the iterative initial value can be x 0 ∈(1,2]Any number of (2); if the iteration initial value is x 0 ∈(2,+∞]No equation solution can be found;
let the root of f (x) be x k When the root of the equation is x epsilon 2, ++ infinity]The iteration initial value may be x 0 ∈[2,x k ]When the iteration initial value is x 0 E (1, 2) or x 0 ∈[x k ,+∞]No root of the equation is available.
4. The method of estimating the number of RFID tags for radio frequency identification according to claim 1, wherein the second frame length F is adjusted when the number of successful slots is 0 2 ＝F 1 X 2, then estimating the number of tags of the second frame, and so on until the proportion of the successful time slot to the total time slot is not 0; wherein F is 1 Is the initial frame length.
5. The method of estimating the number of RFID tags for radio frequency identification according to claim 1, wherein the small range of estimation errors is adjusted: the relative error is defined as:wherein (1)>For the estimated number of tags, n is the actual number of tags, let the adjusted estimated number of tags +.>Wherein (1)>For the number of tags estimated before adjustment, a is the adjustment factor.
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