Twice Labels Number Estimation Algorithm Based on Gaussian Fitting and Chebyshev Inequality
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摘要: 针对射频识别技术(RFID)系统中现有标签数量估计算法存在的估计误差大、识别时延长、时间复杂度高的问题，该文提出一种基于高斯拟合与切比雪夫不等式的标签数量2次估计算法(TLNEGC)。首先根据碰撞因子与碰撞时隙比例的关系建立碰撞模型，采用高斯函数对碰撞模型中的离散数据点进行拟合逼近获得高斯估计模型；然后利用高斯估计模型初次估计标签的数量，根据初次估计的结果判断是否需要进行2次估计，2次估计是利用切比雪夫不等式对估计区间进行2次搜索以获得最佳估计值。MATLAB仿真分析表明，该文所提TLNEGC算法的平均估计误差和总时间消耗明显低于现有的高精度标签估计算法，同时具有较低的时间复杂度和较高的稳定性。Abstract: In order to solve the problems of large estimation error, prolonged identification and high time complexity, which exist in tag quantity estimation algorithm in Radio Frequency IDentification (RFID) system, The Twice Labels Number Estimation algorithm based on Gaussian fitting and Chebyshev inequality (TLNEGC) is proposed. Firstly, a collision model is established based on the relationship between the collision factor and the collision time slot ratio, and a Gaussian estimation model is obtained by fitting the Gaussian function to the discrete data points. Afterward, the Gaussian estimation model is used to initially estimate the number of labels, and then according to the results of the initial estimation, judge whether a second estimation is required. The second estimation is performed by using Chebyshev's inequality to search the estimation interval twice to obtain the best estimate. The MATLAB simulation analysis indicates that the average estimation error and total time consumption of the TLNEGC algorithm are significantly lower than those of existing high-precision label estimation algorithms, and it also has lower time complexity and higher stability.
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表 1 TLNEGC的算法流程
(1) Initialization $L$ (2) Read ${{ESC}}$ (3) $F \leftarrow C/L$ (4) $B \leftarrow {\rm{Gaussian}}(F)$ (5) ${N_{\rm{e}}} \leftarrow S{ + }B C$ (6) If $N_{\rm{e} } < L_{\rm{then} }$ (7) Output ${N_{\rm{e}}}$ (8) Else if (9) Initialization $L = {N_{\rm{e}}}$ (10) For $i$ from $0.94N$ to $1.06N$ (11) ${c_{\rm{e}}} \leftarrow L{(1 - 1/L)^{{{{N}}_{\rm{e}}}}}$ (12) ${c_{\rm{s}}} \leftarrow N{(1 - 1/L)^{{{{N}}_{\rm{e}}} - 1}}$ (13) ${c_{\rm{c}}} \leftarrow L - {c_{\rm{e}}} - {c_{\rm{s}}}$
(14) Output $D(L,{c}_{{\rm{e}}},{c}_{{\rm{s}}},\;{c}_{{\rm{c}}})\leftarrow \underset{\varDelta ;n}{{\rm{Arg}}\mathrm{min} }\left|[E,S,C]-\right.$
$\left.{c}_{{\rm{e}}},{c}_{{\rm{s}}},\;{c}_{{\rm{c}}} \right|$(15) End for (16) End if 
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