Research on Non-Line-Of-Sight Recognition Method Based on Weighted K-Nearest Neighbor Classification
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摘要: 超宽带(UWB)定位系统中，针对复杂的环境下，信号的遮挡、直达信号的错误判断严重影响定位精度问题，该文基于信道冲激响应(CIR)提出一种新型特征参量——饱和度(S)，结合前人提出的特征参量利用Relief算法和互信息特征选择(MIFS)算法进行特征选择，在相关性的基础上赋予特征相应的权重，选择最优的特征子集进行加权K-近邻(WKNN)分类，提高了非视距(NLOS)识别系统准确度。并且分析了WKNN算法中的训练数据集数量与近邻数K对算法的影响，确定优选方案，减小了算法计算量，提高了NLOS识别系统实时性。在不同环境下进行实验验证，结果表明，该方法具备较高的识别准确度和环境适用性，识别精度达到95%。Abstract: In the Ultra-WideBand (UWB) positioning system, the signal occlusion and the misjudgment of the direct signal affect seriously the positioning accuracy in complex environment. To solve this problem, Saturation (S) is proposed, which is a new characteristic parameter based on Channel Impulse Response (CIR). In this study, the Relief algorithm and the Mutual Information Feature Selection (MIFS) algorithm are used for feature selection combined with feature parameters proposed by researchers. Based on the correlation of the parameters, the optimal feature subset with corresponding weights is used for weighted K-nearest neighbor classification, which improves the accuracy of the Non-Line-Of-Sight (NLOS) recognition system. The influence of the number of training dataset and the value of K on the Weighted K-Nearest Neighbor (WKNN) algorithm is analyzed. An optimization scheme is proposed to reduce the amount of calculation and improve the real-time performance of the NLOS recognition system. The experimental results in different environments show that the method has high recognition accuracy and wide applicability, and the recognition accuracy reaches 95%.
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表 1 各特征参量的数学模型
特征参量 数学模型 峭度 (kurtosis, $ k $) $k = \dfrac{ {{\rm{E}}\left\{ { { {\left[ {\left| {h\left( t \right)} \right| - {\mu _{\left| h \right|} } } \right]}^4} } \right\} } }{ {{\rm{E}}{ {\left\{ { { {\left[ {\left| {h\left( t \right)} \right| - {\mu _{\left| h \right|} } } \right]}^2} } \right\} }^2} } } = \dfrac{ {{\rm{E}}\left\{ { { {\left[ {\left| {h\left( t \right)} \right| - {\mu _{\left| h \right|} } } \right]}^4} } \right\} } }{ {\sigma _{\left| h \right|}^4} }$ 偏度 (skewness, $ {\text{ske}} $) ${\text{ske = } }\dfrac{ {{\rm{E}}\left[ { { {\left( {\left| {h\left( t \right)} \right| - {\mu _{\left| h \right|} } } \right)}^3} } \right]} }{ {\sigma _{\left| h \right|}^3} }$ 最大振幅 (maximum amplitude, $ {r_{\max }} $) $ {r_{{\text{max}}}} = \max \left\{ {\left| {r\left( {{t_i}} \right)} \right|} \right\} $ 总能量 (total energy, $ \varepsilon $) $ \varepsilon = {\displaystyle\sum\limits_{i = 1}^N {\left| {r\left( {{t_i}} \right)} \right|} ^2} $ 上升时间 (rise time, $ {t_{\rm{rise}}} $) $\begin{gathered}{t_{ {\text{rise} } } } = {t_{ {\text{stop} } } } - {t_{ {\text{start} } } } \\ \left\{ {\begin{array}{*{20}{c} }{ {t_{ {\text{start} } } } = \min \left\{ { {t_i}:\left| {r\left( { {t_i} } \right)} \right| \ge 0.1{r_{\max } } } \right\} } \\ { {t_{ {\text{stop} } } } = \min \left\{ { {t_i}:\left| {r\left( { {t_i} } \right)} \right| \ge 0.9{r_{\max } } } \right\} } \end{array} } \right. \\ \end{gathered}$ 平均附加时延 (mean excess delay, $ {\tau _{{\text{med}}}} $) $ {\tau _{{\text{med}}}} = \dfrac{1}{\varepsilon }\displaystyle\sum\limits_{i = 1}^N {\left( {{t_i}{{\left| {r\left( {{t_i}} \right)} \right|}^2}} \right)} $ 均方根延迟传播 (root-mean-squre delay spread, $ {\tau _{{\text{rms}}}} $) $ {\tau _{{\text{rms}}}} = \dfrac{1}{\varepsilon }\displaystyle\sum\limits_{i = 1}^N {\left[ {{{\left( {{t_i} - {\tau _{{\text{med}}}}} \right)}^2}{{\left| {r\left( {{t_i}} \right)} \right|}^2}} \right]} $ 
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表 2 各参量与分类标签的相关性
特征参量 $ {\text{ske}} $ $ k $ $ {r_{\max }} $ $ \varepsilon $ 权值 0.1607 0.2537 17.2957 1.9692 特征参量 $ {t_{{\text{rise}}}} $ $ {\tau _{{\text{med}}}} $ $ {\tau _{{\text{rms}}}} $ $ S $ 权值 26.3062 13.0316 1.8136 34.2643
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表 3 两特征参量之间的冗余度
$ {t_{{\text{rise}}}} $ $ {\tau _{{\text{med}}}} $ $ {r_{\max }} $ $ S $ $ {t_{{\text{rise}}}} $ 1 $ {\tau _{{\text{med}}}} $ 0.4932 1 $ {r_{\max }} $ 0.4774 0.8345 1 $ S $ 0.6050 0.7305 0.7223 1
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表 5 单一参量在不同信道(CM)下的识别精度
CM1 CM2 CM3 CM4 CM5 CM6 $ k $ 0.5717 0.8917 0.8567 0.8750 0.5950 0.6417 $ {\text{ske}} $ 0.5450 0.5983 0.6900 0.6867 0.5517 0.5400 $ {r_{\max }} $ 0.8083 0.8583 0.9583 0.8150 0.9733 0.9450 $ \varepsilon $ 0.8983 0.8167 0.9550 0.8167 0.9967 0.8867 $ {t_{{\text{rise}}}} $ 0.9267 0.9217 0.9067 0.6933 0.6617 0.7333 $ {\tau _{{\text{med}}}} $ 0.8817 0.9250 0.9800 0.7983 0.9000 0.8967 $ {\tau _{\rm{rms} }} $ 0.5667 0.9083 0.5900 0.7867 0.7200 0.8167 $ S $ 0.9133 0.9267 0.9067 0.6967 0.6827 0.7467
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表 6 多参量对不同信道(CM)的识别精度
CM1 CM2 CM3 CM4 CM5 CM6 $ {r_{{\text{max}}}} + {t_{{\text{rise}}}} $ 0.9675 0.9225 0.9825 0.9825 0.9550 0.9500 $ {t_{{\text{rise}}}} + S $ 0.9125 0.9250 0.9000 0.9325 0.6475 0.6875 $ k + {\tau _{{\text{rms}}}} $ 0.4925 0.7750 0.7925 0.7625 0.7550 0.7975 $ {\tau _{{\text{med}}}} + {\tau _{{\text{rms}}}} $ 0.8775 0.9125 0.9525 0.9475 0.9100 0.7500 $ {\text{ske}} + k + {\tau _{{\text{med}}}} $ 0.6775 0.7575 0.7800 0.7750 0.9225 0.8200 $ {\text{ske}} + k + {t_{{\text{rise}}}} $ 0.8900 0.8600 0.8750 0.4925 0.8025 0.7900 $ k + {\tau _{{\text{med}}}} + {\tau _{{\text{rms}}}} $ 0.8450 0.8875 0.9300 0.9325 0.8500 0.7375 $ {r_{{\text{max}}}} + {t_{{\text{rise}}}} + {\tau _{{\text{med}}}} $ 0.9400 0.9375 0.9775 0.9775 0.9575 0.9525 $ {{\boldsymbol{r}}_{{\bf{max}}}} + {{\boldsymbol{t}}_{{\bf{rise}}}} + {\boldsymbol{S}} $ 0.9725 0.9525 0.9875 0.9825 0.9675 0.9600 $ {r_{{\text{max}}}} + {t_{{\text{rise}}}} + k $ 0.7950 0.8525 0.8050 0.9750 0.8025 0.7600 $ {t_{{\text{rise}}}} + {\tau _{{\text{med}}}} + S $ 0.9275 0.9575 0.9700 0.9725 0.8825 0.7625 $ {t_{{\text{rise}}}} + \varepsilon + {\tau _{{\text{med}}}} $ 0.9300 0.9325 0.9825 0.9725 0.9625 0.9525 $ \varepsilon + {\tau _{{\text{rms}}}} + {\tau _{{\text{med}}}} $ 0.9025 0.9200 0.9725 0.9675 0.9800 0.8925
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