﻿ 基于LS_SVM的超宽带定位算法
 计算机系统应用  2018, Vol. 27 Issue (8): 237-240 PDF

Ultra-Wideband Location Algorithm Based on LS_SVM
CHENG Qi-Guo
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China
Foundation item: Joint Research Project on Joint Venture Capital of Jiangsu Province (BY2014023-31); Project for Six Kinds of Talents of Jiangsu Province (WLW_007)
Abstract: Designated to solve the problem of large positioning error caused by large ranging errors in the non-line-of-sight (UWB) environment, a tracking error based on Least Squares Support Vector Machine (LS_SVM) is proposed. The method divides the indoor area into several equal small areas, establishes the non-linear relationship between the eigenvalues of the sampled signals and the node locations in each area, classifies and regulates them by using LS_SVM. For non-line-of-sight distance measurement results, a smaller weight is given. Experimental results show that the error of K-Nearest Neighbors (K-NN) is improved by 10% within 7 cm, which shows that this algorithm can effectively improve the positioning accuracy.
Key words: UWB     location     support vector machine     error elimination

1 超宽带信号特征

 $h\left( t \right) = \sum\limits_{i = 1}^N {{a_i}p\left( {t - {\tau _i}} \right)} + n\left( t \right)$ (1)

(1)采样信号最大幅度: 在视距环境下, 接收机接收到的采样信号能量比较集中, 幅度最大值会在直达径分量周围, 与其他的分量比较, 幅度差异比较明显. 在非视距环境下, 接收机接收到的采样信号能量比较分散, 幅度跟视距环境下没有那么明显区别.

 $r = \max \left| {h\left( t \right)} \right|\;\;\;\;$ (2)

(2)采样信号均值

 $u = \frac{{\sum\limits_{i = 1}^N {h\left( {n{T_s}} \right)} }}{N}$ (3)

(3)采样信号方差

 ${\sigma ^2}{\rm{ = }}\frac{{\sum\limits_{i = 1}^N {{{\left( {h\left( {n{T_s}} \right) - u} \right)}^2}} }}{N}$ (4)

(4)能量: 随着测距的增加, 信号能量会逐渐衰减. 视距环境下, 接收到的采样信号能量大部分都集中在直达径附近, 非视距环境下, 信号能量没有那么集中.

 $E = {\int_T {\left| {h\left( t \right)} \right|} ^2}dt$ (5)

(5)峭度(kurtosis): 反映接收机接收到信号陡峭程度. 假如信号峭度越大说明信号波形陡峭, 有较大的峰值, 波形能量越集中, 说明直达径的分量是最强. 如果峭度较小说明直达分量比较弱, 直达分量受到较大的干扰.

 $k = \frac{{E\left[ {{{\left( {{{\left| {h\left( t \right)} \right|}^2} - {u_{\left| h \right|}}} \right)}^4}} \right]}}{{\sigma _{\left| h \right|}^4}}$ (6)

(6)超量时延(Mean Excess Delay, MED): 多径分量的时延扩展, 时延越大说明采样信号的多径分量比例比较大, 直达分量相比比较弱.

 ${\tau _{\rm{MED}}}{\rm{ = }}\frac{{\int_T {t{{\left| {h\left( t \right)} \right|}^2}dt} }}{{\int_T {{{\left| {h\left( t \right)} \right|}^2}dt} }}$ (7)

(7)均方根时延(Root Mean quare delay Spread, RMS): 描述一个信号的时延特性和时间色散程度的重要参数.

 ${\tau _{\rm{RMS}}}{\rm{ = }}\frac{{\int_T {{{\left( {T{\rm{ - }}{\tau _{\rm{MED}}}} \right)}^2}{{\left| {h\left( t \right)} \right|}^2}dt} }}{{\int_T {{{\left| {h\left( t \right)} \right|}^2}dt} }}$ (8)

(8)距离估计值 $\hat d$ : 测距误差与测距大小也有一定的关系.

 ${X} = \left[ {r,u,{\sigma ^2},k,{\tau _{\rm{RMS}}},{\tau _{\rm{MED}}},E,\hat d} \right]$ (9)
2 基于最小二乘支持向量机误差处理 2.1 非视距鉴别

 $y\left( x \right) = {W^{\rm T}}\varphi \left( x \right) + b$ (10)

 $\left\{ \begin{gathered} \begin{array}{*{20}{c}} {\arg }&{\begin{array}{*{20}{c}} {\mathop {\min }\limits_{w,b,e} }&{\frac{1}{2}} \end{array}} \end{array}{\left\| w \right\|^2} + \gamma \frac{1}{2}\sum\limits_{k = 1}^N {e_k^2} \\ \begin{array}{*{20}{c}} {\rm{s.t.}}&{{y_k} = \phi \left( {{x_i}} \right) \cdot w + b + {e_k},\forall k} \end{array} \\ \end{gathered} \right.$ (11)

 $L = \frac{1}{2}{\left\| w \right\|^2} + \frac{1}{2}\gamma \sum\limits_{k = 1}^N {e_k^2} - \sum\limits_{k = 1}^N {{\alpha _k}} \left( {\varphi \left( {{x_k}} \right) \cdot w + b + {e_k} - {y_k}} \right)$ (12)

 $\left\{ \begin{gathered} w = \sum\limits_{k = 1}^N {{\alpha _k}\left( {{\varphi _k}} \right)} \\ \sum\limits_{k = 1}^N {{\alpha _k}} = 0 \\ {\alpha _k} = \gamma {e_k} \\ w\varphi \left( {{x_k}} \right) + b + {e_k} - {y_k} = 0 \\ \end{gathered} \right.$ (13)

 $\left( {\begin{array}{*{20}{c}} 0&1& \ldots &1 \\ 1&{K\left( {{x_1},{x_1}} \right) + \frac{1}{\gamma }}& \ldots &{K\left( {{x_1},{x_k}} \right)} \\ \vdots & \vdots & \vdots & \vdots \\ 1&{K\left( {{x_k},{x_1}} \right)}& \ldots &{K\left( {{x_k},{x_k}} \right) + \frac{1}{\gamma }} \end{array}} \right) \cdot \left[ {\begin{array}{*{20}{c}} b \\ {{\alpha _1}} \\ {{\alpha _2}} \\ \begin{gathered} \vdots \\ {\alpha _k} \\ \end{gathered} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 0 \\ {{y_1}} \\ {{y_2}} \\ \vdots \\ {{y_k}} \end{array}} \right]$ (14)

 $y\left( x \right) = \sum\limits_{k = 1}^N {{\alpha _k}K\left( {x,{x_k}} \right)} + b$ (15)

2.2 误差处理

Step 1. 构建样本库: 记录接收机接收到的波形和测距误差.

Step 2. 提取特征值和真实误差: 提取采样信号中的波形畸变量 ${X}$ , 记录真实误差 ${y_i}$ 得到训练集 $T = \left\{ {\left( {{{X}_1},{y_1}} \right),\left( {{{X}_2},{y_2}} \right),\cdots,\left( {{{X}_N},{y_N}} \right)} \right\}$ .

Step 3. 选取合适的核函数: 在室内环境下, 选取的核函数为:

 $K\left( {x,{x_i}} \right) = \exp \left\{ {\frac{{ - \left\| {x - {x_i}} \right\|}}{{2{\sigma ^2}}}} \right\}$ (16)

Step 4. 样本预处理: 将采样点信号进行训练, 对非视距的信号测距结果赋予一个较小的权重.

Step 5. 测试样本: 将采样数据点的波形畸变量, 带入到回归器中, 得到回归误差. 然后以实际的误差减去回归器得到的误差, 即为消除的误差.

 图 1 LS_SVM误差消除

3 仿真与分析

 图 2 定位场景图

 图 3 不同特征鉴别率

 图 4 消除误差累计分布

4 结论

 图 5 不同信噪比定位误差

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