-
随着卫星导航、移动互联网及人工智能技术的发展,室内外一体化应急定位服务的需求增长非常迅猛。特别是在浓烟、浓雾、高粉尘、断电、通信中断、无定位网络覆盖的复杂室内环境下,如何能快速地对救援者、被救者以及救援设备进行精确定位,为现场勘察和指挥决策服务成为研究的重点和难点。近年来,国内外很多学者尝试利用“声、光、电、磁、力”等基本物理场特性进行探测来获得与室内位置相关的参量[1-5],但是受室内空间环境、信号种类及传感器性能等因素影响,已有的各种单信号源、单传感器源、组合导航、融合定位方法在定位精度、稳定性、可靠性、快速性等方面还不够完善,无法满足室内应急定位需要。不受恶劣环境影响、能快速部署、覆盖范围广、自主可靠、高精度定位、多系统融合、室内外一体化等是室内应急定位亟需解决的一些关键问题。以无线高精度实时定位确定的位置作为控制校准点,结合微惯导的短时高精度组成“微惯导+”的融合定位方法比视觉、激光雷达等更适合应急定位场景,其中基于无线信号的高精度应急定位技术是研究重点之一。
无线室内定位按照其测量的电信号参量种类可分为幅度式、相位式、频率式和时间式, 按照信号参量量测方法又可分为:(1)接收信号强度(received signal strength, RSS)/信道状态信息(channel state information, CSI)的指纹特征匹配测量法;(2)信号到达时间(time of arrive, TOA)/时间差(time difference of arrive, TDOA)/飞行时间(time of flight, TOF)的时间距离测量法;(3)到达角(angle of arrive, AOA)/到达方向(direction of arrive, DOA)的角度测量法。其中,(1)因需要预先布设定位设备、先验指纹信息、定位精度不高等原因无法满足室内高精度应急定位需求,(2)可以实现高精度定位,目前的时分码分正交频分复用(time code division-orthogonal frequency division multiplexing, TC- OFDM)[5]、超宽带[6](ultra wide band, UWB)、伪卫星[7-8]、WiFi单基站多天线[9]以及谷歌的WiFiRttScan[10]等无线测时间距离的方法都可以获得较高定位精度,但是TOA/TDOA/TOF定位法需要预先布设多个位置准确已知的基站才能定位,且基站间时间同步精度要求高,无法满足快速应急定位需要。
无线电测角可以实现高精度定位。采用天线阵列超分辨角度估计方法[11]可以精确估计飞机等运动体的方位角、俯仰角信息。现有方法[12-18]中用于测角的阵列天线可以采用线阵和面阵。基于WiFi基站的多天线通常是线阵并且需要同时进行测角和测距,难以达到真正的高精度广覆盖;采用面阵的测角系统需要多通道信号同步采集,硬件成本高,运算量大,还存在多个接收通道之间幅相不一致等问题,严重影响实时定位精度。有学者提出了利用极化敏感阵列并通过射频开关切换单通道轮采阵列天线的方法[19-21],获得了较好的测角精度,成本代价较低, 但受频率同步误差、信源信号相位等因素影响,单通道轮采方法定位精度较低。
本文提出了一种适合应急场景使用的单基站双通道阵列天线测角定位方法,单基站即可定位,适合应急快速部署,并且能对蓝牙及WiFi等多种同频段信号同时进行探测和定位。它采用单通道开关切换轮采双极化天线阵,外加比对天线的双通道比相方法进行测角定位。首先构建了双通道比对天线的回波信号模型,然后在此基础上给出了角度和极化解耦的超分辨估计算法,降低了目标角度估计的计算量。
-
图 1给出了双通道轮采天线的阵列示意图,其中中间天线9作为比对天线接一路接收通道,周围6对正交极化天线共12个阵元作为轮采天线接另一路接收通道。图 2给出了阵列天线观测示意图,假定入射信号波形为为s (t),载频为f0, 波长为λ,入射俯仰角为θ,方位角为ϕ,采用均匀正交双极化阵元加中间比对天线构成的圆阵天线对入射信号进行接收,轮采天线的切换时间间隔为T,那么轮采天线和比对天线的接收回波信号可以表示为:
$$ {x_n}\left( t \right) = b{p_n}\left( {\theta , \phi , \gamma , \eta } \right)s\left[ {t + \left( {n - 1} \right)T - {\tau _n}\left( {\theta , \phi } \right)} \right]{{\rm{e}}^{{\rm{j}}2{\rm{ \mathit{ π} }}\left( {{f_0} + {f_d}} \right)\left[ {t + \left( {n - 1} \right)T - {\tau _n}\left( {\theta , \phi } \right)} \right]}} $$ (1) $$ {x_{n0}}\left( t \right) = b{p_0}\left( {\theta , \phi , \gamma , \eta } \right)s\left[ {t + \left( {n - 1} \right)T - {\tau _0}\left( {\theta , \phi } \right)} \right]{{\rm{e}}^{{\rm{j}}2{\rm{ \mathit{ π} }}\left( {{f_0} + {f_d}} \right)\left[ {t + \left( {n - 1} \right)T - {\tau _0}\left( {\theta , \phi } \right)} \right]}} $$ (2) 式中,xn (t)为第n个轮采天线接收回波信号;xn0 (t)为比对天线接收回波信号;b表示与信源发射功率、距离等因素有关的分量;pn (θ,ϕ,γ,η)表示第n个轮采天线与极化有关的分量,γ和η为两个极化参数;τn (θ,ϕ)表示信号到第n个阵元的时间延迟;fd为信源多谱勒频率。
需要说明的是T的选取有一定的条件,它需要满足信号帧时间结束时所有轮采天线至少要遍历一遍。在这个条件约束下,T需要满足$T \le \frac{{{T_0}}}{{12}} $,其中T0为信号帧时间。为了让每个轮采天线对应的采样数尽量相同,T越小越好,最小的T为$T = \frac{1}{{{f_s}}} $,其中fs为采样率。虽然信源速度会带来多谱勒频率,而多谱勒频率会导致不同轮采天线的相位变化,但由于本文采用的是双通道轮采天线,由多谱勒频率引起的轮采天线相位变化可以通过干涉去除,因此T的选择不用考虑信源速度的影响。
对于均匀正交双极化圆阵天线,第n个阵元的极化矢量hn为:
$$ {\mathit{\boldsymbol{h}}_n} = \left\{ {\begin{array}{*{20}{l}} {{{\left[ {{\rm{cos}}\frac{{2{\rm{ }}\pi }}{N}\left( {\frac{{n + 1}}{2} - 1} \right) - {\rm{sin}}\frac{{2{\rm{ }}\pi }}{N}\left( {\frac{{n + 1}}{2} - 1} \right)} \right]}^{\rm{T}}},n为奇数}\\ {{{\left[ {{\rm{sin}}\frac{{2{\rm{ }}\pi }}{N}\left( {\frac{n}{2} - 1} \right){\rm{cos}}\frac{{2{\rm{ }}\pi }}{N}\left( {\frac{n}{2} - 1} \right)} \right]}^{\rm{T}}},n为偶数} \end{array}} \right. $$ (3) 式中,N为阵元数。而且来波电场矢量为:
$$ \mathit{\boldsymbol{e}}\left( {\theta ,\phi ,\gamma ,\eta } \right) = \left[ {\begin{array}{*{20}{c}} { - {\rm{sin}}\phi }&{{\rm{cos}}\phi {\rm{cos}}\theta }\\ {{\rm{cos}}\phi }&{{\rm{sin}}\phi {\rm{cos}}\theta } \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{\rm{cos}}\gamma }\\ {{\rm{sin}}\gamma {{\rm{e}}^{j\eta }}} \end{array}} \right] $$ (4) 那么第n个阵元的极化分量为:
$$ \begin{array}{*{20}{l}} {{p_n}\left( {\theta ,\phi ,\gamma ,\eta } \right) = \mathit{\boldsymbol{h}}_n^{\rm{T}}\mathit{\boldsymbol{e}}\left( {\theta ,\phi ,\gamma ,\eta } \right) = }\\ {\mathit{\boldsymbol{p}}_n^{\rm{T}}\left( {\theta ,\phi } \right)\left[ {\begin{array}{*{20}{c}} {{\rm{cos}}\gamma }\\ {{\rm{sin}}\gamma {{\rm{e}}^{j\eta }}} \end{array}} \right]} \end{array} $$ (5) 其中,pn (θ,ϕ)为第n个阵元的极化矢量,而且
$$ \mathit{\boldsymbol{p}}_n^{}\left( {\theta , \phi } \right) = \left\{ {\begin{array}{*{20}{l}} {{{\left[ {\begin{array}{*{20}{c}} { - {\rm{sin}}\phi }&{{\rm{cos}}\phi {\rm{cos}}\theta }\\ {{\rm{cos}}\phi }&{{\rm{sin}}\phi {\rm{cos}}\theta } \end{array}} \right]}^{\rm{{\rm T}}}}{{\left[ {\begin{array}{*{20}{c}} {{\rm{cos}}\frac{{2{\rm{ \mathit{ π} }}}}{N}\left( {\frac{{n + 1}}{2} - 1} \right)}&{ - {\rm{sin}}\frac{{2{\rm{ \mathit{ π} }}}}{N}\left( {\frac{{n + 1}}{2} - 1} \right)} \end{array}} \right]}^{\rm{{\rm T}}}}, n为奇数}\\ {{{\left[ {\begin{array}{*{20}{c}} { - {\rm{sin}}\phi }&{{\rm{cos}}\phi {\rm{cos}}\theta }\\ {{\rm{cos}}\phi }&{{\rm{sin}}\phi {\rm{cos}}\theta } \end{array}} \right]}^{\rm{{\rm T}}}}{{\left[ {\begin{array}{*{20}{c}} {{\rm{sin}}\frac{{2{\rm{ \mathit{ π} }}}}{N}\left( {\frac{n}{2} - 1} \right)}&{{\rm{cos}}\frac{{2{\rm{ \mathit{ π} }}}}{N}\left( {\frac{n}{2} - 1} \right)} \end{array}} \right]}^{\rm{{\rm T}}}}, n为偶数} \end{array}} \right. $$ 经过混频处理后,回波信号可以表示成:
$$ \begin{array}{*{20}{l}} {{x_n}\left( t \right) = {x_n}\left( t \right){{\rm{e}}^{\left( { - {\rm{j}}2{\rm{ \mathit{ π} }}{{\bar f}_0}\left( {t + \left( {n - 1} \right)T} \right)} \right)}} = }\\ {{\rm{}}b{p_n}\left( {\theta , \phi , \gamma , \eta } \right)s\left[ {t + \left( {n - 1} \right)T - {\tau _n}\left( {\theta , \phi } \right)} \right] \cdot }\\ {{\rm{}}{{\rm{e}}^{ - {\rm{j}}2{\rm{ \mathit{ π} }}{f_0}{\tau _n}\left( {\theta , \phi } \right)}}{{\rm{e}}^{{\rm{j}}2{\rm{ \mathit{ π} }}\left( {{f_{\rm{\Delta }}} + {f_d}} \right)\left[ {t + \left( {n - 1} \right)T - {\tau _n}\left( {\theta , \phi } \right)} \right]}}} \end{array} $$ (6) $$ \begin{array}{*{20}{l}} {{x_{n0}}\left( t \right) = {x_{n0}}\left( t \right){{\rm{e}}^{\left( { - {\rm{j}}2{\rm{ \mathit{ π} }}{{\bar f}_0}\left( {t + \left( {n - 1} \right)T} \right)} \right)}} = }\\ {{\rm{}}b{p_0}\left( {\theta , \phi , \gamma , \eta } \right)s\left[ {t + \left( {n - 1} \right)T - {\tau _0}\left( {\theta , \phi } \right)} \right] \cdot }\\ {{\rm{}}{{\rm{e}}^{ - {\rm{j}}2{\rm{ \mathit{ π} }}{f_0}{\tau _0}\left( {\theta , \phi } \right)}}{{\rm{e}}^{{\rm{j}}2{\rm{ \mathit{ π} }}\left( {{f_{\rm{\Delta }}} + {f_d}} \right)\left[ {t + \left( {n - 1} \right)T - {\tau _0}\left( {\theta , \phi } \right)} \right]}}{\rm{}}} \end{array} $$ (7) 式中,f0为接收机的本振频率,由于频率同步误差影响,f0与f0存在偏差,频率偏差为fΔ = f0 -f 0。假设入射信号为远场窄带信号,那么接收信号包络沿阵列的延迟可以忽略不计,则:
$$ \begin{array}{*{20}{l}} {{x_n}\left( t \right) = b{p_n}\left( {\theta , \phi , \gamma , \eta } \right)s\left( t \right) \cdot }\\ {{{\rm{e}}^{ - {\rm{j}}2{\rm{ \mathit{ π} }}{f_0}{\tau _n}\left( {\theta , \phi } \right)}}{{\rm{e}}^{{\rm{j}}2{\rm{ \mathit{ π} }}\left( {{f_{\rm{\Delta }}} + {f_d}} \right)\left[ {t + \left( {n - 1} \right)T - {\tau _n}\left( {\theta , \phi } \right)} \right]}}} \end{array} $$ (8) $$ \begin{array}{*{20}{l}} {{x_{n0}}\left( t \right) = b{p_0}\left( {\theta , \phi , \gamma , \eta } \right)s\left( t \right) \cdot }\\ {{{\rm{e}}^{ - {\rm{j}}2{\rm{ \mathit{ π} }}{f_0}{\tau _0}\left( {\theta , \phi } \right)}}{{\rm{e}}^{{\rm{j}}2{\rm{ \mathit{ π} }}\left( {{f_{\rm{\Delta }}} + {f_d}} \right)\left[ {t + \left( {n - 1} \right)T - {\tau _n}\left( {\theta , \phi } \right)} \right]}}} \end{array} $$ (9) 为了消除信源调制信号和轮采带来的多余相位,采用比对天线进行相位比对,即:
$$ {y_n}\left( t \right) = \frac{{{x_n}\left( t \right)}}{{{x_{n0}}\left( t \right)}}\left| {{x_{n0}}\left( t \right)} \right| = \bar b{p_n}\left( {\theta , \phi , \gamma , \eta } \right){{\rm{e}}^{ - {\rm{j}}2{\rm{ \mathit{ π} }}{f_0}\left( {{\tau _n}\left( {\theta , \phi } \right) - {\tau _0}\left( {\theta , \phi } \right)} \right)}} $$ (10) 式中,b= b| s (t) |。
将2N个阵元数据排成列向量得:
$$ {y_l} = \left[ {\begin{array}{*{20}{c}} {{y_1}\left( {{t_l}} \right)}\\ {{y_2}\left( {{t_l}} \right)}\\ \vdots \\ {{y_{2N}}\left( {{t_l}} \right)} \end{array}} \right] = {\bar b_l}\mathit{\boldsymbol{p}}\left( {\theta , \phi , \gamma , \eta } \right) \odot {\mathit{\boldsymbol{a}}_s}\left( {\theta , \phi } \right) $$ (11) 式中,⊙表示Hardmard积;
$$ \mathit{\boldsymbol{P}}\left( {\theta , \phi } \right) = \left[ {\begin{array}{*{20}{c}} {\mathit{\boldsymbol{p}}_1^{\rm{{\rm T}}}\left( {\theta , \phi } \right)}\\ {\mathit{\boldsymbol{p}}_2^{\rm{{\rm T}}}\left( {\theta , \phi } \right)}\\ \vdots \\ {\mathit{\boldsymbol{p}}_{2N}^{\rm{{\rm T}}}\left( {\theta , \phi } \right)} \end{array}} \right] $$ $$ w\left( {\gamma , \eta } \right) = \left[ {\begin{array}{*{20}{c}} {{\rm{cos}}\gamma }\\ {{\rm{sin}}\gamma {{\rm{e}}^{{\rm{j}}\eta }}} \end{array}} \right] $$ $$ \mathit{\boldsymbol{p}}\left( {\theta , \phi , \gamma , \eta } \right) = \mathit{\boldsymbol{P}}\left( {\theta , \phi } \right)w\left( {\gamma , \eta } \right) $$ $$ {\mathit{\boldsymbol{a}}_s}\left( {\theta , \phi } \right) = \left[ {\begin{array}{*{20}{c}} {{{\rm{e}}^{ - {\rm{j}}2{\rm{ \mathit{ π} }}{f_0}\left( {{\tau _1}\left( {\theta , \phi } \right) - {\tau _0}\left( {\theta , \phi } \right)} \right)}}}\\ {{{\rm{e}}^{ - {\rm{j}}2{\rm{ \mathit{ π} }}{f_0}\left( {{\tau _2}\left( {\theta , \phi } \right) - {\tau _0}\left( {\theta , \phi } \right)} \right)}}}\\ \vdots \\ {{{\rm{e}}^{ - {\rm{j}}2{\rm{ \mathit{ π} }}{f_0}\left( {{\tau _{2N}}\left( {\theta , \phi } \right) - {\tau _0}\left( {\theta , \phi } \right)} \right)}}} \end{array}} \right] $$ 以圆心为坐标原点,各对双极化阵元的空间矢量可以表示为:
$$ \mathit{\boldsymbol{r}} = \left[ {{\mathit{\boldsymbol{r}}_1}{\rm{}}{\mathit{\boldsymbol{r}}_2}{\rm{}} \cdots {\rm{}}{\mathit{\boldsymbol{r}}_N}} \right] $$ (12) 式中,rn = [r cos ϕn r sin ϕn 0],n= 1,2…N。
同时,信号来波的单位矢量d为:
$$ \mathit{\boldsymbol{d}} = \left[ {{\rm{sin}}\theta {\rm{cos}}\phi \;{\rm{sin}}\theta {\rm{sin}}\phi \;{\rm{cos}}\theta } \right] $$ (13) 假设光速为c,则信号入射到第n对双极化阵元上相对于中间参考阵元的时延为:
$$ {\tau _{2n - 1}}\left( {\theta , \phi } \right) - {\tau _0}\left( {\theta , \phi } \right) = {\tau _{2n}}\left( {\theta , \phi } \right) - {\tau _0}\left( {\theta , \phi } \right) = \frac{{{\mathit{\boldsymbol{r_n}}} \cdot \mathit{\boldsymbol{d}}}}{c} = \frac{{r{\rm{sin}}\theta {\rm{cos}}\left( {\phi - {\phi _n}} \right)}}{c} $$ (14) 由此可以得到阵列的空域导向矢量as (θ,ϕ)为:
$$ {\mathit{\boldsymbol{a}}_s}\left( {\theta ,\phi } \right) = \left[ {\begin{array}{*{20}{c}} {{{\rm{e}}^{ - {\rm{j}}\frac{{2{\rm{ \mathit{ π}}} }}{\lambda }r{\rm{sin}}\theta {\rm{cos}}\left( {\phi - {\phi _1}} \right)}}}\\ {{{\rm{e}}^{ - {\rm{j}}\frac{{2{\rm{ \mathit{ π}}} }}{\lambda }r{\rm{sin}}\theta {\rm{cos}}\left( {\phi - {\phi _2}} \right)}}}\\ \vdots \\ {{{\rm{e}}^{ - {\rm{j}}\frac{{2{\rm{ }}\pi }}{\lambda }r{\rm{sin}}\theta {\rm{cos}}\left( {\phi - {\phi _N}} \right)}}} \end{array}} \right] \otimes \left[ {\begin{array}{*{20}{c}} 1\\ 1 \end{array}} \right] $$ (15) 考虑接收机噪声的情况下回波信号矢量可以写成如下形式:
$$ {\mathit{\boldsymbol{y}}_l} = {\bar b_l}\mathit{\boldsymbol{a}}\left( {\theta , \phi , \gamma , \eta } \right) + {\mathit{\boldsymbol{n}}_l} $$ (16) 式中,a (θ,ϕ,γ,η) = p (θ,ϕ,γ,η) ⊙as (θ,ϕ);nl为服从零均值、协方差矩阵为Rn的复高斯噪声矢量。
在室内环境下,阵列接收的信号中不仅包含直达波,还有经过墙壁桌子地板等各种障碍物反射后到达阵列的多径回波。实际上,除了单个信源的直达波和多径回波外,其他信源的直达波和多径回波也会存在于回波信号中,但考虑到室内环境下很多信源,比如蓝牙信源是采用时分复用模式,其本身就可以避免大部分情况下的多信源相互干扰问题。不过随着信源数增多,信源间相互干扰会偶尔发生,此时可以根据帧头信息和校验码判断出该信号是不是单个信源,如果不是则进行丢弃处理。如果信源数增多到信源干扰一直存在,那么就没有单信源的情况了,此时就需要考虑多信源的情况,对阵列的规模有更高的要求。
一般情况下,只要单个基站对应的信源数少于100个,基本上不会存在多信源干扰,所以本文暂时只考虑单个信源情况下的直达波和多径回波分辨问题。考虑这些因素后的接收机回波信号yl可以写为:
$$ {\mathit{\boldsymbol{y}}_l} = \mathit{\boldsymbol{A}}{\mathit{\boldsymbol{s}}_l} + {\mathit{\boldsymbol{n}}_l} $$ (17) 式中,阵列流形矩阵A为:
$$ \mathit{\boldsymbol{A}} = \left[ {\begin{array}{*{20}{c}} {\mathit{\boldsymbol{a}}\left( {{\theta _1}, {\phi _1}, {\gamma _1}, {\eta _1}} \right)}&{\mathit{\boldsymbol{a}}\left( {{\theta _2}, {\phi _2}, {\gamma _2}, {\eta _2}} \right)}& \cdots &{\mathit{\boldsymbol{a}}\left( {{\theta _P}, {\phi _P}, {\gamma _P}, {\eta _P}} \right)} \end{array}} \right] $$ (18) 其中,P为直达波和多径信号个数;信号矢量sl为:
$$ {s_l} = {\left[ {{b_{1l}}{\rm{}}{b_{2l}}{\rm{}} \cdots {\rm{}}{b_{Pl}}} \right]^{\rm{T}}} $$ (19) -
存在多径环境下,为了能够准确地估计目标方向,需要将直达波信号和多径信号进行分离,此时需要采用超分辨角度估计方法。常用的超分辨算法包括Capon谱估计算法[22]、MUSIC谱估计算法[23-26]、ESPRIT算法[27]、稀疏贝叶斯学习[28]等,考虑到Capon谱估计不需要估计信源数目,避免了信源估计数目不准确对估计性能的影响,所以本文采用Capon谱估计算法。首先构造Capon零点谱:
$$ J\left( {\theta , \phi , \gamma , \eta } \right) = {a^{\rm{{\rm H}}}}\left( {\theta , \phi , \gamma , \eta } \right){\mathit{\boldsymbol{R}}^{ - 1}}\mathit{\boldsymbol{a}}\left( {\theta , \phi , \gamma , \eta } \right) $$ (20) 式中,$\mathit{\boldsymbol{R}} = \frac{1}{L}\mathop \sum \limits_{l = 1}^L {y_l}y_l^{\rm{{\rm H}}}$为采样协方差矩阵。
目标参数可以通过参数搜索获得,其中$\hat \theta、 \hat \phi、 \hat \gamma 、\hat \eta $为估计得到的目标参数,即:
$$ \left[ {\hat \theta \;\hat \phi \;\hat \gamma \;\hat \eta } \right] = \mathop {{\rm{argmin}}}\limits_{\theta ,\phi ,\gamma ,\eta } J\left( {\theta ,\phi ,\gamma ,\eta } \right) $$ (21) 由于上述过程需要四维搜索,计算量非常大。为了降低计算量,可以利用Hardmard积的性质将导向矢量写为:
$$ \begin{array}{*{20}{l}} {\mathit{\boldsymbol{a}}\left( {\theta , \phi , \gamma , \eta } \right) = \mathit{\boldsymbol{p}}\left( {\theta , \phi , \gamma , \eta } \right) \odot {\mathit{\boldsymbol{a}}_s}\left( {\theta , \phi } \right) = }\\ {{\mathit{\boldsymbol{ \boldsymbol{\varLambda}}} _s}\left( {\theta , \phi } \right)\mathit{\boldsymbol{p}}\left( {\theta , \phi , \gamma , \eta } \right) = }\\ {{\mathit{\boldsymbol{ \boldsymbol{\varLambda}}} _s}\left( {\theta , \phi } \right)\mathit{\boldsymbol{P}}\left( {\theta , \phi } \right)w\left( {\gamma , \eta } \right)} \end{array} $$ (22) 式中,Λs (θ,ϕ)是由as (θ,ϕ)构造的对角矩阵。
将式(22)代入到式(20)可得:
$$ J\left( {\theta ,\phi ,\gamma ,\eta } \right) = {w^{\rm{H}}}\left( {\gamma ,\eta } \right){\mathit{\boldsymbol{P}}^{\rm{H}}}\left( {\theta ,\phi } \right)\mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_s^{\rm{H}}\left( {\theta ,\phi } \right){\mathit{\boldsymbol{R}}^{ - 1}}{\mathit{\boldsymbol{ \boldsymbol{\varLambda} }}_s}\left( {\theta ,\phi } \right)\mathit{\boldsymbol{P}}\left( {\theta ,\phi } \right)w\left( {\gamma ,\eta } \right) = {w^{\rm{H}}}\left( {\gamma ,\eta } \right)\mathit{\boldsymbol{D}}\left( {\theta ,\phi } \right)w\left( {\gamma ,\eta } \right) $$ (23) $$ \mathit{\boldsymbol{D}}\left( {\theta , \phi } \right) = {\mathit{\boldsymbol{P}}^{\rm{{\rm H}}}}\left( {\theta , \phi } \right)\mathit{\boldsymbol{ \boldsymbol{\varLambda}}} _s^{\rm{{\rm H}}}\left( {\theta , \phi } \right){\mathit{\boldsymbol{R}}^{ - 1}}{\mathit{\boldsymbol{ \boldsymbol{\varLambda}}} _s}\left( {\theta , \phi } \right)\mathit{\boldsymbol{P}}\left( {\theta , \phi } \right) $$ 由于代价函数为二次型形式,为了使代价函数最小,D (θ,ϕ)对应的最小特征值应该尽可能小。因此,可以通过如下方式来估计目标角度:
$$ \left[ {\hat \theta \;\hat \phi } \right] = \mathop {{\rm{argmin}}}\limits_{\theta ,\phi } {\lambda _{{\rm{min}}}}\left( {\mathit{\boldsymbol{D}}\left( {\theta ,\phi } \right)} \right) $$ (24) 式中,λmin (D (θ,ϕ))表示矩阵D (θ,ϕ)的最小特征值。由于矩阵D (θ,ϕ)为2 × 2矩阵,最小特征值具有解析表达式,因此式(24)的计算量并不大。将2 × 2矩阵的最小特征值表达式代入式(24)得:
$$ \left[ {\hat \theta {\rm{}}\hat \phi } \right] = \mathop {{\rm{argmin}}}\limits_{\theta , \phi } \left( {{D_{11}} + {D_{22}} - \sqrt {{{\left( {{D_{11}} - {D_{22}}} \right)}^2} + 4{{\left| {{D_{12}}} \right|}^2}} } \right) $$ (25) 式中,$\mathit{\boldsymbol{D}}\left( {\theta , \phi } \right) = \left[ {\begin{array}{*{20}{c}}{{D_{11}}}&{{D_{12}}}\\{D_{12}^{\rm{*}}}&{{D_{22}}}\end{array}} \right] $。同时,可以得到w (γ,η)的估计为D (θ,ϕ)最小特征值对应的特征向量,即:
$$ \hat w\left( {\gamma , \eta } \right) = {v_{{\rm{min}}}}\left( {D\left( {\hat \theta , \hat \phi } \right)} \right) $$ (26) 估计出目标二维角度后,利用假设已知的目标高度信息,就可以实现目标的三维坐标估计,即:
$$ \left\{ {\begin{array}{*{20}{l}} {x = h{\rm{ctan}}\theta {\rm{sin}}\phi }\\ {y = h{\rm{ctan}}\theta {\rm{cos}}\phi }\\ {z = h} \end{array}} \right. $$ (27) 将式(27)的反变换直接代入到式(25)中进行代价函数搜索,此时搜索得到的就是目标的二维坐标。
-
为验证本文方法的有效性,在中国测绘创新基地5楼一个长7 m、宽6 m的实验场内进行了应急定位实测,受场地条件限制只进行了定位精度验证。图 3是定位实验现场图。天线阵列基站置于天花板上,测试采用的信源是蓝牙标签。为便于长期功能测试,参与实验测试的基站连接有线电源,实际基站可移动供电。实测时基站接收机控制电路对外围一圈极化天线(1-2,3-4,5-6,7-8,10-11,12-13)信号进行分时轮采获得采集数据,而中间天线9作为比对天线采集的数据通过另外一个通道进入接收机。
图 4给出了蓝牙标签信号经过相位差分后的结果图,从图 4中可以看出,该蓝牙标签信号的前面部分是蓝牙帧头,后面部分是单频信号。为了体现双通道的优势,天线轮采采用比较大的轮采周期(这里轮采周期为蓝牙帧周期的1/12),这样就能观察存在信号随机相位时的波程差相位提取性能。
图 5给出了双通道与单通道数据阵列相位的比较结果。从图 5(b)中可以看出,单通道轮采天线在蓝牙帧头处的相位呈现随机起伏的特性,这主要是由于蓝牙帧头信号相位引起的,因此单通道轮采天线不能解决存在随机调制信号相位的波程差相位提取。但后面的单频信号直接利用单通道轮采天线就可以获得波程差相位。因此,单通道轮采天线更适合单频信号的应用场景。从图 5(a)和图 5(b)的对比可以看出,采用双通道轮采天线具有更好的相位稳定性,而采用单通道轮采天线的相位受信号相位以及各种非理想因素影响比较大,导致相位稳定性较差,对后续的定位的准确度和稳定性影响较大。从图 5(c)中可以看出双通道的数据相位更稳定,也更准确。
图 6给出了信源位置在(-1.5 m, 0 m)处的多帧定位结果,其中图 6(a)和图 6(b)为连续多帧的水平二维位置定位结果。为了比较,真实的水平二维位置也一并给出,图 6(c)为单帧的代价函数图,其中颜色表示代价函数大小,颜色越深,代价函数越大。为了得到定位结果,假设信源高度是已知的,也就是在估计中将信源真实的高度代入到式(27)。
需要指出的是,如果信源高度不准,那么由此代入的信源高度将会影响定位精度。另外,天线高度也会影响定位精度,天线高度越高,相同位置偏离阵面法线方向越小,定位精度越高。图 6中,x和z坐标表示水平面上的两个坐标,y坐标表示高度,坐标系定义如图 2所示。为了降低计算量,搜索范围限制在阵元的波束宽度范围内。从图 6(a)和图 6(b)可以看出,对于该位置数据,x方向估计精度稍好,估计偏差在0.09 m左右,z方向估计精度稍差,估计偏差在0.15 m左右。另外,不同帧之间的定位结果存在着小的波动性,这主要是由于信源随时间的变化以及环境随时间变化等原因引起的,但由于基于阵列的定位方法是基于瞬时信号的波程差相位,在信噪比足够的情况下信源随机性影响并不严重。从图 6(c)中可以看出,代价函数具有比较明显的峰值,其峰值位置与目标真实位置很接近,而且代价函数的形状在近距离比较窄,远距离比较宽,这主要是由阵列特性决定的,也就是在阵列法线的位置分辨率较高,偏离阵列法线方向的位置分辨率较低。
图 7和图 8给出了信源位置在(-2 m, 2 m)处和(-2.5 m, 0 m)处的多帧定位结果, 其定位结果与图 6基本类似,说明了本文方法的有效性。
图 9给出了动态测试结果图,其中实验人员拿着蓝牙标签沿着环形轨迹行走多圈。首先采用定位算法获得标签的粗定位结果,然后采用卡尔曼滤波对定位结果进行滤波跟踪。从图 9中可以看出,阵列天线基站附近的定位结果比较好,离基站较远位置的定位结果稍差,而且在拐弯处的偏差更大。这主要是由两个方面的原因引起的:(1)阵列本身的因素,因为阵列法线方向的定位精度是最高的,偏离法线方向越大,定位精度越差;(2)跟踪滤波算法的因素,因为在跟踪滤波中量测协方差矩阵设置偏大,导致在目标大机动时跟踪误差增大。
-
应急室内定位需要快速部署、高精度定位、多目标场景覆盖。采用单基站双通道比相超分辨角度估计方法,可有效消除信源信号相位以及频率同步误差对轮采天线的相位影响,降低目标角度估计的运算量。用蓝牙标签发射信号作为信源的单双通道采样数据,处理结果表明,双通道比对天线方法可有效消除信号调制方式对相位的影响。该方法的接收信号形式不受限,可以是2.4 GHz单频信号,也可以是蓝牙、WiFi等其他同频点调制信号,适用于应急定位环境下多种未知信源的定位和跟踪。静态及动态定位结果表明双通道比相测角定位方法比单通道轮采方法定位精度高。单基站可以实现快速二维定位,更易于应急定位部署和低成本商业化应用。
A High Accuracy Positioning Method for Single Base Station in Indoor Emergency Environment
-
摘要: 针对复杂室内环境下的高精度应急定位需求,提出了采用单通道开关切换轮采双极化天线阵,外加比对天线的双通道比相测角方法。该方法首先构建了双通道比对天线的回波信号模型,然后在此基础上给出了角度和极化解耦的超分辨估计算法,降低了目标角度估计的计算量。理论推导和测试结果都证明所提出的双通道方法可有效消除信源信号相位以及频率同步误差对轮采天线的相位影响,比单通道轮采方案具有更稳定的性能和更广的适用范围,并且该方法用单基站即可实现精确二维定位,更适用于应急定位的快速部署和低成本商业推广。Abstract:
Objectives In recent years, the demand of indoor and outdoor emergency location service is growing rapidly. Affected by indoor space environment, signal types, sensor performance and other factors, the existing positioning methods of single signal source, single sensor source, integrated navigation, fusion positioning are not perfect in accuracy, stability, reliability, rapidity and other aspects. The main objective of this study is to propose a high precision wireless location method for single base station in emergency positioning environment. Methods A method of angle measurement with high precision was proposed to eliminate redundant phase caused by modulated signal and sequential sampling. Firstly, a circular antenna array was constructed which sampling received signal on one channel by switching the dual polarized antenna array element in turn, and on the second channel by comparison antenna. Then, the echo signal mathematical model of dual channel antenna was established. Finally, the super-resolution angle estimation algorithm of Capon spectral and polarization decoupling was given for multipath indoor environment. In order to reduce the computational complexity of four-dimensional search, the steering vector was rewritten by hardard product, and target angle estimation was obtained by solving the minimum eigenvalue to minimize the cost function. Results From the comparison results of array phases between single channel and dual channel, it can be seen that the proposed two channel antenna has better phase stability. Experimental results on several fixed location points demonstrate that the root mean square(RMS) positioning error in X direction and Z direction is better than 0.5 m. Both static and dynamic tests show that the influence of source signal phase and frequency synchronization error to switch-antenna array can be effectively eliminated. Conclusions The proposed method can achieve two-dimensional accurate localization with a single base station, which has wider application than the single channel switch-antenna array and is easy to rapid deployment in emergency positioning environment. -
[1] Liu H, Darabi H, Banerjee P, et al. Survey of Wireless Indoor Positioning Techniques and Systems[J]. IEEE Transactions on Systems, Man and Cyberne-tics, 2007, 37(6):1067-1080 doi: 10.1109/TSMCC.2007.905750 [2] Kang W, Han Y. Smart PDR: Smartphone-Based Pedestrian Dead Reckoning for Indoor Localization[J].IEEE Sensors Journal, 2015, 15(5): 2 906- 2 916 https://ieeexplore.ieee.org/document/6987239 [3] IndoorAtlas Ltd. IndoorAtlas Positioning Overview[EB/OL].[2019-11-10].https://indooratlas.freshdesk.com/support/solutions/articles/36000079590-indooratlas-positioning-overview https://indooratlas.freshdesk.com/support/solutions/articles/36000079590-indooratlas-positioning-overview [4] Sun W, Xue M, Yu H, et al. Augmentation of Fingerprints for Indoor WiFi Localization Based on Gaussian Process Regression[J].IEEE Transactions on Vehicular Technology, 2018, 67(11): 10 896-10 905 doi: 10.1109/TVT.2018.2870160 [5] Hu E, Deng Z, Xu Q, et al. Relative Entropy-Based Kalman Filter for Seamless Indoor/Outdoor Multi-source Fusion Positioning with INS/TC-OFDM/GNSS[J]. Cluster Computing: The Journal of Networks, Software Tools and Applications, 2019, 22 (4): 8 351-8 361 [6] Ruiz A R J, Granja F. S. Comparing Ubisense, BeSpoon, and DecaWave UWB Location Systems: Indoor Performance Analysis[J]. IEEE Transactions on Instrumentation and Measurement, 2017, 66(8): 2 106-2 117 [7] 夏炎, 潘树国, 蔚保国.基于载噪比加权融合的异步伪卫星室内定位方法[J].中国惯性技术学报, 2019, 27(2): 154-159 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zggxjsxb201902003 Xia Yan, Pan Shuguo, Yu Baoguo, et al. Asynchronous Pseudolite Indoor Positioning Method Based on C/N0 Weighted Fusion[J]. Journal of Chinese Inertial Technology, 2019, 27(2):154-159 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zggxjsxb201902003 [8] Rizos C. Locata: A Positioning System for Indoor and Outdoor Applications Where GNSS Does not Work[C]. The 18th Association of Public Authority Surveyors Conference, Canberra, Australia, 2013 [9] Vasisht D, Kumar S, Katabi D. Decimeter-Level Localization with a Single WiFi Access Point[C]. The 13th USENIX Symposium on Networked Systems Design and Implementation, Santa Clara, CA, USA, 2016 [10] Google.WifiRttManager[EB/OL].[2020-01-10].https://developer.android.google.cn/reference/kotlin/android/net/wifi/rtt/WifiRttManagerhttps://developer.android.com/reference/android/net/wifi/rtt/WifiRttManager [11] Schmidt R. Multiple Emitter Location and Signal Parameter Estimation[J].IEEE Transactions on Antennas and Propagation, 1986, 34(3):276-280 http://cn.bing.com/academic/profile?id=1a986170d569f82df401fe651848baff&encoded=0&v=paper_preview&mkt=zh-cn [12] Xiong J, Jamieson K. Array Track: A Fine-grained Indoor Location System[C]. The 10th USENIX Conference on Networked Systems Design and Implementation, Lombard, IL, USA, 2013 [13] Gaber A, Omar A. A Study of Wireless Indoor Positioning Based on Joint TDOA and DOA Estimation Using 2-D Matrix Pencil Algorithms and IEEE 802.11ac[J]. IEEE Transactions on Wireless Communications, 2015, 14(5): 2 440-2 454 doi: 10.1109/TWC.2014.2386869 [14] Mariakakis A T, Sen S, Lee J, et al. SAIL: Single Access Point-Based Indoor Localization[C]. The 12th International Conference on Mobile Systems, Applications, and Services, Bretton Woods, New Hampshire, USA, 2014 [15] Sen S, Lee J, Kim K H, et al. Avoiding Multipath to Revive Inbuilding WiFi Localization[C]. The International Conference on Mobile Systems, Applications, and Services, Taipei, Taiwan, China, 2013 [16] Sen S, Kim D, Laroche S. Bringing CUPID Indoor Positioning System to Practice[C]. The 24th International Conference on World Wide Web, Florence, Italy, 2015 [17] Kotaru M, Joshi K, Bharadia D, et al. SpotFi: Decimeter Level Localization Using WiFi[J]. ACM SIGCOMM Computer Communication Review, 2015, 45(5): 269-282 doi: 10.1145/2785956.2787487 [18] Bluetooth SIG. Bluetooth Core Specification Version 5.1[EB/OL].[2019-11-10]. https://www.bluetooth.com https://www.bluetooth.com [19] 陈显舟, 陈周, 杨旭, 等.阵列单通道轮采式快速高精度定位算法[J].现代雷达, 2017, 39(8): 49-53 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=xdld201708011 Chen Xianzhou, Chen Zhou, Yang Xu, et al. Fast High-Resolution Passive Localization Algorithm Based on Single-Channel Using Switch-Antenna Array[J]. Modern Radar, 2017, 39 (8): 49-53 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=xdld201708011 [20] 孟祥豪, 罗景青, 吴世龙.圆阵单通道顺序采样二维超分辨测向算法[J].探测与控制学报, 2011, 33(4):56-59 doi: 10.3969/j.issn.1008-1194.2011.04.013 Meng Xianghao, Luo Jingqing, Wu Shilong.Two- Dimensional Direction Finding Algorithm Based on Single-Channel Sequential Sampling with Circular Array[J]. Journal of Detection and Contrl, 2011, 33(4):56-59 doi: 10.3969/j.issn.1008-1194.2011.04.013 [21] Belloni F, Richter A, Koivunen V. Reducing Excess Variance in Beamspace Methods for Uniform Circular Array[C].IEEE Workshop on Statistical Signal Processing, Bordeaux, France, 2005 [22] Capon J. High-Resolution Frequency-Wavenumber Spectrum Analysis[J]. Proceedings of the IEEE, 1969, 57:1408-1418 doi: 10.1109/PROC.1969.7278 [23] Wu J, Wang T, Bao Z. Fast Realization of Root MUSIC Using Multi-taper Real Polynomial Rooting[J]. Signal Processing, 2015, 106:55-61 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=9fcc4deba56c32b5e75664fcbfa2ffe3 [24] Selva J. Computation of Spectral and Root MUSIC Through Real Polynomial Rooting[J].IEEE Transactions Signal Processing, 2005, 53(5) :1923-1928 doi: 10.1109/TSP.2005.845489 [25] Zoltowski M D, Kautz G M, Silverstein S D. Beamspace Root-MUSIC[J]. IEEE Transactions Signal Processing, 1993, 41(1): 344-364 https://ieeexplore.ieee.org/document/193151 [26] Hyberg P, Jansson M, Ottersten B. Array Interpolation and Bias Reduction[J]. IEEE Transactions Signal Processing, 2004, 52(10): 2 711-2 720 doi: 10.1109/TSP.2004.834402 [27] Ottersten B, Kailath T. Direction-of-Arrival Estimation for Wide-Band Signals Using the ESPRIT Algorithm[J]. IEEE Transactions on Acoustics, Speech, and Signal Processing, 1990, 38(2): 317-327 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=d0443e51b04bf3fd26aa7d598e83d56a [28] Wang Z, Xie W, Duan K, et al. Clutter Suppression Algorithm Based on Fast Converging Sparse Bayesian Learning for Airborne Radar[J]. Signal Processing, 2017, 130: 159-168 doi: 10.1016/j.sigpro.2016.06.023 -