Single Base Station Localization Algorithm Based on B-LM Ring of Scattering Model Using NLOS Information
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摘要: 针对当前室外蜂窝网多基站定位需要基站之间时间同步、数据同步的要求，以及NLOS环境造成的非服务区基站的信号可测性问题，该文提出基于B-LM圆环模型的NLOS信息约束单基站定位算法。首先根据散射体、目标和基站间的几何位置关系以及NLOS多路径信息构建定位方程，然后将定位方程转化为最小二乘优化问题，之后基于LM算法海森矩阵修正思想和拟牛顿2阶偏导构造思想提出B-LM算法，保证算法收敛于最优解，以得到目标位置。仿真结果表明，所提单基站定位算法能在宏蜂窝NLOS环境实现较高的定位精度。Abstract: Considering the requirements of time and data synchronization in multi-BS (Base Station) positioning in the current outdoor cellular network and the problem of signals’ detectability in area without service BS due to NLOS (Non-Line-Of-Sight) environment, a single base station localization algorithm based on B-LM (Broyden Fletcher Goldfarb Shanno-Levenberg Marquard) ring of scattering model using NLOS information is proposed. Firstly, the localization objective equation is constructed according to the geometric positions of the scatterers, the target, the base station and the NLOS multipath information. Then, the localization equation is transformed into the least square optimization problem. Finally, the B-LM algorithm based on Hessian matrix modification methodology in LM algorithm and the construction of second order partial derivative in quasi-Newton algorithm is proposed, which ensures the localization algorithm converges to the optimal solutions to obtain the target’s location. The simulation results show that the proposed single base station localization algorithm can achieve a high positioning accuracy in the NLOS environment for macrocell.
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表 1 B-LM算法伪代码
输入： 每条路径到达时间 ${\tau _i}$和到达角 ${\alpha _i}$； 输出： 目标位置 $\left( {x,y} \right)$； (1) 选取可行域内目标初始位置 ${{{X}}} \in \operatorname{int} {{{g}}}\left( {{{X}}} \right)$，设置算法参数
$\varepsilon = 0.01$，尺度因子 $\sigma = 10$, ${{B}} = {{I}}$，最大容忍误差 $\xi = {10^{ - 3}}$
和最大迭代次数 $T = 50$；(2) for $k = 1:T\;$ (3) 计算 ${ψ} \left( {{{{{X}}}_k}} \right)$, $\nabla {ψ} \left( {{{{{X}}}_k}} \right)$, ${{{{J}}}_k}$； (4) 根据式(14)更新迭代方向 ${{δ} _k}$； (5) 根据Armijo准则[17]确定搜索步长 ${\lambda _k}$，根据式(11)更新 ${{{{X}}}_{k + 1}}$； (6) 计算下一时刻目标函数1阶偏导 $\nabla {ψ} \left( {{{{{X}}}_{k + 1}}} \right)$，计算 ${{{{q}}}_k}$和 ${{{{p}}}_k}$； (7) 根据式(15)更新 ${{{B}}_{k + 1}}$； (8) 计算 ${ψ} \left( {{{{{X}}}_{k + 1}}} \right)$； (9) if ${ψ} \left( {{{{{X}}}_{k + 1}}} \right) < {ψ} \left( {{{{{X}}}_k}} \right)$ then (10) if ${\left\| {\Delta {{{{X}}}_k}} \right\|_2} \le \xi $ then (11) ${{{X}}} = {{{{X}}}_{k + 1}}$ and break； (12) else (13) $\mu : = \mu /\sigma $, $k: = k + 1$并且返回第3行； (14) end if (15) else (16) if ${\left\| {\Delta {{{{X}}}_k}} \right\|_2} \le \xi $ then (17) ${{{X}}} = {{{{X}}}_k}$ and break； (18) else (19) $\mu : = \mu \sigma $, $k: = k + 1$，并且返回第3行； (20) end if (21) end if (22) end for 
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