基于格拉斯曼投影判别分析的室内定位算法

Indoor location algorithm based on Grassmann projection discriminant analysis

针对于现有室内无线电指纹算法定位精度受限于特征描述子噪声的问题,引入信号子空间分析并提出一种新的无线电信号特征提取和定位算法。通过格拉斯曼流形上的投影尺度函数,构建投影同位和异位离散程度函数,加大了各信号子空间的投影矩阵之间的差异。采用格拉斯曼投影判别分析算法(GPDA)优化信号子空间的投影矩阵,使得最佳投影特征向量和余弦距离判决抑制了信号噪声,实现了室内目标鲁棒精确定位。为了模拟室内电磁传播,使用三维射线跟踪电波传播模拟器,模拟室内无线数据,仿真数据表明格拉斯曼投影判别分析定位算法定位精度优于1 m。

In allusion to the problem that the positioning accuracy of the existing indoor radio fingerprint algorithm is subject to characteristic descriptor noise,the signal subspace analysis is introduced and a novel radio signal characteristic extraction and location algorithm is proposed. The projection homotopic and heterotopic discrete degree functions are constructed by using the projection scale function in Grassmann manifold to expand the difference among projection matrixes of various signal subspaces. The Grassmann projection discriminant analysis algorithm(GPDA)is adopted to optimize the projection matrix in signal subspace so that the signal noise can be suppressed by optimal projection characteristic vector and cosine distance discrimination,and the accurate robustness positioning of indoor target can be achieved. To simulate the indoor electromagnetic propagation,three-dimensional ray-tracing electric wave propagation simulator was adopted to simulate indoor wireless data. The simulation data shows that the positioning accuracy of GPDA is better than 1 m.