基于Pearson相关系数的快速虚拟网格匹配定位算法

针对室内环境下位置指纹匹配定位算法中离线数据库采集工作量较大的问题，提出了一种基于Pearson相关系数的快速虚拟网格匹配的定位算法。首先，将接收信号强度指示（RSSI）进行高斯滤波预处理得到接收信号强度向量；然后，利用Bounding-Box方法确定初始虚拟网格区域，将该网格区域快速迭代细分并计算网格中心点到各信标节点的距离对数向量，计算接收信号强度向量和距离对数向量之间的Pearson相关系数；最后，选取Pearson相关系数接近于-1的k个近邻坐标以相关系数加权估计确定待定位节点的最优估计位置。仿真实验结果表明，在1m虚拟网格且RSSI噪声标准差为3dBm的条件下，算法定位误差小于2m的概率大于94.2%，其定位精度优于位置指纹匹配算法，且无需建立RSSI指纹数据库，大大减少了定位工作量。

Fast virtual grid matching localization algorithm based on Pearson correlation coefficient

Focused on the issue that the location fingerprint matching localization algorithm has a large workload of offline database collection in an indoor environment, a fast virtual grid matching algorithm based on Pearson correlation coefficient was proposed. Firstly, the Received Signal Strength Indicator (RSSI) was preprocessed with Gaussian filter to obtain the received signal strength vector. Then, the Bounding-Box method was used to determine the initial virtual grid region. The grid region was rapidly and iteratively subdivided, the distance log vectors of the grid center point to beacon nodes were calculated, and the Pearson correlation coefficients between the received signal strength vector and the distance log vectors were calculated. Finally, the k nearest neighbor coordinates whose correlation coefficients close to -1 were selected, and the optimal estimation position of the undetermined node was determined by the weighted estimation of correlation coefficients. The simulation results show that the localization error of the proposed algorithm is less than 2m in 94.2% probability under the condition of 1m virtual grid and RSSI noise standard deviation of 3dBm. The positioning accuracy is better than that of the location fingerprint matching algorithm, and the RSSI fingerprint database is no longer needed, which greatly reduces the workload of localization.