引用本文: 师泽源, 赵俭辉, 张文昱, 胡勇, 武小平. 基于扩展场强模型的稀疏AQI空间插值新算法[J]. 武汉大学学报 ( 信息科学版), 2017, 42(7): 968-974.
SHI Zeyuan, ZHAO Jianhui, ZHANG Wenyu, HU Yong, WU Xiaoping. New Spatial Interpolation Algorithm for Sparse AQI Based on Extended Field Intensity Model[J]. Geomatics and Information Science of Wuhan University, 2017, 42(7): 968-974.
 Citation: SHI Zeyuan, ZHAO Jianhui, ZHANG Wenyu, HU Yong, WU Xiaoping. New Spatial Interpolation Algorithm for Sparse AQI Based on Extended Field Intensity Model[J]. Geomatics and Information Science of Wuhan University, 2017, 42(7): 968-974.

## New Spatial Interpolation Algorithm for Sparse AQI Based on Extended Field Intensity Model

• 摘要: 针对空气质量指数（AQI）监测点分布稀疏，现有空间插值算法精度不高问题，提出了新的扩展场强模型与算法。扩展场强单参数模型引入参数c控制场强衰减程度，通过c与误差关系图并借助二分查找法计算最优c值。扩展场强双参数模型加入参数k调整场强影响范围，通过ck与误差关系图并借助迭代双线性插值法求解最优ck组合。以北京、天津、武汉、郑州四个城市2014-08~2015-04的50组AQI监测值为实验数据，采用交叉验证法并以RMSE、AME、PAEE为评价指标，实现了单参与双参模型及参数选取，然后与克里金法及类似的反距离加权法进行对比。实验证明，扩展场强模型能够得到针对稀疏AQI的更高插值精度，且双参数模型精度高于单参数模型。本文算法适用于采样点数目与位置均固定的稀疏数据插值，并可推广至其他类型与维度的空间数据。

Abstract: The monitoring stations for air quality index (AQI) are sparsely distributed, and spatial interpolations are less accurate from the existing methods. A new algorithm is proposed based on the extended field intensity model. The single parameter model controls intensity attenuation by parameter c, while the optimal c value is computed from the relationship between c and deviation data with binary search method. The double parameters model adjusts intensity range by additional parameter k, while the optimal c and k are computed from the relationship among c, k and deviation data with iterative bilinear interpolation method. The 50 monitored sets of AQI value are taken as experimental data from Beijing, Tianjin, Wuhan and Zhengzhou Between August 2014 and April 2015. Based on cross validation and evaluation criteria RMSE, AME, PAEE, both single parameter model and double parameters model are implemented with their optimal parameters, then the extended field intensity model is compared with Kriging and inverse distance weighted methods. Experimental results prove that the precision of AQI interpolation from our algorithm is higher, while double parameters model obtains the highest precision. Our algorithm is suitable for spatial interpolation of sparse data with fixed number and locations, and can be used for spatial data with other types and dimensions.

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