空间数据插值的杨赤中滤波与推估法

doi:10.11947/j.AGCS.2025.20240370

测绘学报 ›› 2025, Vol. 54 ›› Issue (8): 1501-1517.doi: 10.11947/j.AGCS.2025.20240370

• 地图学与地理信息 • 上一篇

空间数据插值的杨赤中滤波与推估法

刘启亮(), 阳洁, 毛先成(), 刘占坤, 邓敏

中南大学地球科学与信息物理学院，湖南　长沙　410083

收稿日期:2024-09-05 修回日期:2025-07-07 发布日期:2025-09-16
通讯作者: 毛先成 E-mail:qiliang.liu@csu.edu.cn;mxc@csu.edu.cn
作者简介:刘启亮（1986—），男，博士，教授，研究方向为多尺度空间统计与数据挖掘。E-mail：qiliang.liu@csu.edu.cn
基金资助:
湖南省自然资源厅科技计划(HBZ20240132);国家自然科学基金(42271484);中南大学教学改革项目(2024jy202)

Yang Chizhong filtering and estimation methods for spatial data interpolation

Qiliang LIU(), Jie YANG, Xiancheng MAO(), Zhankun LIU, Min DENG

School of Geo-informatics, Central South University, Changsha 410083, China

Received:2024-09-05 Revised:2025-07-07 Published:2025-09-16
Contact: Xiancheng MAO E-mail:qiliang.liu@csu.edu.cn;mxc@csu.edu.cn
About author:LIU Qiliang (1986—), male, PhD, professor, majors in multi-scale spatial statistics and data mining. E-mail: qiliang.liu@csu.edu.cn
Supported by:
Research Foundation of the Department of Natural Resources of Hunan Province(HBZ20240132);The National Natural Science Foundation of China(42271484);Teaching Reform Project of Central South University(2024jy202)

摘要/Abstract

摘要：

地学研究普遍面临数据缺失与稀疏分布的问题，空间插值是地学数据分析的核心任务之一。现有基于统计学与几何学的方法在小样本、非平稳空间过程建模方面长期存在缺陷。杨赤中滤波与推估法（简称“杨赤中法”）是一种融合几何与统计思维的空间相关性建模方法，在矿体几何制图等小样本、非平稳空间过程插值应用中具有优势。本文首先完善了杨赤中法解决空间异质环境下空间插值问题仍存在的缺陷，然后重点介绍了杨赤中法近年来的新发展及相对现有方法的优势，最后对未来研究问题进行了展望。杨赤中法可广泛应用于地学现象分布特征分析与演化规律发现。

Abstract:

Geoscience research generally faces the problem of missing data and sparse distribution. Spatial interpolation is one of the primary and core tasks of geoscience data analysis. Statistics- and geometry- based spatial interpolation methods are widely used in spatial data analysis; however, they have long had defects in modeling non-stationary spatial processes. Yang Chizhong filtering and interpolation methods (abbreviated as Yang Chizhong methods) integrate geometric and statistical strategy to quantify spatial autocorrelation structure, which provides a new idea for modeling non-stationary spatial processes. Yang Chizhong methods have unique advantages in modeling small samples and non-stationary spatial processes, such as geometrisation of ore body. In this study, we first overcome two long-standing theoretical shortcomings of Yang Chizhong methods. Then, we focus on the new progress of Yang Chizhong methods in recent years. Finally, we provide an outlook on future research directions. Yang Chizhong methods can widely serve the analysis of distribution characteristics and discovery of evolutionary laws of geo-phenomena.

Key words: spatial statistics, spatial autocorrelation, nonstationary spatial processes, spatial compound variable, Yang Chizhong filtering and interpolation

中图分类号:

P208

刘启亮, 阳洁, 毛先成, 刘占坤, 邓敏. 空间数据插值的杨赤中滤波与推估法[J]. 测绘学报, 2025, 54(8): 1501-1517.

Qiliang LIU, Jie YANG, Xiancheng MAO, Zhankun LIU, Min DENG. Yang Chizhong filtering and estimation methods for spatial data interpolation[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(8): 1501-1517.

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空间数据插值的杨赤中滤波与推估法

Yang Chizhong filtering and estimation methods for spatial data interpolation

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