一种基于Markov模型和协同克里格的插值方法

Interpolation Method Using Cokriging and the Markov Model

协同克里格是一种具有无偏性和最小预测方差的插值方法.它的主要优点在于充分考虑了空间信息点的相关性和不同变量间的交叉相关性,从而可以将不同信息进行融合.最初的协同克里格方法不能解决不同变量间交叉矩阵不稳定的问题.然而,根据Markov模型的屏蔽效应假设,可对协同克里格方法进行逼近.Markov模型的屏蔽效应假设:硬数据可以屏蔽在其位置以外的其他硬数据对其所在位置软数据的影响.因此在同位置协同克里格中引入Markov模型实现上述逼近.实验说明了该方法的有效性:(1)对该方法模拟结果与真实参考数据的方差和均值进行计算,误差分别为3.8%和2.9%;(2)插值结果具有与真实参考数据相似的直方图分布;(3)在模拟效果上要优于全局协同克里格和简单克里格方法.

Cokriging is an unbiased interpolation method with minimum prediction variance. The main advantage of cokriging is that it takes into account the correlation and cross-correlation of information at the same time, which provides a way to consider different kinds of information simultaneously. Original cokriging cannot solve the problem of instability in matrix. However, according to the hypothesis of screening effect provided by the Markov model, cokriging can be successfully approximated. The screening hypothesis indicates that the hard （ primary ） datum screens the influence of any other datum on the soft （ secondary ） colocated datum, which leads to the approximation. Therefore, a colocated cokriging is used with the Markov model to realize the above approximation. Experimental results show that： （ 1 ） the deviation of the mean and the deviation of the variance on the simulated result and the true refer- ence data are respectively 3.8% and 2.9% ; （2） the simulated result and the true reference data have similar histograms; （3） the simulated results of cokdging under the Markov model are much better than those of full cokriging and simple kriging.