A novel interpolation method using a Markov model and COSGSIM

The accuracy of space interpolation can be improved by using the multiple data with different dimensions, resolutions or types. Cokriging can estimate unknown states by multiple known data, with an unbiased prediction value and minimum prediction variance. However, because of the large smoothing effect of itself, cokriging can only reflect the extensive tendency of interpolation, not capable of showing the variability in small regions. Essentially, cokriging is a low-pass filter that causes the smaller values being overestimated and the higher ones being underestimated. To overcome the disadvantage of cokriging, COSGSIM (sequential Gaussian co-simulation), as a full-pass filter for interpolation, can describe the full variability of space variables. When ccdf (conditional cumulative distribution function) is to be determined, COSGSIM cannot solve the instability in matrix of full cokriging. However, according to the hypothesis of screening effect provided by a Markov model, COSGSIM under the full cokriging model 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. Experimental results show that the simulated results of COSGSIM under the Markov model are much better than those of COSGSIM under the full cokriging and simple kriging.