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Ordinary Kriging Estimation

 

 

When the mathematical expectation of the Kriging regionalized variable Z(x)is and m is an unknown constant, we use the Ordinary Kriging. Assuming that the region to be estimated is V, the center of it is x, its average is Zv, we can know

 

 

 

Where a dataset has n known sample points,, in the range of estimation zone V, its observed value is Z(xi), and mathematical expectation is m. Therefore,

. Assuming that is the linear estimator of Zv, the linear combination consisting of observed values Z(xi) of n known samples, we can obtain:

 

 

 

Under the same condition of satisfying the unbiased and optimization, is the best linear unbiased estimator of Zv. After calculation, we can obtain the Ordinary Kriging variance . It is:

 

 

 

Under the condition of the existence of a variable function, we can also use a variablefunction to represent the Ordinary Kriging liner equations and Ordinary Kriging estimated variance:

 

 

 

Where when we put the solution into the formula (3), we can obtain a Ordinary Kriging estimator , which is B:

 

 

 

When the zone vi with its center xi is within the extent of the estimation zone V, the Ordinary Kriging liner equations and Ordinary Kriging estimated variance are:

 

 

 

They are also could be presented by the variable functions:

 

 

 


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