Q3:(10 Marks)
Consider the following estimate problem of 3 measurements $Z_1 = 2$, $Z_2 = -2$, $Z_3 = 1$. Write down the equations of a
Simple Kriging system for an estimation $Z_0$. For the variogram, range (a) is 8 and the covariance function is assumed below.
$\text{COV} (h) = \exp(-\sqrt{\frac{h_x^2}{2a^2} + \frac{h_y^2}{a^2}})$ (1)
The Simple Kriging Estimation is $Z_0 = \sum_{i=1}^n \lambda_i Z_i + (1 - \sum_{i=1}^n \lambda_i)\mu$. Assume $\mu$ represents the mean of the known data.
$Z_1$
$Z_3$
4 m
8 m
$Z_0$
8 m
$Z_2$
Figure 1: A sketch showing 3 measurements Z(u) for points u = 1,2, and 3.
Where $h_x$ and $h_y$ represent the horizontal and vertical distances betweeen the three 3 measurements Z(u) for points u =
1,2, and 3.
