Unbiasedness condition in ordinary kriging and simple kriging I have this confusion. In ordinary kriging we have used the unbiasedness condition which gave the sum of weights equal to one. However, in the case of simple kriging we have no such conditions why?
I used ordinary kriging and simple kriging in my dataset and I have a huge difference in kriging in predicting the values. AFAIK, simple kriging is a linear regression which ordinary kriging is a constrained linear regression where sum of weights equal to 1.
 A: In SK the sum of weights is one as well as in OK.
The weights given to the samples and the weight given to the mean must sum to one, making the estimate unbiased.
A: In ordinary kriging, the unknown $\mu$ is updated in each prediction for new location as the control data points is added with every and the newly simulated value. Because the $\mu$ is dependent of location $s$, we don't need to fragment the predictor into the model plus residual $\mu + \delta(s)$. The simulated value at $s_0$ will simply follow $\sum^n_{i=1}\lambda_iZ(s_i)\pm t\sigma_k(s_0)$. Generally, the model could be a polynomial which depends on location. In that case of universal kriging, the predictor should be fragmented into the deterministic part (based on location) and the interpolated residual, so the simulated value at $s_0$ will be as follows : $\sum^{p+1}_{j=1}f_{j-1}(s_0)\beta_{j-1}+\sum^n_{i=1}\lambda_i(Z(s_i)-\sum^{p+1}_{j=1}f_{j-1}(s_i)\beta_{j-1})\pm t\sigma_k(s_0)$
In simple kriging, we regress the mean first only using the sample data, the mean will remain constant along the prediction for the entire domain. The simulated value at $s_0$ will follow $\mu+\sum^n_{i=1}\lambda_i(Z(s_i)-\mu)\pm t\sigma_k(s_0)$.
