Stochastic Kriging

Dear all,
I am trying to implement a Stochastic Kriging for a heteroscedastic noise problem. Reading the kriging manual of UQLab, I can’t find major differences between formulas of the manual and stochastic kriging described by Ankenman . However the article is not cited, so I assume UQLab make something different. Am I missing something ?
The only thing I note is that equation 1.16 of UQLab manual uses the exact heteroscedastic noise matrix, while equation (24) of Ankenmann uses the replication-estimated noise matrix.

Thanks in advance