"Learning occupancy grid maps with forward sensor models, S.Thurn,2008" a formula that is difficult to overcome I am reviewing the document" Learning occupancy grid maps with forward sensor models, S.Thrun, 2008" (http://faculty.iiit.ac.in/~mkrishna/ThrunOccGrid.pdf)

i am really confused about formula (26), which is merged by formula (22), (24), (25) in an "intersection of probabilities" computed in (22),(24),(25). So, it should be a product of factors in (22),(24),(25). If it is correct, the first factor of (26), 1/sqrt(2*π*σ), should be powered.

any one can tell me why 1/sqrt(2*π*σ) isn't powered?
The vector $c_t$ has exactly one coordinate which is 1, and the rest are 0s. You can check that if, for example, $c_{t,k}=1$, when you substitute $c_{t,k}=1$ and $c_{t,\ell}=0$ for all $\ell \neq k$ in (26) you get (22). The same happens for (24) and (25).