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**), should be powered.any one can tell me why 1/sqrt(2**) isn't powered?
Learning occupancy grid maps with forward sensor models, S.Thurn,2008 a formula that is difficult to overcome
artificial intelligence;probability theory;probabilistic algorithms
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).