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 Quote by kasraa Does it also imply: $$E \left[ \left( x - E \left[ x|Z \right] \right) ^2 | Z \right] = E \left[ \left( x - E \left[ x|Z \right] \right)^2 \right]$$? Is it correct? Thanks.
As I said, I don't know what the double conditional on Z means. I can only guess that it might mean something like $$P_{k|k}$$ which indicates the successor state to $$P_{k|k-1}$$. If so, you need to introduce a system of subsripts.

Also, I don't see any problem to getting the MSE from any sample vector. It's the MMSE that can be a challenge.