6.13. Consider the 1-dimensional linear filtering problem (6.2.3), (6.2.4). Find E[] and E[(t)] . (Hint: Use...

 

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6.13. Consider the 1-dimensional linear filtering problem (6.2.3), (6.2.4). Find E[] and E[(t)] . (Hint: Use Theorem 6.1.2 and use the definition of the mean square error S(t).) Theorem 6.1.2 Xt=Pk+(X+) = E[Xt|Gt] This is the basis for the general Fujisaki-Kallianpur-Kunita equation of fil- tering theory. See for example Bensoussan (1992), Davis (1984) or Kallianpur (1980). 6.13. Consider the 1-dimensional linear filtering problem (6.2.3), (6.2.4). Find E[] and E[(t)] . (Hint: Use Theorem 6.1.2 and use the definition of the mean square error S(t).) Theorem 6.1.2 Xt=Pk+(X+) = E[Xt|Gt] This is the basis for the general Fujisaki-Kallianpur-Kunita equation of fil- tering theory. See for example Bensoussan (1992), Davis (1984) or Kallianpur (1980).