The maximum likelihood
p(x|y): probability that x= xt given that y has been observed
- A posteriori probability distribution associated with that of the analysis error
p(y|x): probability of y given that x is the true value
- Hx: estimate of the mean value of y.
- If x = xt, then Hxt = yt+ eR .
- (y - Hx) = yt + em + eR - Hx = yt + eo - Hx
- (y - Hx) is normally distributed with mean Hx and covariance R