Let's say I have 2 measuremnts of the same thing (for example current temperature) and I want to find the MMSE estimator, i.e to minimize the MSE. the measurements are independent and the noise in each one is gaussian. the mathematical formation:
$$ Y_1[n] = X[n] + V[n]$$ $$ Y_2[n] = X[n] + W[n]$$
X[n] is the real temperature at time n
Y1[n] and Y2[n] are the measurements at time n
V[n] and W[n] are normally distributed random variables which represent the noise $$ V(0,\sigma_v^2) $$ $$ W(0,\sigma_w^2) $$
I need at clue or reference for how to solve it
Thank you
Nir