However intuitive, I don't understand the formulas for the conditional mean and variance from 2 gaussian measurements. I have not found anything relevant mainly because I don't think I'm searching for the right terms.
$$ \mu = [\sigma_{z_2} ^2 / \sigma_{z_1} ^2 + \sigma_{z_2} ^2)] . z_1 + [\sigma_{z_1} ^2 / \sigma_{z_1} ^2 + \sigma_{z_2} ^2)] . z_2 $$
$$ 1/\sigma^2 = 1/(\sigma_{z_1}^2) + 1/(\sigma_{z_2}^2) $$
It seems this result is explained on p118 of Maybeck 1979 p118. The proof relies on Kalman filters. Isn't there a more intuitive explanation ?