This question is somewhat basic but I miss some background that helps me to grasp it entirely.
I have a arbitrary frame of center$\ o $ and a point$\ p $ in this frame of coordinates $\ p = (x_p, y_p, z_p)$. I know $\ \mathbf{n} = \frac{\mathbf{op}} {\left \| \mathbf{op} \right \|} $ and I measure this point with a range sensor, meaning that I get an estimate of $\ \left \| \mathbf{op} \right \|$ that follows a normal distribution $ d \sim \mathcal{N}(d, \sigma_d^2) $.
How can I convert this variance along$\ \mathbf{n} $ to a 3x3 covariance matrix of the coordinate of the point in the frame $\ p \sim \mathcal{N} \left( \begin{pmatrix} x_p\\ y_p \\ z_p \end{pmatrix}, \begin{pmatrix} \sigma_{xx}^2 & \sigma_{xy} & \sigma_{xz}\\ \sigma_{yx} & \sigma_{yy}^2 & \sigma_{yz} \\ \sigma_{zx} & \sigma_{zy} & \sigma_{zz}^2 \end{pmatrix}\right)$? Do I simply project the variance along axes?
Thanks for your answers.
Well, it turns out it's a whole well documented thing known as Uncertainty Propagation (Wikipedia page).