\kappa_\text{prior} = \frac{\text{Precision}_\text{prior}}{\text{Precision}_\text{prior}+\text{Precision}_\text{measure}} &= \frac{\frac{1}{\sigma_\text{prior}^2}}{\frac{1}{\sigma_\text{prior}^2}+\frac{1}{\sigma_\text{measure}^2}}=\frac{\sigma_\text{measure}^2}{\sigma_\text{prior}^2+\sigma_\text{measure}^2}\\ \kappa_\text{measure} = \frac{\text{Precision}_\text{measure}}{\text{Precision}_\text{prior}+\text{Precision}_\text{measure}} &= \frac{\frac{1}{\sigma_\text{measure}^2}}{\frac{1}{\sigma_\text{prior}^2}+\frac{1}{\sigma_\text{measure}^2}}=\frac{\sigma_\text{prior}^2}{\sigma_\text{prior}^2+\sigma_\text{measure}^2}\\ \[ \begin{aligned} z_{n,\text{measure}} &= x_{1,n} + x_{2,n} + \text{measurement noise} \\\\ &= \begin{bmatrix} 1 & 1 \end{bmatrix}\begin{bmatrix} x_{1,n} \\ x_{2,n}…