I am studying the Kalman filter algorithm but i can't understand one point. The k factor has to be chosen in order to minimize the variance of the signal. This lead to following equation:
where $\sigma^2_f$ is the variance of the forecast signal and $\sigma^2_o$ is the variance of the observed signal. I don't understand why they in general have to be different? Why $\sigma^2_f\neq \sigma^2_o$ ? Why the distributions of the two variables (forecast and observed) are different?