#observation-noise

Question 1: Single choice

In a one-dimensional Kalman filter the update is $\mu_s = A\mu_{s-1} + K_s(v_s - C A \mu_{s-1})$ , $\sigma_s^2 = (1 - K_s C) P_s$ , with gain $K_s = P_s C / (C^2 P_s + D^2)$ , where $D^2$ is the observation-noise variance and $P_s$ the predicted variance. What happens as $D^2 \to 0$ ?

$\mu_s \to A\mu_{s-1}$ and $\sigma_s^2 \to P_s$ 1
$K_s \to 0$ , so the filter keeps its prediction2
$\mu_s \to v_s / C$ and $\sigma_s^2 \to 0$ 3
$\mu_s \to v_s / C$ but $\sigma_s^2$ stays at $P_s$ 4

Timed test