Extended Kalman Filter

A natural extension of Kalman Filter. First, it’s non-linear:

Next, we use Jacobian, which is just first order Taylor expansion, so we use $G_t$ and $H_t$ to replace $A_t$, $B_t$ and $C_t$.

The goodness of approximation depends on two things:

• The degree of local non-linearity. Note here it’s local. If overall the thing is pretty wild, but around our mean it’s linear, that’s okay.
• The degree of uncertainty. See this image: