Compute the Extended kalman filter can be done in several ways.
The first one compute the convariance matrix $P(t)$ from the Riccati Equation:
$$\dot{P} = F(t)P(t) + P(t)F^T(t) - P(t)H^T(t) R^{-1}H(t)P + Q$$
The second one compute the covariance matrix $P$ from this equation: $$ \dot{P} = F(t)P(t) + P(t)F^T(t) - K(t)H(t)P(t) + Q(t)$$ https://en.wikipedia.org/wiki/Extended_Kalman_filter#Continuous-time_extended_Kalman_filter
So which one is it? It dosen't matter right? I still can find $P$ by using:
$$P(t) = P(t) + \dot{P} dt $$
Where:
- $dt$ is the sampling time
Or I can use $fsolve$ in MATLAB to solve $P(t)$ from this equation: $$0= F(t)P(t) + P(t)F^T(t) - K(t)H(t)P(t) + Q(t)$$
What is best?
