Articles of kalman filter

Forecast equivalence between two steady-state Kalman filters

I have two related steady-state Kalman filter problems that I want to prove satisfy a condition associated with their respective Kalman gains. I am not really looking for a complete proof since this is likely require quite a bit of work. However, any ideas about where to start or useful results that I could use […]

Robust Control VS Optimal Control

What’s the diffrents between Optimal Control and Robust Control? I know that Optimal Control have the controllers: LQR – State feedback controller LQG – State feedback observer controller LQGI – State feedback observer integrator controller LQGI/LTR – State feedback observer integrator loop transfer recovery controller (for increase robustness) And Robust Control have: $H_{2}$ controller $H_{\infty}$ […]

Connection between the Kalman filter and the multivariate normal distribution

Consider at dynamic linear model where $$ \theta_{1} \sim N(\mu_{1}, W_{1}), $$ $$ \theta_{i}=G\theta_{i-1} + w_{i}, w_{i}\sim N(0,W), $$ $$ Y_{i} = F\theta_{i} + v_{i}, v_{i}\sim N(0,V) $$ and $ \theta_{1}, w_{i}, v_{i} $ all independent random vectors. Let $ \theta_{0:t} : = (\theta_{t}, \theta_{t-1},\ldots, \theta_{0}) $ and $ Y_{1:t}:= (Y_{t},Y_{t-1},\ldots, Y_{1})$. A generel result […]

Is there any guaranteed stability margins for Extended Kalman Filter (EKF)?

LQR controllers have guaranteed stability margins, but LQG controllers has not guaranteed stability margins, due to the linear kalman filter. But what will happen if I replace the linear kalman filter with the Extended Kalman Filter(EKF), which is a nonlinear kalman filter? Do I receive guaranteed stability margins then?

An Explanation of the Kalman Filter

In the past 3 months I’ve been trying to understand the Kalman Filter. I have tried to implement it, I have watched youtube tutorials, and read some papers about it and its operation (update, predicate, etc.) But I still am unable to understand it fully , or in depth. Can someone explain it in a […]