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 […]

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 $H_{\infty}$ […]

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 […]

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?

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 […]

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