State Observers | Understanding Kalman Filters, Part 2

Learn the working principles of state observers, and discover the math behind them. State observers are used to estimate the internal states of a system when you can’t directly measure them.
You will learn how a state observer uses the input and output measurements to estimate system states. The example will walk you through the mathematical derivation of a state observer.
You will discover how the state observer utilizes feedback control to drive the estimated states to the true states. Kalman filtering provides an optimal way of choosing the gain of this feedback controller.

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[soorkie]

Giving a cookie to Timmy disturbs the quantum state of Timmy's happiness. You cannot measure Timmy's happiness without altering the state.

[droxid]

Hello, I was wondering what happened to the part 3 (or it's deadline)? thank you very much!

[arnaudeportola]

6:20 "Because even without the feedback loop that adds the KC term to the equation, we would have a decaying exponential function "...what?! When did you impose A negative definite? This is blatantly false unless you impose that condition

[mohannadtakrouri]

Excellent explanation.
Question:
If you get to 6:03, Shouldn't K(y-y^) be negative because it is subtracted from the first equation?

[omarel-ghezawi]

Oversimplification may lead to incorrect information. First : the eigenvalues of A-KC should have negative real parts, not that A-KC should be <0 ; this is only true for the trivial uninteresting special case of a single state system . Second: K is a must in cases where the original system is unstable, i.e. A has eigenvalues of positive real parts, otherwise the error signal will grow without bound in the absence of K as the error dynamics is now governed by A . It’s important to point out that observers are also needed in the design of unstable systems.
Dr.Omar El-Ghezawi, the University of Jordan, Amman, Jordan

[cristian-bull]

Leave it to mathworks to explain a simple theory using a more complex one.

[fifaham]

@3:45 what guarantees that if [ T(ext) and (cap)T(ext) ] are equal then [T(in) and (capT(int) ] are also equal? Was that your assumption? If not then we need to find a spot where this assumption is near real, and that we are taking measurements based on the real "Dynamic Range" of linear correlation of those two measurements. If those measurements are beyond the real "Dynamic Range" operation then I assume that we can not make this assumption.

[tmwu]

6:12, why the solution to this equation is an exponential function?

[AniketSharmacodes]

Great explanation! I love the way you have broken down Kalman filter in parts and explained in a layman's language with such intuitive examples! (y)

[yingma]

Hi, I also have the same confusion as totoxahc. To be specific, I think we should use \hat A, \hat B and \hac C in the mathematical model, which are different to the real measure model. Then in 6:09, the error function would be e(with a point on it)_obs=((\hat A-A)-K(\hat C-C))e_{obs}. We can not adjust A, C(which we don't have access to) and either\hat A and \hat C. So in order to make the error converge to zero, we must have a feedback loop, in this way, we can adjust K to make the error go to zero. I think this would make more sense. How do you think?

[yuchendu]

It's a very clear explanation! I just have a question about 6:00. Why does the real system have the same equations as the model? In this video, it says model is simply an approximation of the real system, but at 6:00, the equations in both blocks are same. Also, if they are same, why do we need a state observer, why can't we can calculate x directly by using y=Cx?

[TankNSSpank]

What is the X_dot in this video. I don't understand. THanks

[KARABNAS]

In my opinion you need to link better the qualitative description of the problem with the formulas and the "loops" used in electrical engineering... it is not a self contained presentation.

[CommanderUtka]

why the hell you use letter e as an error and as an exp in one expression?

[pokerboy]

This video started from cookies to sme real shit in 60 secs

[atle]

6:12 I dont understand why there is an expornential (A-KC)t come out of nowhere.

[prfontaine]

Semble clair à la première écoute puis l'est moins quand on creuse. On part sur un modèle parfait puis on dit qu'en pratique il ne l'est jamais. Et pourtant il est affirmé qu'une convergence sur les températures externes (réelle vs modèle) assure une convergence sur les températures internes (réelle et modèle). Pourquoi? Quelle hypothèse permet d'affirmer cela?
Et si le modèle n'est pas parfait, pourquoi on retrouve ses équations dans la boîte figurant le système réel ? On pourrait admettre à la rigueur que les équations du modèle et celles représentant le système aient la même forme, mais là ils ont la même forme et les mêmes paramètres A, B, C !
Bref cette notion de modèle imparfait est assez confuse...

[jayaramjonnada]

But why are they measuring by taking T-ext(cap), when they already know what is T-ext. They W-fuel and T-ext, so they can find T-int. Why are they making it complex by estimating T-ext and making the error zero.

[mikgigs]

what means x with dot? Why suddenly A, B and C appears? Why suddenly an exponential function appears! BS guys! The worst Kalman filter presentation.

[totoxahc]

At 6:20 why are you saying that A and B matrices of both models are the same? I always see this in observer explanations but we know it is not true. Edit: I forgot C matrix.