Optimal State Estimator | Understanding Kalman Filters, Part 3

Download our Kalman Filter Virtual Lab to practice linear and extended Kalman filter design of a pendulum system with interactive exercises and animations in MATLAB and Simulink: bit.ly/3g5AwyS
Watch this video for an explanation of how Kalman filters work. Kalman filters combine two sources of information, the predicted states and noisy measurements, to produce optimal, unbiased estimates.
Download code to explore the example shown in this video: bit.ly/2QbbFOt
The example introduces a linear single-state system where the measured output is the same as the state (the car’s position). The video explains process and measurement noise that affect the system. You’ll learn that the Kalman filter calculates an unbiased state estimate with minimum variance in the presence of uncertain measurements. The video shows the working principles behind Kalman filters by illustrating probability density functions. You can create the probability density functions discussed in the video using the MATLAB script provided in the Controls Tech Talks repository (please see the link above).
Check out additional resources:
- Download examples and code - Design and Simulate Kalman Filter Algorithms: bit.ly/2Iq8Hks
- Kalman Filter Design Example: bit.ly/3a0nLWs
- Design and use Kalman filters in MATLAB and Simulink: bit.ly/3i4VKwG
--------------------------------------------------------------------------------------------------------
Get a free product trial: goo.gl/ZHFb5u
Learn more about MATLAB: goo.gl/8QV7ZZ
Learn more about Simulink: goo.gl/nqnbLe
See what's new in MATLAB and Simulink: goo.gl/pgGtod
© 2022 The MathWorks, Inc. MATLAB and Simulink are registered trademarks of The MathWorks, Inc.
See www.mathworks.com/trademarks for a list of additional trademarks. Other product or brand names may be trademarks or registered trademarks of their respective holders.

[@cleansky6415]

you may also be interested in reading the paper "understanding the basis of the Kalman filter via a simple and intuitive derivation" by R. Faragher

[@JoseCLopez-bf7qu]

Very nice paper, thank you!

[@utkarsh-21st]

synapticlab.co.kr/attachment/[e-mail]

[@Sungjun0228]

Thank you

[@xicai2290]

The best KF explanation ever. Thanks.

[@Aviation437]

One of the best explanations I've seen. Good Job!

[@droxid666]

I have been waiting so long for this! Thank you, I love this module and the lecturer's approach.

[@pedropauloliborio]

Thanks for explain this in a graphical way. A lot of details, but now things makes more sense to me.

[@AbdulSamad-hd1sr]

simply short and detailed explanation .can realize the hard work behind this video.

[@mehmetnuriozdemir3933]

This video made my day. Best Kalman Filter explanation from a Turkish Woman Scientist. Proud.

[@anilkumarsharma8901]

Osteoporosis testing 〰curves 〰 are example of the most important thing in practical experience and natural nature of the nature🌿🍃

[@thanhcongai8478]

This video is very helpful. Thank you so much

[@jumabekalikhanov5237]

u guyz r the beast. keep amazing us with ur excellence

[@sergiorosales8658]

love your videos!

[@andrewjewett1056]

Great visual explanation! (Humourous cartoons appreciated)

[@Alhamdou_lilah]

hello i have a simple question please: why you didn't use the derivation of x instead of x(k) ?are they the same ?

[@miiirskiii]

Very nice! I love the example with the car.

[@awaisahmad5908]

best explanation thank you so much

[@piccio281]

Great video!! just a thing, I maybe wrong but, in the state-space model at 2:57 the output shouldn't depend on x(k-1) as we've indicated the future state as x(k)?

[@afthablamperouge8010]

I think the reason why it's not x(k-1) is because it doesn't make sense the output is a previous state. Generally the output is written in the form y(k) = Cx(k-1) +Du(k) which is equivalent to x(k). However, here it's just simplified to be y(k) = Cx(k) where C represents a matrix with the desired outputs and x(k) = Ax(k-1) + Bu(k) --> you can see this in the equation of the Kalman filter. At least that's what I think is going on.

[@TheLesly1990]

that was perfect

[@HamadaAlmasalma]

Really fantastic explanation :) When Part 4 will be published?

[@meldaulusoy8389]

Hi Hamada, Part 4 will be published soon. I'll be happy to let you know when the video goes live.

[@hassanjb83]

Please also let me know when Part 4 goes live. Thanks

[@a.n.7956]

me too. Can't wait to see the next video.

[@adrianaguzman5576]

I need to know about the developing of the algorithm asap hahaha. Hope it's already coming, it would be really usefull for the proyect I have to present.

[@adrianaguzman5576]

Also, thanks a lot for the video! Came in the perfect time :D

[@sathyanarayanankulasekaran1674]

Isn't it variance R, rather than Covariance R...for the Gaussian dist representing error

[@susanius]

Why x_hat is distributed? Doesn't we suppose that the mathematical model for x_hat is deterministic?

[@nicolenatsai]

I am a bit unclear on how the equations for x and y were derived, even carrying on from part 2. Please assist

[@parthi2929]

Shouldnt we differentiate by variable between predicted state estimate and optimal? Both are denoted by x_hat_k

[@meldaulusoy8389]

Hi Parthiban, please refer to the part4 video where we explain more on the notation and "a priori" and "a posteriori" estimates. The common notation for the estimate in the prediction part is represented by x_hat^- and the optimal estimate found in the update part is shown with x_hat.

[@RandomUser20130101]

What's the difference between "Car dynamics" and "Car model"?

[@RandomUser20130101]

1:54 Why does the input u_k change from the throttle to the velocity just a few seconds later?

[@ssljasontw]

Maybe throttle decides input velocity, and velocity's mathematical value is easier to use for this system.

[@siddhantjaiswal4231]

what is xk and yk. At 2:20 both are written as position???

[@garrettryan701]

Xk is what you would receive from a prediction matrix. In a simple constant velocity for x position that could just be x = previous x + v*dt. Yk would also be a position, but it is given to you by sensors. You have your predicted position you extrapolated from your previous state as well as the position the sensors gave you.

[@muthukkumarar2694]

shart and sweet

[@posthocprior]

In the previous video, the equations for the Kalman filter were transferred to an exponential distribution. That is, a distribution that doesn’t have to be normalized. In this video, pdfs are used and are multiplied together. This can only be done if the distributions are normalized. There is a large difference between a normalized pdf and an exponential distribution. With a pdf, you need enough data to find the true mean, in order to normalize the data. If you can’t, you can’t multiply the two distributions. So, this example wouldn’t work. My point, either the example of an exponential distribution should have carried to this video or it should have been mentioned which cases that this example can be used.

[@azezegizachew3713]

how to drive robustnuss of kalman filter

[@TheMechatronicEngineer]

R and Q are variances, not the covariances. Sigma is the standard deviation.

[@drangertornado]

What does x represent at 2:16 if y represents the position?

[@sebreens]

position is both the state and the output variable here.

[@samirelzein1095]

At 03:03 I dont know why you mentioned covariance to begin with It s just variance, no comparison here Even tho you brought it back by saying it s a single process later on, you cannot call it covariance first then say it s a particular case then variance here Just variance Just to avoid terminology confusion for students. Or what do you all think?

[@tanakaaiko-]

有中文字幕太好了

[@dumamayful]

Why in part 2, you compare x and x_hat, now you compare x_hat and y. it's confusing!

[@meldaulusoy8389]

Hi Tran, in part2 we're not really comparing x and x_hat but we try to explain that a state observer can be used to make the state estimate (x_hat) converge to its real value(x). You can think of a Kalman filter as a state observer, too. You still want to estimate states but this time you're also dealing with uncertainties and Kalman filter gives you the optimal estimate. The way it calculates this optimal estimate is that it incorporates both measurement and predicted state estimate. Part4 video explains more on the working principle of the filter which might give you a better understanding of how y and x_hat are used by the filter.

[@germankoster4910]

Isnt it just because both y(hat) and x(hat) are the same (both are position and C=1)?. So it would be the same to use y(hat) and x(hat).

[@giorgostsilivis6771]

here my project comes

[@alesnovotny7331]

I think, system should be described by equations: x(k+1)=Ax(k)+Bu(k)+w(k) and y(k)=Cx(k)+v(k) as a discrete state space model definition. This seems to me to be incorrect.

[@valeriuok]

Why is the car dynamics linear?

[@meldaulusoy8389]

Hi, here we assumed a linear system but in case you have a nonlinear one you can use a nonlinear state estimator. Please check out the part 5 video where we discuss nonlinear state estimators. For an example in Simulink you can also watch part 7 video where we use an extended kalman filter to estimate the angular position of a nonlinear pendulum system.

[@VysakhRemesh]

Is this the sound of Fei Fei Li?

[@Frankx520]

For some reason, it feels like quantum mechanics. My car is a probability wave and a particle at the same time.

[@sosyopolcom9559]

so do ı

[@alfonshomac]

does that voice teach at Columbia? intro to AI, maybe?

[@meldaulusoy8389]

No, I'm not teaching at Columbia:)

[@michaelsilverhouse2122]

it's very obvious that the voice is from Turkey :) a very nice job in part 3, Melda. really very teaching illustrations. looking forward to see part 4.

[@RatedA4Aliens]

@3:12 If you measured the position of the car - let's say a million times (not just hundred) at the SAME LOCATION, you will get the same result ;-]