Special Topics - The Kalman Filter (10 of 55) 4: The Control Variable Matrix

[@meshackamimo1945]

no words to appreciate the good job u have done. honestly, no one like you in exclaining the basics of kalman filtering. thanx a million times!

[@FreeMarketSwine]

I've been reading about this for a couple days and this tutorial is so much better than anything I've seen so far. It's greatly appreciated.

[@MichelvanBiezen]

Glad it helped!

[@gotbread2]

Your Kalman filter explanation was one of the reason i passed a control theory exam. Thank you for your good work!

[@EvilSpeculator]

Congrats!

[@jorgwillems5133]

I am already retired for many years, and now I finally know what is in the "Kalman Filter Black Box." Thank you very much!

[@realitytx]

I feel exactly the same way. I wish I saw this when I started working in navigation.

[@mustafaeid2705]

@@realitytx I started working in Navigation now, all I knew during my studies was LS, felt amazing watching this and knowing what each variable stood for instead of looking back at the documentation at each step. Amazing work, thanks @michelvanbiezen

[@xiyun6281]

From one teacher to another, this is incredibly well explained. I've rarely come across such quality content. Also, love the bow tie.

[@MichelvanBiezen]

Thank you for the comment. We appreciate it.

[@ZottelMD]

i could write it below every video of your kalman series. you did / doing a fantastic job in explaining difficulty things. perfect speed ! perfect voice ! perfect pronunciation ! perfect acoustic ! perfect panel paintings and charts ! ..... it's so incomparable easy to follow you and to get what you want to be to get. best video series in complicated background topic i've ever seen ! thank you very much a million times as well ( german master course studend in electrical engineering who's absolutely not fit in english (so even more worth to appreciate it ) )

[@AliTAfnid]

This is without doubt the best and complete tutorial on Kalman Filter on YT.

[@MichelvanBiezen]

Thank you. Glad you like our videos. 🙂

[@Surftech09]

i have never seen a teacher as good as you in my entire life. maybe i have been unfortunate. How best can i say thanks to this teacher.

[@MichelvanBiezen]

+sonic sonic You already have. I appreciate the feedback. Glad to give back to the world.

[@Surftech09]

Thanks alot... I'm actually working on kalman filter based face tracking in video. I sent you an email earlier

[@romitjivani4367]

Best Professor in the World. my Fav. Prof.

[@MichelvanBiezen]

Thank you. Glad you think so. 🙂

[@dovilenoreike4218]

I wish I have this teacher for other topics as well.. Million thanks for your efforts!!!

[@nguyenthanhdat93]

Best explanation ever... I greatly appreciate your wonderful work!!!

[@dssrkanth]

One of the best lectures I ever attended. Appreciate it a lot

[@MichelvanBiezen]

Glad this helps to demistify the Kalman Filter.

[@cosmokannada9655]

Respected Sir, Thanks a lot. Your videos helped me a lot in understanding kalman filter. May god bless you with good health.

[@andruha1067]

Love the short video format. I can learn a topic in 5-10 minute increments which is seemingly the longest stretches of free time I have being a parent. Lol.

[@RESC_Eng]

Thank you so much // this is a unique demonstration about KF // as there is no sufficient resources to get the same knowledge that you have .

[@MichelvanBiezen]

Glad it was helpful!

[@RESC_Eng]

@@MichelvanBiezen I hope after this series to be able to use these equations with matlab and go a head with mobile robots 😁😁

[@AmitaKapoor]

A very good explanation, Specially the examples make it very clear. Thanks

[@lokeshwar4093]

its ruin my whole semester finally I understand black box of Kalman Filter

[@sakuranooka]

Why is the top entry of B equal to dT^2/2? If x(t) = x0 + x' t + x'' t^2/2, it follows that dx = x(t+dT) - x(t) = x' dT + x'' dT t (after removal of the very small dT^2 term). So, shouldn't the top entry of B be dT t?

[@israrkhattak6297]

Very nice detailed explanation...your method of explanation forces me watch all 55 clips...Great job! I just want to add...may be helpful. New velocity is calculated using motion equation Vf=Vi+at (in above example Vi is previous velocity and Vf is updated velocity and t is "delta t" i.e. a small amount of time

[@a3igner]

Thanks for explaining it so well! Very easy to grasp!

[@hariprasanth764]

One doubt, for the first example, the rising fluid, why the control variable is zero, not negative gravity, since it is accelerated against the gravity??

[@santiagoinigo5045]

Again great class! Very good explanation!

[@martintorres5829]

Muy bien explicado el calculo de cada matriz y la relación con la ecuación que describe el proceso. Tengo la duda de, ¿que ventaja tenemos en no agregar la señal de aceleración en la matriz A? tal vez es porque asumimos que es una señal de control y no una medición propiamente dicha

[@klausrtmr]

That explanation is extremely good, but I have one question: Why do we need the matrix B and vector u? Why don't we integrate that into A and x? Then x would be [y; y_point; y_point_point] and A would be [1, delta_t, 1/2delta_t^2; 0, 1, delta_t; 0, 0, 1] Does it depend on on the measurement variables we have, or on the output variables we need?

[@wozzinator]

I actually came to ask this exact same question!

[@EmptySpace0]

I'll agree with this. If it's in your A matrix than you can easily grab acceleration out of the third state In the end, its just a different way to setup the model. Potato Potato type of thing

[@mikesmusicmeddlings1366]

is the reason that u_k is indexed at k instead of k-1 because the acceleration is assumed to always be constant? Same for the noise? so u_k = u_k-1? Thanks for the lecture!

[@adiai6083]

very nice explained...superb

[@MichelvanBiezen]

Thank you. 🙂

[@ericpage369]

Excellent explanation! I really appreciate the time you've taken to make these videos. For the falling object example, could you have made the state matrix 3-dimensional to include the acceleration and avoid having to create a B matrix?

[@MichelvanBiezen]

+Eric Page The B-matrix is made for that purpose. I will show a multi-state example in the near future.

[@simonclemente]

If I want to apply kalman filter for rssi values (they are dBm), do I need to apply this for one-dimensional matrix? I think that I only need one dimensional matrix because after this, I would convert that values to distances. I'd appreciate if you answer my question. Thanks

[@jorgerive7335]

Excellent video series....good job. You are a great teacher. I had no problem with the derivation of the A matrix on the previous video. However, i'm not sure why the B matrix looks like it does --in particular the delta-t term at location (1,2) in the matrix. Can you expand on how that comes to be? I expected the B matrix to just be the 1/2*(delta-t)^2. Thanks!

[@slimxiedy]

Kinematic equation for position: position = previous position + (velocity * change in time) + (1/2 change in time squared * acceleration) Kinematic equation for velocity: velocity = previous velocity + acceleration * change in time Why we use A: if we're looking for some constant A times [ position, velocity ] to calculate position and velocity then think about what we need to do to position and velocity in the equations above. We need 1*position to calculate position, and the change in time * velocity to calculate position. We need 0*position to calculate velocity, and 1*velocity to calculate velocity. Hence [[1, change in time] [0, 1]] for A. Why we use B: if we're looking for some constant B times [acceleration] to calculate position and velocity then think about what we need to do to acceleration in the equations above. We need 1/2 change in time squared * acceleration for position, and then acceleration * change in time for velocity, hence B = [1/2 change in time squared, change in time]. Hope that makes sense

[@MrSerozka]

My like was 800!) Excelent lessons, thank you!

[@godspeedyou]

Hi Michel, First of all I would like to say, awesome videos! I really like how you explain the kalman filter step by step and make it so easy to understand! Secondly, I have a question, in your examples when you model falling object/moving vehicle, why do you put the acceleration in the Bu_k term instead of the AX_K-1 term? Thanks! Aaron

[@MichelvanBiezen]

That is just the way the KF is formulated, by separating the velocity and acceleration into 2 separate equations and matrices.

[@godspeedyou]

I see. But would it still work if you put everything into the first term A X_k_1 ? i.e for X_k you are keep track of 3 things position velocity and acceleration ?

[@MichelvanBiezen]

I haven't tried that. It would be interesting to see if it would. I don't think it would work, but I'll hold my judgement, until I see it worked out.

[@nishantvpatel7976]

greater explanation sir

[@MichelvanBiezen]

Thank you. Glad you found our videos. 🙂

[@nishantvpatel7976]

@@MichelvanBiezen the way you sir explaining each and every steps with details whether its 3 phase system kalman filter or any other topics. Its Phenomenal.

[@MichelvanBiezen]

Thank you. It was the only way to make sense on how the KF works. 🙂

[@mohannadaldakhil9068]

Great explanation :)

[@afiqyahya3398]

Coming from non-engineering background, how do you construct the B matrix? why the 0.5 first?

[@RahulNair-r4h]

Thank U so much Sir!!

[@MichelvanBiezen]

Most welcome!

[@parthi2929]

Why previous position neglected in constant acceleration model, that is B? It should be | 1 (1/2)(delta_t)^2 || x_prev | | 0 delta_t || a | Shouldn't it? Can some one please explain?

[@parthi2929]

Got it. It is already included in A

[@mojiheydari]

So great seri

[@luanguyenthi2115]

Excuse me! I have a problem. Can you help me? I have a data of aeromagnetic. I want to use the Kalman filter but I don't know how to determind the A, B matrics. Can you show me, please? Thank you so much!

[@MichelvanBiezen]

Take a look at the other (multi-dimensional) videos to see if that helps you figure it out. Essentially the matrices are determined such that when you multiply them with the control variable matrix you get the variable on the left side of the equation, (the variable you are trying to keep track off).

[@ahmedmahdi8580]

it becomes more easy

[@saswatibhattacharjee7387]

can any one give me a real data set to implement kalman filter?

[@redjr242]

I'm a little confused. Why does the acceleration need to be separated? Could you not do: |1 dt dt^2/2| |x| |0 1 dt | * |v| |0 0 1 | |a| in one step???

[@MichelvanBiezen]

That is how the Kalman Filter was devised. If you look at the examples you can see why it works.

[@redjr242]

Michel van Biezen Okay. But could it be done with a single 3x3 matrix instead? It seems simpler.

[@MichelvanBiezen]

My answer usually is: Try it both ways and see if you get the same answer.

[@redjr242]

Fair enough. Thanks for taking the time to respond. These videos are excellent :)

[@maheshpadmanabh6564]

why is the B matrix for rising fluid = 0? shouldn't it be -g ?

[@HimothyOHooligan]

The fluid isn't in free fall.

[@maheshpadmanabh6564]

Thank you for your swift reply sir. I thought the force acting on the system should be considered. Whereas it's just the net acceleration.

[@mysnapshotdiary]

GOD SENT!!!!

[@MichelvanBiezen]

Glad it was helpful. 🙂

[@JohnDemetriou]

What if the acceleration is also uknown?

[@MichelvanBiezen]

The acceleration can be calculated from knowing the position and the velocity over time.

[@JohnDemetriou]

But isn't the whole goal here to estimate the position?

[@Indraneel-Ahluwalia]

Thanks But did not understand why B matrix has 1/2daltaT on top and not the bottom

[@EvilSpeculator]

Easy - see here: screencast.com/t/eQQkNTIz5YUc screencast.com/t/H3A0krxArYtK Clear now?

[@evrenbingol7785]

yeah but why the first derivative on top and not bottom? X Matrix(vector) has the (X on Top and X(dot) ) buttom. So if X is location its next derivative is at the bottom which is velocity(x dot) So in case of displacement first derivative should be on top which is velocity and second should be in bottom which is Acceleration. Fi we stick to the order. Or it is because of Matrix multiplication. ?

[@Junaidalvi-ut5ki]

I cant understand the B matrix in relationship to the equation.

[@Leo31Par]

It is a "dynamic equation" not "kinematic equation"!

[@shengwencheng8040]

dynamic is about the Force, and kinetic is about how the object move or where is the object

[@Jetcodelab]

The amount of joy i got when i finally understood this i cant thank you enough, i have struggled with so many tutorial 🥲🥲🥲🥲

[@MichelvanBiezen]

It is indeed difficult to find material on the KF that is understandable. Glad you found our videos. 🙂