Special Topics - The Kalman Filter (19 of 55) What is a Variance-Covariance Matrix?

[@johnktejik9847]

Crying with happiness that I finally found a concise, common sense explanation of what a covariant matrix is

[@jorgearagon8053]

Same dude

[@gzitterspiller]

The notation is wrong, be careful, the nondiagonal elemwnts are Oxy not Ox*Oy. He wrote it like a multiplication and it is not like that.

[@Venuscat007]

@@gzitterspiller You are right, but the result is the same. The multiplication of two "square of N"s result in N in the denominator. and the numerator will be the same as well.

[@ElPikacupacabra]

@@Venuscat007 That's wrong. For the top part, it doesn't work.

[@marshall7253]

superman, i've never been more grateful to youtube in my life till i found your kalman series. you totally demystified the boogie man. Thank you.

[@ezasokotela7523]

Boogie man....I know right. Hehehehe....

[@EvilSpeculator]

I'm basically spending my summer working myself through this lecture series. So much fun.

[@anneoni691]

You are an amazing teacher. You are blessed! I'm impressed by how you could explain this technical concept with simple english. Thank you for blessing us with your gift.

[@MichelvanBiezen]

Thank you! 😃 Glad you find these videos helpful.

[@ezasokotela7523]

Thank you so much sir for the down-to-earth explanation of covariance and variance! What an amazing presentation of abstract concepts! Hats off!

[@cabdolla]

Hi Michel, great videos. Id like to point out an error at 2:35. You said that the variance squared would be what we expect almost 100% of the values to fall into that range. Consider the case where the variance is 1. Then the variance squared is still 1. We expect 100% of the variance to fall within 6-sigma, which is 6. Not 1. What you said only holds true if sigma >1

[@MichelvanBiezen]

+cabdolla You are correct. Thank you for the input.

[@loveforsberg530]

To the top!

[@andreastroster285]

Actually this makes no sense at all. If x is measured in some physical unit such as e.g. meters, then the standard deviation has dimension meters, whereas the variance has dimensions meter^2. A numerical comparision of variance and standard deviation is meaningless.

[@ayenewyihune]

Good point, I was wondering how

[@thanhbinhdo6290]

I cant stop to watch all of your 55 lesson at once. I compare your explanation with mine and it is really good.

[@MichelvanBiezen]

Do you have your explanations on video or in writing?

[@thanhbinhdo6290]

@@MichelvanBiezen I just write a small document for my group. We use it in the calibration of our robot 's odometry. I have a question, normally I consider H is observation Matrix this mean y_k= H.x_k +z_k. And z_k ~N(0,R). Normally each element of R represents respectively the variances of the observations. For example if y_k=[y_k1,y_k2,y'k1,y'k2 ] then R= mat(4*4)= R_yk1_yk1 R_yk1_yk2 R_yk1_yk1' R_yk1_yk2' | | R_yk2_yk1 R_yk2_yk2 R_yk2_yk1' R_yk2_yk2' | | R_yk1'_yk1 R_yk1'_yk2 R_yk1'_y1' R_yk1'_yk2'| | R_yk2'_yk1 R_yk2'_yk2 R_yk2'_yk1' R_yk2'_yk2'| In your video, I saw that y_k = C.x_k+ z_k Is that the same or different? Thanks a lot for your helpful video with clear block diagram.

[@MichelvanBiezen]

I think it depends on the application, but I would say that is probably the same.

[@hemantyadav6501]

because of you sir we fellows now know what is kalman filter.

[@LaRadical]

Dar un "pulgar hacia arriba", no expresa, cuán satisfecha me siento al ver estos videos. Muchas Gracias! Giving a like, it´s not enough to me, to express how much satisfy I feel with these videos. THANKS YOU A LOT!

[@MichelvanBiezen]

Your comment is very much appreciated!

[@nadekang8198]

The best lecturer with 0 dislike!

[@anaibrahim4361]

where have you hidden all that time sir what a rekief after all that time jumpnig from a video to an other finally i found the cure and the pure solution to what i was struggling about thanks

[@MichelvanBiezen]

Glad you found us.

[@s.s.sithole8102]

wow the video is clear and amazing you are a lifesaver chief

[@MichelvanBiezen]

Glad it helped

[@TinhNguyen-om6yg]

Thanks so much professor for this series!

[@miliandmichaelstangeland5327]

Variance is broader (bigger) only if the standard deviation is > 1, which is not always the case ;)

[@MichelvanBiezen]

That is correct.

[@gencalicicek9528]

awesome ! Thanks a lot sir. We are waiting the next :)

[@gojakangas1]

Enjoying the videos. Very clear! But I think SIGMAxy is a better notation than SIGMAx SIGMAy, because it looks like a product when it is not....

[@MichelvanBiezen]

Yes, I have seen both notations. There are advantages to both

[@absurdengineering]

But… it is a product! Look carefully. Sigma x has sqrt(N) in the denominator. Sigma x times Sigma y gives N in the denominator. The sigma xy notation is shorthand for exact notation sigma x sigma y. Covariance matrix can be obtained by multiplying two standard deviation vectors together (one of them transposed).

[@kalapriyan]

Nice playlist on Kalman Filters. I have an observation to make. It is implied in this video and subsequent videos that σₓσᵧ is covariance. But cov(x,y) = σₓσᵧ only when random variables X and Y are 100% correlated.

[@timdahealth]

전공 공부중에 헷갈리는 개념이 있어서 들렀습니다. 강의 정말 잘 들었습니다. 감사합니다.

[@MichelvanBiezen]

Glad it was helpful to you. 🙂

[@yahiafarghaly7472]

thank you Dr for the great lecturing

[@qianhuisun814]

Great teaching and really helpful!

[@hemayatullahziarmal4694]

love the explanation thank you so much.

[@jairam2788]

Thanks for explaining statistics 🙏

[@MichelvanBiezen]

Happy to help

[@hayfahvytsen]

Great explanation!

[@juancarlosr.h.2853]

hello Professor. Excellent and very clear video! Question: I've learned that the division is by n-1, but you use just n. Why? Best regards

[@MichelvanBiezen]

You divide by n is you are dealing with the entire population and you divide by one if you are only using a sample of the entire population

[@romitjivani4367]

Your videos are so helpful, thank you so much!

[@MichelvanBiezen]

Glad you like them! 🙂

[@Torvald80]

[sigma]x[sigma]y is not the same as multiplying the standard deviations together, because covariance may be negative (this is mostly a not for myself).

[@moonyounglee7546]

great intuition once again. I'm amazes

[@MichelvanBiezen]

Thank you!

[@whabw1999]

great explanation ,thanks

[@patricksampaiodossantosbra7259]

Genious explanation

[@bouthaina7846]

thank you so much, could you please do a course about principal components analysis (PCA)!

[@ma888u]

There could be a little bit more explanation during the video about the practical use for one of the recent examples (falling stone, car movement, etc.) to better understand the meaning for the kalman filter

[@andrewkelley8196]

Writing the covariance of x and y as sigma_x sigma_y is misleading, I think, because sigma_x sigma_y looks like the product of the standard deviations. If you want to use sigma rather than Cov(x,y), then I think you should write only one simga.

[@darshuetube]

where do the degrees of freedom or sample vs population come in here? should it be N-1 or N-2 for the covariance since we have 2 means?

[@MichelvanBiezen]

We have a playlist on variance and covariance that describe the details: COVARIANCE AND VARIANCE

[@awadelrahman]

is the covariance of two variables equal to the multiplication of the standard deviation of each variable? (sigmaX)*(sigmaY)? Thanks for the valuable illustrations!

[@OttoFazzl]

No, you cannot just multiply standard deviations to get the covariance.

[@loveforsberg530]

The notation does suggest that, which is why it is questionable. I would denote it by double indicies instead.

[@1bzoro206]

thank you very much Dr., what does the name of the refrence you depend on?

[@MichelvanBiezen]

I didn't use any particular reference, since I couldn't find a good one, so I developed this myself to enhance the understanding of the KF

[@elchill684]

Brilliant

[@andrewvirtual]

Beautiful explanation. Keep up the good work

[@MichelvanBiezen]

Thank you!

[@absurdengineering]

Variance is covariance of the variable with itself :)

[@MichelvanBiezen]

Thank you

[@brilianto98]

is variance-covariance matrix initialized first and will it be constant for every iteration?

[@MichelvanBiezen]

In most applications, the matrix is updated with every iteration

[@brilianto98]

@@MichelvanBiezen Thank you for your answer sir, does it mean the covariance matrix updated depend on it's updated measurement?

[@MichelvanBiezen]

Yes it does

[@SuperKreyszig]

I will donate money to you as soon as I can, meaning when I get a job :)

[@meryemnaseerqureshi7691]

Thank you for this. Amazingly explained :)

[@MichelvanBiezen]

Glad it was helpful!

[@ahmedmahdi8580]

thanks pro this is what i need exactly

[@MichelvanBiezen]

+Ahmed Mahdi Wow, you are watching all of them. Enjoy!

[@ahmedmahdi8580]

+Michel van Biezen : hello pro , I am wor;king on a robot project and I need to understand the Kalman filter , thank you so much.

[@airblue5312]

Thanks a lot

[@RESC_Eng]

I hope you to be muslim , you may rewarded just from god because of this great job (teaching ) , you are change the world to be a better place by this knowledge , I took a look on your channel , it is imaginary , wow it is an amazing channel with a great person . Thank you so much , I wish you to be muslim .

[@darkyodd]

Michel van Biezen, I turned adblock off just for you, bro

[@MichelvanBiezen]

Thank you.

[@ernest987987]

Same here very nice, althought I'm looking forward to the more complexe stuff :) (Always very good to provide this refresh though)

[@Surftech09]

Have you done stuffs like tracking face in a video using k.f in the past? using matlab?

[@ernest987987]

+sonic sonic I haven't unfortunately. I use the Kalman Filter mostly in Economics and Finance application, to estimate latent processes and stuff, with Matlab. So I'm not that advanced :) Sorry

[@Surftech09]

Prof. can you please show the 4 by 4 arrangement of this ??

[@MichelvanBiezen]

+sonic sonic When I have some more time, I'll put a multi-dimensional example together and an extended Kalman Filter example as well. Right now I am working 3 jobs and have little time for it.

[@Surftech09]

+Michel van Biezen yes you actually said how busy you are the last time. three more question prof. when tracking a human face in a video, (1)how do you get the initial values for for variance and standard deviation? (2) where does the values for measurement come from? or rather on what basis do you assume values for measurements y? for instance when implementing it in matlab. (3) what should be taken into account when assuming the values for initial position both for x and y position. these three questions will go a long way in my project. thanks

[@alirezapakdaman7397]

Hello, I looked to another literature and there , the is defined as follows ( N-1 instead of N in the formula) ci.columbia.edu/ci/premba_test/c0331/s7/s7_5.html

[@MichelvanBiezen]

Yes, there are differences in the notation used, and it depends on how it is defined. In the end, it makes no difference and it comes down to what you are used to.

[@elirox100]

N-1 is used for estimating from a sample, so we really should be using it here

[@OttoFazzl]

In practical applications with large samples, N - 1 and N converge rather quickly. But to be rigorous, yes, N - 1 is the way to go.

[@fishermanwithfishes2286]

This is why my lab should pay for my Matlab license and KZbin premium.

[@nwsteg2610]

It is better to write \sigma_{xy} for the covariance rather than \sigma_x\sigma_y. The product of the standard deviations is not equal to the covariance!

[@MichelvanBiezen]

Thank you for the feedback. Yes we realized afterwards there are some inconsistencies here, so we made a new series on explaining the variance and covariance matrix.

[@nwsteg2610]

@@MichelvanBiezen Thanks for all your great content!

[@codyheiner3636]

Careful, the discussion of the relationship between variance and standard deviation is very wrong. Standard deviation tells us precisely how much data is contained within a distance from the mean. Variance is simply the standard deviation squared, and tells us nothing about how much data is inside that range. Simple example: std = 1, so variance = std and the same amount of data is inside the variance as the std. If std = 100, then the variance contains 100 standard deviations worth of data (almost all). If std = 1/100, then the variance contains 1/100th of a standard deviation of data (very little). TLDR: The variance is simply the standard deviation squared, don't get trapped into assuming more than that.

[@ElPikacupacabra]

You forgot a correlation coefficient for the off-diagonal terms in the covariance matrix. Otherwise, a nice sequence of videos.

[@MichelvanBiezen]

Thanks for the input.

[@berndlucke1968]

You souldn't write the covariance of x and y as sigma_x sigma_y! This suggests that it is equal to the product of the standard deviations. This is only the case if x and y are actually the SAME except for a shift of the mean value. If they are to independent random variables the covariance will be 0. You really sould write sigma_xy!

[@ПавелНазаров-я1п]

Agreed. Also there must be 1/n before the summ on the right hand side

[@rabiulislamsikder344]

Why life is so simple?

[@MichelvanBiezen]

This is from a friend of our, "Life is simple, but it's not easy."

[@imakill99]

sta302 unite