Optimal State Estimator Algorithm | Understanding Kalman Filters, Part 4

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
Discover the set of equations you need to implement a Kalman filter algorithm. You’ll learn how to perform the prediction and update steps of the Kalman filter algorithm, and you’ll see how a Kalman gain incorporates the predicted state estimate (a priori state estimate) and the measurement in order to calculate the new state estimate (a posteriori state estimate).
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.

[@darthvador6768]

This is amazing, it makes Kalma filters so much easier to understand.

[@anshumansharma6758]

Oh! the drag Kalman filter was in my life, and the satisfaction videos 2 and 4 of this series have given me are unimaginable.

[@MrAnna1406]

This is such a good series by MATLAB. Thanks alot. A video about Multisensor data fusion for LiDAR, Ulrasonic and Infrared with the help of Kalman Filter implementation for Ranging Application in MATLAB/Simulink would be helpful alot.

[@thorsten9211]

What if we turn everything upside down? Doesn't change much, does it? - Best laugh of the day :D Great Videos!

[@passoswell]

A video about system identification using the Kalman filter would be great.

[@NathaliaK.QuinteroGomez]

thank you so much for these series of videos, helped me a lot to finally understand the Kalman Filter

[@lomef3308]

Thanks a lot! quite useful and easy to understand! looking forward for EKF!!

[@fusionlabs6215]

Best series I found on Kalman Filter. Love the sense of humor too.

[@mingjiezhao44]

The series videos are sooooo good! Thanks for your work!!!

[@andruha1067]

Error Alert at t=5:30.They accidentally swapped a minus for a plus when substituting 1/C for K, which if left as is would result in x_k = 2*x_k(pred)+ y_k.

[@jpstang]

Wow! So much easier to understand Kalman Filters by listening to your video, than reading chapter 6 on State Space Models, in Time Series Analysis and its Applications by Shumway and Stoffer.

[@Khashayar-qy7it]

The best explanation I have seen so far!

[@bryankerr6725]

You wanna win the big prize right?

[@tmd4951]

LMAO

[@Reed81315]

Literally came here to make that same comment

[@engineeringoyster6243]

Nice video. Generally very practical. However, you ignore the topic of how to define the matrices Q and R. You say very broadly what they are. But, thru Part 4 of this video series, it is impossible to know how to calculate either matrix.

[@robegatt]

Exactly, all these videos they start great then they get lazy and throw stuff in... damn.

[@camilogarcia9459]

best video ever for understanding Kalman Filter

[@S25plus]

After 6 years, good works still stand.

[@emilianotca]

Thanks for the amazing explanation!

[@asifnizamani7513]

What a lovely explanation

[@PeekPost]

superb explanation, well done

[@vincentporras1459]

These videos are excellent!

[@tedchou12]

I like how she tries to put a sense of humor into this serious stuff.

[@robegatt]

she is just reading something some nerd wrote

[@samisuraj]

thanks for the effort

[@saharkhawatmi660]

Very nice explanation

[@borderlandsgamer9001]

I think at 5:43 the sign for Cx_hat- (the last term of the equation on the second line) was erroneously flipped to "+". It seems to cancel a + term later too so I'm think it should've stayed "-".

[@traviskeller340]

agreed

[@beoptimistic5853]

kzbin.info/www/bejne/ppK5gHifbMiMqKM👍👍👍👍👍💐

[@tomasfranco4870]

think so too

[@kirar2004]

agreed!

[@andrewschroeder4167]

I thought I was going crazy for a moment until I realized

[@CarLos302DaviiD]

I love this Videos Thanks!!!

[@RudradeepMukherjee]

Thank you for the video. They are concise and helpful. Can someone let me know, how these animations within video are created? Could be helpful for broader teaching purposes.

[@stekim]

perfect video for 4am studying

[@dshong8139]

awesome lecture

[@akarshjain2277]

Really excellent content

[@huso7796]

When will the next part about Extended Kalman Filters be released? By the way very useful and informative videos!!

[@meldaulusoy8389]

Hi Huso, Understanding Kalman Filters, Part 5 - Nonlinear State Estimators video will be live next week.

[@user-pe5qr9hv6n]

🤣🤣🤣🤣🤣🤣🤣🤣🤣The most funny and Educative video Thanks you made my day

[@salehaboali1642]

You should've sent it to me then 😂, I just understood what sensor fusion is

[@ChicagoBob123]

Would like to see a series on coding a filter.

[@umitaglar3738]

This is amazing

[@prabhusrinivasan676]

Could you please tell me what is the purpose of using identity matrix (I) in the kalman filter equation?

[@xiangli9963]

There is a wee typo in the video, say, limiting the R approaching the none, and will cancel the prior state estimate. The sign should be plus rather than the minus.

[@stonemannerie]

In the formulas appearing at 5:30 shouldn't it be "... - C\hat{x}_k^-)" and "... - C^{-1}C\hat{x}_k^-)" (the difference being the minus instead of plus symbol)?

[@rzwnhmd]

what is the matrix Pk(prior) with the minus sign to it describes here. What is it called?

[@josephlatham3779]

One thing I am confused by is that it seems like between the equations for the predicted estimate covariance matrix (P-), the Kalman gain matrix (K), and the updated estimate covariance matrix (P) that the Kalman gain will have a pre-determined trajectory, which feels odd. Seems like it should be affected by the feedback error in some way.

[@indranilghosh56]

what advance mathematics topic one must cover to understand these equations??

[@jorgejaramilloherrera4411]

In 5:35, ¿shouldn't the equation result as: xhat_k = 2xhat_k predicted + y_k?, because the value of C=1, and inverse of C =1 too...

[@thomaswynne6688]

it looks like an error in the sign of C*xhat_k predicted after the distribution of K_k. The K_k should be distributed in the multiplication without a change in the sign. So, it should read: xhat_k = xhat_k predicted + (K_k)( y_k - C*xhat_k predicted) xhat_k = xhat_k predicted + (K_k)y_k - (K_k)C*xhat_k predicted xhat_k = xhat_k predicted + (C^-1)y_k - (C^-1)C*xhat_k predicted *the (C^-1)C cancels and the (C^-1)y_k is effectively just y_k which leads to: xhat_k = xhat_k predicted + y_k - xhat_k predicted therefore: xhat_k = y_k **they mess up the signs a good bit. the previous part had corrections all over the place.

[@nicksklavos]

I forgot to transfer the minus

[@hanlovciss2944]

how do we know the covariance of measurement R? and initial covariance of Xhat?

[@kanishkjain7137]

At 1:39....I think in the state observer equation ....it should be y(k+1) instead of y(k) and also u(k+1) instead of u(k) and also Cx(k+1) instead of Cx(k). Correct me if I am wrong

[@tiffany33094]

Why is the State Observer allowed only the previous state estimate, the previous input, and the previous measurement to estimate the current state WHEREAS the KF is allowed the previous state estimate, CURRENT input, and CURRENT measurement?

[@TotallyNotARobot__]

Great. When will the next video be available? Thank you!

[@meldaulusoy8389]

Hi Ali, Understanding Kalman Filters, Part 5 - Nonlinear State Estimators video will be live next week.

[@TotallyNotARobot__]

great! I liked your videos. We will teach a class next fall on dynamic systems and I loved your approach. Keep up the good work!

[@SaeedAcronia]

What if I have only one shot? Should I still be using this method?

[@ridewithserhat]

Thank you for the nice video. At 5:32 how do summing the two x hat_k are cancel each other? They are on the same side of the equation? And both of the x hat_k are "+". One of them should be "-" for the cancel each other?

[@zhangjianfei8081]

It should be an error in the video, the back one should be "-".

[@Eragonfan100]

Hello I have a question concerning the process noise: If I have a distance signal which can change at maximum 5 mm between two measuring points, can I use those 5 mm as process noise? Or did I understand it wrong?

[@robegatt]

You should use 5^2 because if your standard deviation is 5 the variance is 25 in the R matrix.

[@dzimi2233]

Why C^(-1) is equal to 1 in our system? Is it true for every system?

[@jamesaddison81]

Is the predicted state not generated from the IMU? And then the measurement is from the GPS? Or do you use the velocity to predict then the measurement is from both the GPS and IMU?

[@robegatt]

They just double the equations without telling how to mix the values.... that is their "fusion".. duh.

[@HamzaHajeir]

Is it a form of IIR filter?

[@sohamkamat2326]

@MATLAB I'm using an IMU which has an accelerometer as well as a gyroscope and I am double integrating the acceleration data to get distance. should I be using sensor fusion to do this? or can i achieve this using only accelerometer data with a kalman filter?

[@emmanuelrodriguez2346]

At the end what you used?

[@TheMechatronicEngineer]

@@emmanuelrodriguez2346 nothing

[@robegatt]

@@emmanuelrodriguez2346 he just went to sleep

[@TheRosyfancy]

I got confused by this: At 1:40, for the state observer, should x_hat (on the left of the equal sign) have a dot on top? That's what it is in the previous video, no?

[@robegatt]

They abruptly change from continuous domain to discrete steps.

[@tiffany33094]

7:04 why does she say x_hat_k depends on the "error covariance matrix from the previous time step"? Isn't P_k_minus of the CURRENT time step?

[@tiffany33094]

Ah I understand now. She's referring to P_k-1 instead of P_k_minus

[@bottleneck123]

Why did she say the standard deviation of normal distribution as covariance?

[@sawangoyal9069]

I am confused about predicted distribution and measurement distribution. I think they should be interchanged, since in prediction we are using a mathematical model which does not take into account any external errors. On the other hand in the equations of actual measurements there is an error term due to winds and other external issues.

[@robegatt]

I think the point is that the predicted distribution narrows and shifts to the real value using the measured data that have a fixed distribution and is a little off every time.

[@eggonlyegg]

Spending $1m award on some extra sensors sounds like a horrible idea. I love this series of videos though.

[@Richard-vj3vs]

Theres a typo at 5:30 where C⁻1*C*xHatk⁻ should be negative

[@ihabassoun9917]

That is true. I had the same remark

[@delcapslock100]

I wonder if Kalman Filters can be applied to estimating whether a youtube video will force you to watch an advertisement or not. I watched this whole series without having to skip or mute a single commercial.

[@kabascoolr]

Yes. The Kalman filter is a tool. With enough "massaging" you can make it solve very complex problems in novel ways. But the question often is, is it the best tool for solving such problem? KZbin has 300 hours worth of videos uploaded to it 60 seconds. Analyzing such data can be mind boggling. Likely machine learning may be more useful.

[@emotionalmindedstate]

What if you dont have correct current state? What if you dont have predictions?

[@Martin5599]

2:00 Previous time step + current input... does it make sense?? shouldn be rather - Current state = previous state + previous input... same is Next step = current state + current input... So this is really confusing ..

[@robegatt]

previous state is multiplied by A it is not just previous state

[@yashsingla5491]

why you have ignored noise in this equations ?

[@edwardcox7169]

thats what variance is, a measurement of noise

[@jaydenthomas2842]

at 5:32 the signs get flipped

[@imignap]

Gd'it yes I want the big prize!!

[@mariuspy]

2:49 It does look scary

[@AJB2K3]

um when you turned it upside down I read Pk=(I-KkCP)P as P.R.I.C.K! Damn, my head hurts

[@Mr.Tiger.2013]

Ah...now I know where the X model derived from

[@emmanuelameyaw6806]

Did anybody win the competition?..:)

[@alborzjelvani]

I wanna win the big prize

[@edwardcox7169]

a sensor costs 1 million dollars? O_o Let's stick with cameras