Kalman Filter for Beginners, Part 1 - Recursive Filters & MATLAB Examples

[@JC-ns6io]

I'll sum up the video: "Just grab my hand and trust me, I'll show you the way to Kalman filter". Whereas my classes were more like "Just learn these equations, this is Kalman filter, trust me". Thank your Sir for making this concept very intuitive !

[@ProfessorRoss]

Thank you. My approach was to say, "Here are the basics of what the Kalman filter does, and here are the basic things you need to use it." Of course, if you want to know where the equations come from, a deeper dive into their derivation may be good. But not everyone needs that. For example, I can use differential equation solvers without knowing how they work -- and we do this routinely for simulations.

[@lukdasz]

This is exactly what I needed - a clear, easy to follow explanation starting with the basics. Thank you for posting!

[@robintomar3097]

I really liked the way you linked them together it made this so much easy to remember conceptually. Thank you professor.

[@ProfessorRoss]

Glad it was helpful!

[@timstewart2800]

The recursive expression for average was such a beautiful aha moment for me Dr. Ross. I'm looking forward to using that method for similar problems in the future. Thank you!

[@ProfessorRoss]

Glad it was helpful! Thank you for watching!

[@harmonyOfEureka]

I study abroad in Japan and learning these theory in a different language is hard. Thank you professor for your lecture, it helps me a lot. Love the way you explained things also. Oh and my older brother studied in Virginia Tech in the past so it's really nice to came across a professor from his univeristy

[@TheHashian]

Same here. Ryugakusei in Japan

[@khandmo]

Perfect explanations. A great teacher explains why, not what.

[@ProfessorRoss]

Glad you think so! I hope my explanation helped

[@EPICfranky]

I just discovered the Kalman filter. This was the best introduction I've seen. Great lecture!

[@ProfessorRoss]

Glad you enjoyed it! I don't derive it mathematically, but just provide some motivation for how to use it, and that's all most people need.

[@siddhantrao3618]

YOU ARE THE BEST TEACHER IN EXISTANCE

[@ProfessorRoss]

Thanks! But there are a lot of good teachers out there. You just have to find them.

[@siddhantrao3618]

@@ProfessorRoss I have been wanting to understand kalman filters for so long but every textbook or professor goes math heavy where they don't even care to explain what part of it is a scalar and what part of it is a matrix and they just assume you know a bunch of things already. I really loved how you compared the low pass filter with the kalman filter to explain everything it was like watching gold being extracted from it's ore. Too good.

[@dorotheeritter9238]

Awesome! I love your subtle jokes and your calm way of explaining

[@ProfessorRoss]

Glad you appreciate my explanations! My subtle humor appeals to intelligent people 😉 Thanks for watching.

[@stevehageman6785]

The recursive filter is just so useful, easy to use and quite light on system resources. I first learned it as 'Exponential Averaging' in the 1980's from an Analog Devices Application Note. I have used it in countless projects since. It simulates a simple RC filter in hardware terms (something that I also use on every project - RC Filters). Well done explanation. :-)

[@StupidusMaximusTheFirst]

Really good and simple explanations of complicated stuff. Thanks.

[@ProfessorRoss]

Glad it was helpful!

[@MrSocialish]

Great video! I really like the pacing. I noticed at 11:58 you mentioned that the noise was uniformly distributed, but I think you meant normally distributed with standard deviation of 4? randn.m is ~N(0,I) while rand.m is the uniform distribution for the range [0,1].

[@ProfessorRoss]

Good point! Thank you, I've put this correction in the description now.

[@phillipmaser132]

Best Explanation of Kalman Filter with Examples so far. Problem 1: We are trying to measure velocity from the Acceleration sensor no luck so far. All we see is noise and shock from these results. We are moving in fluid with different flows from the pumps and we have restrictions at each collar, and we have a plug that travels in the fluid hoping to see acceleration in those restrictions. We do have magnetics at each location to help out in the sensor fusion calculation. Setting up the Kalman filter in Matlab was the easy part. Tuning the filter is another story. The goal is to go to a position along this path as a function of time and velocity. Finding distance is the goal. Any ideas would be helpful.

[@ProfessorRoss]

Thanks for watching. But sorry, I don't have any good ideas. It's basically a 'dead reckoning' problem, trying to go from acceleration to velocity (and then position). It may depend on the space-time scale of the problem. For example, I'd like to try measuring acceleration while I'm in a car, starting from rest at point A and going to another location, B (say, work), and see if I can reconstruct my trip's position. The accuracy might depend on the accuracy of the accelerometer, the sampling rate, and the rate at which accelerations in time and space occur while driving. All of this would be different depending on the application. Sounds like you have some good ideas with sensor fusion. If you have locations where you expect the acceleration to drop to low values or increase to high values, those could be used as known 'waypoints' used to double-check the accuracy of your algorithm.

[@stevehageman6785]

@phillip... If you have so much noise that you can't filter it properly you may have a fundamental issue with your measurement system. i.e. "You can't make a silk purse out of a pigs ear" problem. If you are using acceleration to get velocity you are (I think) integrating the signal. That in itself should add smoothing if done properly. One thing you might try is to oversample the signal (sample at a faster rate) and then you have more points to filter from. Also it is important to study the signal frequency components (spectrum) to make sure that there are no aliased signals folding back to baseband. As this will make any signal analysis very confusing. Oversampling will help with this also as it is easier to build the antialias filters from you sensor. Hope this helps. :-)

[@PannagaSudarshan]

Its just cool to think about the fact that 'average' equation will translate to 'estimate' in kalman filter

[@americanpride5540]

Thank you for uploading this lecture it's very helpful

[@carmelpule8493]

I am a very old man and this took me back 70 years ago, when I did both analogue and digital filters using the bilinear transformation to change the frequency domain to a circular one, for digital and switched filters. When I started all this, such along time ago, I used to recognise what a particular filter selects by plotting its Impulse function and then superimpose on it the signal that I want to investigate . Multiplying the two and integrating the product, the value of the Integral would be, how much of the signal is contained in the impulse function of the filter. For a low pass filter the Impulse response had to have a DC level plus an oscillation in it, decaying at a rate to decide the bandwidth. For a band pass filter the impulse response had to have a ringing at the frequency required to pass through and no DC.. For a high pass filter an impulse had to go right through, followed by an inverted version of a low pass filter whose area is equal to the initial impulse, and with a decay duration to decide the bandwidth For a band stop filter, I shall let the readers work out its impulse function! Many years ago I constructed three dimensional wooden models using toothpicks as impulses, to show the Laplace and the Convolution integrals of digital filters, The impulse looks like an exponential helix to chose the frequency and its exponential decay to chose the bandwidth. I still got them both. I should write a book showing how filters should be analysed in three dimensions and use three dimensional signals as V.e^( R+jw)t showing the real, imaginary and time axis. I always found it easier to start with analogue filters, as Butterworth and Chebyshev filter versions, then go to FFR then IIR , and then go to the Kalman filter. and other running filters. Congratulations for your video. Thank you for stirring and jolting my memories of my many years in UK, as a poor man, making ends meet with the little money I had to live on, but very rich in signal processing techniques, as used in communications and automatic state control systems, Thank you Oh, I had no computers to work with in those days and it was all hard ware, When about 50 years ago I had my first home computer I cried when, all I did with filters and signal processing, in both analogue and digital filters, for many years, I wrote in software in a 10 line program! . I also did N- path filters, switch8ing multiple low pass filters to obtain a band pass transfer function. Good old days, I do not think I would like to go back to those days, of so much dedication and concentration to this work, before I got married and had my own family. Sir, may I quote and modify what you said in one comment below, as it also applies to me, " I am just a very old man, who stood on the shoulders of giants and two great parents, and assisted by the company of a good wife for 60 years and children and grandchildren, and six great brothers and sisters and friends and a lot of luck in having good health.."

[@gang208]

One minor error here at around 11:00. The Matlab randn() function gives a zero mean Gaussian distributed random number with a variance of 1. So 4*randn() is not bounded within [-4, 4], only that the standard deviation will be 4. If you want uniformly distributed noise between -4 and 4, you can use something like 8*rand - 4. In the context of Kalman filter, however, randn() is more appropriate.

[@danalex2991]

Amazing lecture.

[@ProfessorRoss]

Thank you for watching. Glad it was helpful.

[@telmanmaghrebi3358]

This is like a GOD! Oh my God, Excellent!

[@ProfessorRoss]

I am just a man, standing on the shoulders of giants.

[@omaraissani6255]

The lecture is really helpful, thank you professor

[@ProfessorRoss]

You're welcome. I'm glad you find it helpful.

[@konturgestalter]

Fantastic series

[@ProfessorRoss]

Glad you think so!

[@alihosseiniroknabadi4828]

It was great

[@fernandojimenezmotte2024]

Great lecture Professor Ross ! very didactic , You made it very enjoyable

[@ProfessorRoss]

Glad you enjoyed it!

[@hyperduality2838]

Making predictions is a syntropic process -- teleological. Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics! Target tracking is a syntropic process. "Always two there are" -- Yoda.

[@guangruli4486]

Huge thanks! the explanation is so clear!

[@ProfessorRoss]

Glad you liked it!

[@icanyagmur]

Professor Ross, I liked your style.

[@ProfessorRoss]

Thank you kindly

[@윤현만-n3v]

Thank you professor. 😍😍😍😍😍

[@bloodhound8894]

Thank you sir!

[@ProfessorRoss]

You bet!

[@jaladurgamdhanush8680]

That was a great lecture, Professor.🥳👏 Packing a MATLAB hands-on along with the theory well within a typical class time (< 1 hour) is even more commendable. Sir, could you please share the GetSonar() function file & SonarAlt.mat data files? That would be of great help.🙏

[@ProfessorRoss]

Maybe you didn't look in the video description. The MATLAB code is all here: tinyurl.com/kalmanfilterforbeginners

[@jaladurgamdhanush8680]

​@@ProfessorRoss, thank you sir.

[@jusbejusbe7838]

Very good. Thank you.

[@ProfessorRoss]

Thank you for watching. Glad to help.

[@kalaivanank-nc3vd]

awsome lecture thank you so much proff.

[@ProfessorRoss]

Most welcome! Thanks for watching.

[@tabhashim3887]

This is amazing. Thank you professor!

[@ProfessorRoss]

You're welcome.

[@MichaelRicksAherne]

Wish I had this 15 years ago when I learned this stuff.

[@ProfessorRoss]

Thanks so much. I’m hoping to provide a good intuitive foundation for any future practioners

[@wallacekia4836]

Thanks bro!!!

[@ProfessorRoss]

No problem!! Right back at ya, bro!

[@edleahey2791]

Thanks!

[@ProfessorRoss]

Thanks so much. I'm glad my videos are helpful!

[@mokoepa]

Just WOW!

[@ProfessorRoss]

Just THANKS! Glad you liked it.

[@SaieenTwist]

Correction: randn does not generate values b/w 1 and -1. >> r = randn(10,1) r = -2.1384 -0.8396 1.3546 -1.0722 0.9610 0.1240 1.4367 -1.9609 -0.1977 -1.2078

[@rakmo97]

Yes, the randn randomly generates numbers from a normal distribution with a mean of 0 and a standard deviation of 1.

[@mohankrishnan2022]

Excellent job!

[@abinadiswapp7637]

This is fantastic, thank you so much.

[@AmirBozorgmagham]

Shane Ross is the best!

[@ProfessorRoss]

Only because I have the best students!

[@microprediction]

wonderful

[@ProfessorRoss]

Thank you! Cheers!

[@Rekudom]

For the moving average ( 20:41 ), doesn't Xbar(k-1) contain data outside the window? (i.e., x(k-n))

[@MucaroBoricua]

At 3:55, shouldn't the last term be Xk/(k-1) instead of just xk? Nevermind. It was corrected at 4:25.

[@PannagaSudarshan]

@30:29 Prof. says we want to weight the most recent data higher than the previous one. But why ?

[@PannagaSudarshan]

I mean I know this is an established fact, but I want to know or understand the reason behind it. @ProfessorRoss any idea?

[@ProfessorRoss]

@@PannagaSudarshan I think it's because the most recent data should be the best indication of the most recent state of the system (which is what we're trying to estimate as best we can). Since we care about the current state, and even though our measurements are noisy, the data from 1 second ago is more indicative of the current state than data from 1 minute ago, and data from 1 minute ago is better than data from 10 minutes ago, etc.

[@PannagaSudarshan]

@@ProfessorRoss Oh got it, thank you Professor.

[@LS-oh6po]

How actually to calculate Xk-n+1 ?

[@subramanianchandrasekarapu5126]

Thanks!

[@ProfessorRoss]

Thank so much!

[@ahmedgharieb5252]

How then to forcast the model for example go 30 step forward

[@PannagaSudarshan]

Does giving alpha very low values make it overfit the data?

[@forheuristiclifeksh7836]

1:00

[@MohamedMounirABBES]

thank you so much it was verry helpful to me , sir can i get your E-mail please i'm a PhD student and i need your help

[@MarksmanSnir]

Brilliant lecture, thank you for sharing it with the world.

[@ProfessorRoss]

Thank you!

[@mino99m14]

Does the low pass filter have another name? I'm trying to understand why it gives a nice result. It's a biased estimator, isn't it? So how come it gives a good estimation for the mean of the kth data point?

[@forheuristiclifeksh7836]

1:00

[@BruceWedding]

Very informative and easy to follow. Exactly what I was looking for. Thanks so much for this series on Kalman filters.

[@ProfessorRoss]

You're welcome.

[@Devinci297]

For a second I thought I had commented on this before since we have the same profile picture! lol

[@coolmatt3906]

Nice explanation! Also called EMA exponential moving average.

[@Samphysicsguy]

professor i was struggling to get this concept clear and u did it i have no words but yeah thanks alot looking for some electronics courses from you

[@ProfessorRoss]

Glad it helped! I don't have any current plans to teach electronic courses. My background is physics, and I mostly work on and teach applications of mechanical modeling and dynamical systems.

[@Samphysicsguy]

@@ProfessorRoss how can i connect with you and do some project under you sir please i want to spend some time with you ,and also i have applied for a patent for one algorithm which is giving better results than kalmen filter i want to discuss the same with you.

[@trishamendoza5167]

You are the best Dr. Ross!!!