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

You can use the powerful Kalman Filter, even if you don't know all the theory! Join me for Part 1 of my three-part series, where I introduce the concepts, breaking it down for you. I take a simple approach, starting with recursive filters like the average, moving average, and low-pass filters. I'll even show you real-world MATLAB examples to bring it all to life. Enhance your estimation and data analysis skills and take your understanding to new heights.
((3-Video Series)) Kalman Filters for Beginners: tinyurl.com/kalmanfilters
👩🏽‍💻 Get the MATLAB Code: tinyurl.com/kalmanfilterforbe...
This special lecture series takes us into dynamic attitude estimation, using time-varying gyroscope data, as opposed to the previously covered static attitude estimation, which uses simultaneous measurements of known external objects.
► Next: Kalman Filter for Beginners, Part 2 - Estimation and Prediction Process & MATLAB Example
• Kalman Filter for Begi...
► Previous, Attitude Determination, Davenport's Q-Method for Optimal State Estimation | Theory & MATLAB Demo
• Attitude Determination...
► Chapters
0:00 Introduction
0:21 Recursive expression for average
5:52 Simple example of recursive average filter
10:21 MATLAB demo of recursive average filter for noisy data
17:55 Moving average filter
21:14 MATLAB moving average filter example
26:49 Low-pass filter
37:03 MATLAB low-pass filter example
41:03 Basics of the Kalman Filter algorithm
► More lectures posted regularly
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► Dr. Shane Ross 🌠 aerospace engineering professor, Virginia Tech
Background: Caltech PhD | worked at NASA/JPL & Boeing
Research website for ​⁠​⁠‪@ProfessorRoss‬
shaneross.com
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► Space Vehicle Dynamics course videos (playlist)
is.gd/SpaceVehicleDynamics
► Lecture notes for Kalman Filter series (PDF)
tinyurl.com/kalmanfilterforbe...
► MATLAB Code
tinyurl.com/kalmanfilterforbe...
► Reference
Kalman Filter for Beginners: with MATLAB Examples
by Phil Kim (Author), Lynn Huh (Translator), 2010
www.amazon.com/dp/1463648359
► Video Courses & Playlists by Professor Ross
▶️ Kalman Filters for Beginners:
tinyurl.com/kalmanfilters
▶️ Nonlinear Dynamics & Chaos
is.gd/NonlinearDynamics
▶️ Hamiltonian Dynamics
is.gd/AdvancedDynamics
▶️ 3-Body Problem Orbital Dynamics
is.gd/3BodyProblem
▶️ Center Manifolds, Normal Forms, & Bifurcations
is.gd/CenterManifolds
▶️ Space Vehicle Dynamics
is.gd/SpaceVehicleDynamics
▶️ Lagrangian & 3D Rigid Body Dynamics
is.gd/AnalyticalDynamics
▶️ Space Manifolds
is.gd/SpaceManifolds
Implement a Kalman filter for dummies unscented extended dynamics control and estimation uncertainty propagation multiple shooting Visually Explained tutorial MATLAB aerospace attitude estimation sensor fusion mathematics recursion orbital mechanics three body problem Lagrange Point space CR3BP 3 Manifolds James Webb Nonlinear Dynamics gravity Travel Superhighway Interplanetary Highway gravitational dynamical Astronomy astronomy wormhole physics chaos unstable Periodic Orbits Saddle Critical Halo Libration Low Energy Virginia Tech Caltech JPL Lyapunov Celestial Mechanics Hamiltonian planets moons multibody Gateway Station Lunar L1 Arches Of cislunar orbital celestial Chaotician Boeing Jet Propulsion Lab Centaurs Asteroids Comets Trojan Jupiter Family Hildas quasi Kuiper Belt
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[@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.

[@pitchyawroll]

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

[@americanpride5540]

Thank you for uploading this lecture it's very helpful

[@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

[@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. :-)

[@abinadiswapp7637]

This is fantastic, thank you so much.

[@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!

[@mohankrishnan2022]

Excellent job!

[@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.

[@guangruli4486]

Huge thanks! the explanation is so clear!

[@ProfessorRoss]

Glad you liked it!

[@tabhashim3887]

This is amazing. Thank you professor!

[@ProfessorRoss]

You're welcome.

[@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.

[@fernandojimenezmotte2024]

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

[@ProfessorRoss]

Glad you enjoyed it!

[@user-mi4hw7wx1v]

Thank you professor. 😍😍😍😍😍

[@MarksmanSnir]

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

[@ProfessorRoss]

Thank you!

[@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

[@omaraissani6255]

The lecture is really helpful, thank you professor

[@ProfessorRoss]

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

[@giannismentz3570]

Really good and simple explanations of complicated stuff. Thanks.

[@ProfessorRoss]

Glad it was helpful!

[@telmanmaghrebi3358]

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

[@user-ml7ld4cx2l]

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

[@coolmatt3906]

Nice explanation! Also called EMA exponential moving average.

[@danalex2991]

Amazing lecture.

[@ProfessorRoss]

Thank you for watching. Glad it was helpful.

[@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.

[@bloodhound8894]

Thank you sir!

[@ProfessorRoss]

You bet!

[@konturgestalter]

Fantastic series

[@ProfessorRoss]

Glad you think so!

[@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.

[@mokoepa]

Just WOW!

[@ProfessorRoss]

Just THANKS! Glad you liked it.

[@wallacekia4836]

Thanks bro!!!

[@ProfessorRoss]

No problem!! Right back at ya, bro!

[@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.

[@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. :-)

[@icanyagmur]

Professor Ross, I liked your style.

[@ProfessorRoss]

Thank you kindly

[@edleahey2791]

Thanks!

[@ProfessorRoss]

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

[@microprediction]

wonderful

[@ProfessorRoss]

Thank you! Cheers!

[@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.

[@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.

[@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

[@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?

[@user-ml7ld4cx2l]

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

[@AmirBozorgmagham]

Shane Ross is the best!

[@ProfessorRoss]

Only because I have the best students!

[@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.

[@ahmedgharieb5252]

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

[@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.

[@LS-oh6po]

How actually to calculate Xk-n+1 ?

[@user-ml7ld4cx2l]

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

[@user-ml7ld4cx2l]

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

[@ProfessorRoss]

@@user-ml7ld4cx2l 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.

[@user-ml7ld4cx2l]

@@ProfessorRoss Oh got it, thank you Professor.

[@user-to3gd2ut9f]

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

[@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!

[@subramanianchandrasekarapu5126]

Thanks!

[@ProfessorRoss]

Thank so much!