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

You can use the Kalman Filter—even without mastering all the theory. In Part 1 of this three-part beginner series, I break it down step by step, starting with simple recursive filters: average, moving average, and low-pass filters. You’ll see how these relate to the Kalman Filter--and watch MATLAB demos bring them to life (Python provided below as well). No jargon, just clear explanations to build your estimation and data analysis skills.

🎥 *Watch the Full Kalman Filter Series:*

👩🏽‍💻 *This video covers:*
• What is a recursive filter?
• How do moving average and low-pass filters work?
• MATLAB examples for noisy data
• Foundations of the Kalman Filter algorithm

🛠️ *Resources:*

⚠️ *Corrections:*
• At 10:58, I say the noise was uniformly distributed. It was actually normally distributed (std. dev. = 4).
• At 14:10, I clarify that randn in MATLAB gives a normal distribution.

📺 *Related Videos:*

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.

⏱️ *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

👨‍🏫 *About Me:*

► *Space Vehicle Dynamics course videos (playlist)*

► *Video Courses & Playlists by Professor Ross*

▶️ Kalman Filters for Beginners:

▶️ Nonlinear Dynamics & Chaos

▶️ Hamiltonian Dynamics

▶️ 3-Body Problem Orbital Dynamics

▶️ Center Manifolds, Normal Forms, & Bifurcations

▶️ Space Vehicle Dynamics

▶️ Lagrangian & 3D Rigid Body Dynamics

▶️ Space Manifolds

Keywords & Topics:
Kalman filter, estimation, MATLAB, recursive filter, moving average, low-pass filter, dynamic systems, orbital mechanics, space dynamics, sensor fusion, attitude estimation, CR3BP, nonlinear dynamics, celestial mechanics, Lyapunov orbits, Lagrange points, interplanetary highways, space manifolds, cislunar space, Virginia Tech, Caltech, JPL, NASA, aerospace

#kalmanfilter #MATLAB #lowpass #python #mathematics #recursion #nonlineardynamics #CR3BP #spacemanifolds #estimation #dynamics #cislunar #aerospace #chaos #dynamicalsystems #spaceengineering

[JC-nsio]

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 !

[vinaykumarnainapatruni]

You made this a piece of cake....Thank you Mr. Ross

[emrekarapaca]

sir, you've removed all of the noise from my learning path. thanks for great explanation

[timstewart]

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!

[almostrockets]

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

[mishenfernando]

your explanations are crystal clear!!! thank you!

[_NguyenManhToan_]

I'm 33 years old this year, and I've worked in automation, information technology, and embedded programming. I thought it would be difficult for me to learn mathematics at this age. However, after watching your video, everything became much simpler than I had imagined. I don't think I'm particularly talented to grasp it easily, but I'm certain that you are an outstanding teacher. Thank you, thank you so much.

[teddynelson]

I watched at least ten other videos that all used the same method to confuse me more. Your video took the long way but the journey is what I needed to help me build just enough scaffolding to put the pieces together at the top. Thanks!

[robintomar]

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

[mainfranklin]

I used to be scared of understanding Kalman Filter until I came across this.
God bless you sir.

[riteshbera]

You are the best, sir! Your one tutorial is a lot more than a full series. I enjoyed the entire class a lot. Thank you, sir.

[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

[EPICfranky]

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

[yyttommy]

i like your teaching, step by step, thank you very much.

[jane]

Sorry if this doesn’t go through. My account is low.. Remember the Kalman filter and this may have to do with Bitcoin’a K NSA NIST RSA key saga (the low pass time patents and the original time footnotes on the paper - read Hero Villian). it’s really good! Thanks again

[gang]

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.

[stevehageman]

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. :-)

[khandmo]

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

[dorotheeritter]

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

[mariosmusik]

haven't watched part 2 yet, but I very much like part 1. Also for the comparison of diskrete low pass filter to moving average, wich gave me a different more intuitive view on them.
Thumbs up!