The Unscented Kalman Filter (UKF): A Full Tutorial. PS. Sampling Methods are Amazing

The Unscented Kalman Filter (UKF) is considered the best Gaussian Filter in terms of performance. It relies on the unscented transform, a powerful tool for transforming distributions. The process involves intelligent sampling of points from the initial distribution, which are then passed through the true transform function. The resulting samples are recombined to estimate the final distribution. Let's see how it's mathematically done!
UKF Presented: ieeexplore.ieee.org/document/...
Generalized Gaussian Filter: asrl.utias.utoronto.ca/~tdb/bi... (page 118) (pdf page 138)
Chapters:
0:00 Video Introduction
0:48 Model Setup
1:15 UKF Intuition
2:30 Unscented Transform - Intuition
2:59 Unscented Transform - Sigma Points
3:19 Unscented Transform - Matrix Square Root
4:51 Unscented Transform - Moment Matching
5:50 Unscented Transform - Tuning Parameters
6:20 The UKF
8:43 UKF Advantages

[@jameshan8]

Full tutorial about the Generalized Gaussian Filter was just released! th-cam.com/video/oPgfa6G2AxE/w-d-xo.html&ab_channel=JamesHan

[@kka107]

You not only explain the algorithm well but also prove it without skipping steps. And you do them in less than 10 mins. Bravo. If I had discovered you earlier, I would not have wasted hours and hours of my time on TH-cam watching videos from people who haven’t fully captured the essence of these algorithms and don’t know how to teach.
Thanks for your service.

[@jameshan8]

Thank you for the very kind words! I'm glad you found it useful :)

[@jameshan8]

Correction: @4:52 the variance should be the second central moment (not the raw moment that I put up). The 2nd central moment is E[(x-M1)(x-M1)^T]

[@tyranids3644]

Excellent video, lots of good information in a very watchable format. Consider also covering the square root UKF, utilizing Cholesky decomposition, QR decomposition, and Cholesky rank 1 updates, it can perform significantly faster than UKF or even EKF while avoiding the UKF’s pesky issue of the covariance matrix losing positive definite-ness in the presence of poor/infrequent sensor updates.

[@jameshan8]

Interesting! I didn't know that! I'll pin this so others can learn from it too :)

[@arjunmohan2908]

Im having voltage, current, acitve power, temperature, rpm of a BLDC motor as the known paramerters. Can i use kalman filter to estimate the torque with the help of the known parameters or is there any other simpler methods to calculate the torque

[@MOHITKUMAR-xe7bg]

amamzing explanantion

[@jameshan8]

Thank you! I really appreciate it :)

[@angelo6082]

How does it compare with the Quadratute KF?

[@jorgemunozburgos4401]

Great video and excellent explanation. I only have one question regarding your last slide where you list the UKF Advantages. In point number 1 you mentioned that we don't need to know the non-linear models of the motion and/or sensor. However, in order to do the Unscented Transform for the sigma point, we need to know the non-linear models. That is the part I am confused. Thank you for your time.

[@jameshan8]

Great question! I meant that we don’t need the analytical form of the models. If the models were a black box, we could still use the UKF since we only need to pass points into the model. For example if the motion model was modelled with a neural network or some lookup table from experimental results, the UKF would still work. Let me know if you still want further clarifications!

[@hudsonyuen]

😍😍😍

[@richchen780]

Great video! Do you mind sharing what music you used?

[@jameshan8]

Thanks! It's Dream Escape - The Tides

[@tuongnguyen9391]

Does the word scent here mean that it has something to do withd armpit deorant ???

[@jameshan8]

Great question! It does actually!
Here's a quote from the author himself (ethw.org/First-Hand:The_Unscented_Transform):
"Initially I only referred to it as the “new filter.” Needing a more specific name, people in my lab began referring to it as the “Uhlmann filter,” which obviously isn’t a name that I could use, so I had to come up with an official term. One evening everyone else in the lab was at the Royal Opera House, and as I was working I noticed someone’s deodorant on a desk. The word “unscented” caught my eye as the perfect technical term. At first people in the lab thought it was absurd-which is okay because absurdity is my guiding principle-and that it wouldn’t catch on. My claim was that people simply accept technical terms as technical terms: for example, does anyone think about why a tree is called a tree?
Within a few months we had a speaker visit from another university who talked about his work with the “unscented filter.” Clearly he had never thought about the origin of the term. The cover of the issue of the March 2004 Proceedings we’re discussing right now has “Unscented” in large letters on the cover, which shows that it has been accepted as the technical term for that approach."

[@tuongnguyen9391]

@@jameshan8 So inclusion , he just made that word up ? I do not see any mention about deorant in your answer

[@jameshan8]

Hey@@tuongnguyen9391! The quote above includes the phrase: "deodorant on a desk"

[@tuongnguyen9391]

@@jameshan8 oh now I see it thank you. But it seems like scientist are bad at naming their product which is why we need the sale team.

[@nurmilati846]

where can we get the article about table of parameters?

[@jameshan8]

Here: ieeexplore.ieee.org/document/882463

[@nurmilati846]

Thanks a bunch @@jameshan8