The Extended Kalman Filter (EKF): Why Taylor Expansions are Awesome

[@summerishere5146]

It is proper insanity how streamlined and efficient your explanations are. Thank you so much for these amazing resources!

[@Daniboy370]

Beautifully explained ! Thanks

[@FawazAlTashah]

Hello Mr. Han, would you be kind enough to recommend two books: 1) Analysis Accuracy Methods (including linearlization) 2) Key Considerations (as mentioned in your video) I am applying for a PhD in Quantitative Marketing and thought highly of your technique.

[@gunnarmundt956]

at 1:43 it says "Lt may not be quadratic in x{t-1}" shouldnt it say linear?

[@jameshan8]

Good question! The text should indeed be "quadratic". We WANT it to be quadratic in x_{t-1} because then it's effectively a Gaussian which has a closed form integral. The issue is that we don't know what f(x_{t-1}, u_t) is, so it could cause the final result to be non-quadratic in x_{t-1}.

[@gunnarmundt956]

@@jameshan8 ah okay i think i get it. If it were linear in x{t-1} we could just use a kalman filter, but we make the assumption that its not?

[@jameshan8]

@@gunnarmundt956 Exactly! For e^something if something is quadratic or less, we're chilling. The EKF is a way to generalize to to ANY motion model 'f'

[@gunnarmundt956]

@@jameshan8 ahh so like since my motion model contains many trig terms it is non-linear and non-quadratic, so we must use an EKF. Seems like almost all motion models would include trig terms :D

[@jameshan8]

@@gunnarmundt956 remeber that the motion model is the mean for that first exponential and so we would have (x-\mu)^2 in the scalar case. If \mu is linear it becomes quadratic, so really the motion model has to a constant or linear for us to use the Kalman filter. Also, 'must' is a strong word haha - there are other techniques like the UKF.

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[@gunnarmundt956]

why the fk everyone writing their address

[@jameshan8]

Literally no idea haha

[@Kiwinov]

@@jameshan8 Streamers and YT content creators block out words from YT Studio that correspond to their address so that nobody is able to dox them in the comment section of their videos. By commenting random addresses, they can find out what comments pass through and what don't, effectively narrowing down your address. It's a big problem these days

[@gunnarmundt956]

@@Kiwinov ay what the fk really? you got any good source?

[@jameshan8]

@@Kiwinov good to know, thanks!