I have found the following answer on the system's dynamics function and what the Jacobian matrix G of the Extended Kalman Filter look like for a 2D robot with a differential drive. Taken from slides and source.

Can someone please show me the full derivation? Or maybe you can show me a link that I can use for generating Jacobians for a given function? Any guide would be appreciated.

Odometry model: enter image description here

The answers: Answers

  • $\begingroup$ The book in the link you've posted shows the the full derivation. $\endgroup$
    – CroCo
    Oct 20, 2021 at 5:32
  • $\begingroup$ I am trying to use one of the following online Jacobian calculators to get the result that is shown above but it seems like my input is wrong. Can you show me how to use those websites to get exactly the output shown above? Online Jacobian calculator example: emathhelp.net/calculators/calculus-3/jacobian-calculator $\endgroup$
    – Gabriele
    Oct 21, 2021 at 7:34

1 Answer 1


Here is the closest I could get to my answer. I hope it helps someone in the future. Please do notice that the result matrix is mirrored.

enter image description here


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