How do we know the Jacobian

[ccwss1232]

Thank you for your grate work,I have two questions about your paper and codes.

1. In the prediction stage of EKF, the calculation formula (11) of the covariance matrix is correct, but in the code, you used third-order Taylor expansion, and the specific formula is (I+F+1/2F^2+1/6F^3) (P+GQG)(I+F+1/2F^2+1/6F^3), which is different from the formula in the paper.
2. Although the appendix gives the Jacobian matrix, F,G and H, and I know that they are obtained by derivation, how to obtain each element in the matrix?Because the nonlinear functions f() and h() don't know how to find their Jacobian.Do you have a specific derivation process there?

Looking forward to your reply, thank you

[hqtang-git]

@ccwss1232
Do you find the difference? I also have the same confusion.
You can find the detail derivation from this [url] (https://aipiano.github.io/2019/03/23/%E4%B8%8D%E5%8F%98%E6%89%A9%E5%B1%95%E5%8D%A1%E5%B0%94%E6%9B%BC%E6%BB%A4%E6%B3%A21/)) for the question 2.