Derivation of the F_x and F_w matrices?
brytsknguyen opened this issue · comments
Hi,
Thanks for the code. I am looking into the maths of the prediction step, which involves calculating the Jacobian F_x and F_w.
I found your calculation of F_x with respect to the rotation and angular velocity errors here:
I2EKF-LO/src/IMU_Processing.hpp
Line 247 in 8c01274
I2EKF-LO/src/IMU_Processing.hpp
Line 248 in 8c01274
Do you have the technical note on these calculations? Just to share some results.
dx_tilde_{k+1} / d_rotation_error = Exp(omega_hat, dt)^{-1},
which is equivalent to Exp(omega_hat, -dt)
My calculation of dx_tilde_{k+1} / d_angular_velocity_error shows that it should be Jr(angular_velocity_estimate * dt)dt, which can be approximated to Eye(3) * dt as in your code.
Hi,
Thank you for your inquiry and for the detailed analysis you've provided regarding the Jacobian calculations in the code.
Currently, I am working on some other projects, but I recognize the importance of your request for the technical notes on these calculations.I will check and organize the necessary documentation and provide it to you within a week.
That's very kind of you. Looking forward to it.