YWL0720 / I2EKF-LO

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

F_x.block<3, 3>(0, 0) = Exp(state_inout.bias_g, -dt);

I2EKF-LO/src/IMU_Processing.hpp

Line 248 in 8c01274

F_x.block<3, 3>(0, 15) = Eye3d * dt;

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.

Derivation of the F_x and F_w matrices?