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YWL0720 / I2EKF-LO

[IROS 2024] I2EKF-LO: A Dual-Iteration Extended Kalman Filter based LiDAR Odometry
GNU General Public License v2.0
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Derivation of the F_x and F_w matrices? #2

Open brytsknguyen opened 2 months ago

brytsknguyen commented 2 months ago

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: https://github.com/YWL0720/I2EKF-LO/blob/8c01274dcf142c0f1ab945c2f151b0214d226132/src/IMU_Processing.hpp#L247 https://github.com/YWL0720/I2EKF-LO/blob/8c01274dcf142c0f1ab945c2f151b0214d226132/src/IMU_Processing.hpp#L248

Do you have the technical note on these calculations? Just to share some results.

dxtilde{k+1} / d_rotation_error = Exp(omega_hat, dt)^{-1},

which is equivalent to Exp(omega_hat, -dt)

My calculation of dxtilde{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.

YWL0720 commented 2 months ago

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.

brytsknguyen commented 2 months ago

That's very kind of you. Looking forward to it.