Question about jacobian derivation process

[codehory]

Hi @narutojxl , thanks for your code notes !
I have some questions:

1. quaternion in Hamilton or JPL？
2. jacobian derivation in lidar_pure_odom_factor.hpp. Could you please show me your derivation process?

Thanks in advance!

[narutojxl]

Hi @codehory,
Q1: quternion convention is hamilton.
Q2: It's been a long time now, and I can't remember the details clearly. Perhaps you can take a look at this question，gogojjh/M-LOAM#8.

[codehory]

Thanks for your reply!

The function LeftQuatMatrix in math.hpp shows the quaternion convention may be in JPL. Could it be that I misunderstood the code?

template<typename Derived> inline Eigen::Matrix<typename Derived::Scalar, 4, 4> LeftQuatMatrix(const Eigen::QuaternionBase<Derived> &q) { Eigen::Matrix<typename Derived::Scalar, 4, 4> m; Eigen::Matrix<typename Derived::Scalar, 3, 1> vq = q.vec(); typename Derived::Scalar q4 = q.w(); m.block(0, 0, 3, 3) << q4 * I3x3 + SkewSymmetric(vq); m.block(3, 0, 1, 3) << -vq.transpose(); m.block(0, 3, 3, 1) << vq; m(3, 3) = q4; return m; }

[narutojxl]

It is wried, i remeber eigen and ceres quaternions are all hamilton and ceres's normal eqaution update is right delta update, namely, x_new = x_old * delta_x.
If the author want to use JPL convention, although eigen's quaternion is hamilton, it should be m.block(0, 0, 3, 3) << q4 * I3x3 - SkewSymmetric(vq); it is a typo?
If it is true, the author's assume eigen quaternion is JPL convention.
I remeber, when i deriving, i assume quaternion is hamilton, and follow right perturbation formula or lie algebra differentiation, I don't remember exactly which one it is, but the two ones are all consistent with ceres's normal eqaution update convention.
Why some jacobians of mine is the same with author, some not, it is a problem.

M-LOAM_noted/mloam_common/libs/include/common/algos/math.hpp

Line 82 in ac27043

m.block(0, 0, 3, 3) << q4 * I3x3 + SkewSymmetric(vq); //

[codehory]

Thanks for your reply!

I used right perturbation to derive jacobian in LidarPureOdomPlaneNormFactor.

Line 68: the result is the same with yours. But the author looks like to use left perturbation equation

Line 84: all consistent

Line 100: my result is jaco_ex.rightCols<3>() = -w.transpose() * Rp.transpose() * Ri * Rext * Utility::skewSymmetric(point_);
the author looks like to use left perturbation equation. But I also can not match your result.

Line 287: the result is the same with yours. May be the author's result is wrong.

I'm not sure whether there are still some errors in my derivation.

If the author really has so many mistakes, why can this project continue to run normally?

M-LOAM_noted/estimator/src/factor/lidar_pure_odom_factor.hpp

Line 103 in ac27043

// jaco_ex.rightCols<3>() = -w.transpose() * Rp.transpose() * Ri * Utility::skewSymmetric(Rext * point_) * Rext;