Jacobian in NavState::Create

[huanglilong]

I'm very confused with jacobians (bold text) with translation and velocity in NavState,
where can i find docs for these. thanks a lot!
code path: https://github.com/borglab/gtsam/blob/develop/gtsam/navigation/NavState.cpp

NavState NavState::Create(const Rot3& R, const Point3& t, const Velocity3& v,
OptionalJacobian<9, 3> H1, OptionalJacobian<9, 3> H2,
OptionalJacobian<9, 3> H3) {
if (H1)
*H1 << I_3x3, Z_3x3, Z_3x3;
if (H2)
*H2 << Z_3x3, R.transpose(), Z_3x3;
if (H3)
*H3 << Z_3x3, Z_3x3, R.transpose();
return NavState(R, t, v);
}

i thinks the jacobian for translation and velocity should be (I know that I was wrong)
*H2 << Z_3x3, R.transpose(), Z_3x3; => *H2 << Z_3x3, I_3x3, Z_3x3
*H3 << Z_3x3, Z_3x3, R.transpose() => *H2 << Z_3x3, Z_3x3, I_3x3

[dellaert]

math.pdf

[huanglilong]

i need more time to deep dive. Thanks a lot!

[huanglilong]

Hi @dellaert, many thanks for your suggestion last time. It's very helpful. I have gone through all the material you recommended. Would you mind help me check with the following formulas one more time? I just want to make sure what i think is correct. Thanks in advance!

Reference: https://github.com/borglab/gtsam/blob/develop/doc/ImuFactor.pdf (page 5); https://github.com/borglab/gtsam/blob/develop/doc/math.pdf

the jacobians in NavState::Create

[dellaert]

No, sorry, don't have time for that.
If you think there is an error anywhere please provide a unit test that fails.

[huanglilong]

thanks a lots!
actually, I just need help to check my derivation procession for jacobians (that same as in the code)