typos in df_dx ?

[narutojxl]

Hello @Joanna-HE
Thanks for your excellent work to share this toolkit. I have some foolish questions to look for your help, thanks in advance!

• I notice when calculating $$F_{\tilde{x}}$$, in pape some items have $\Delta t$, but in the code, it disapper.
  Did we when calculating propagated covariance consider consective imu time diff $\Delta t$ in somewhere?

• $$\frac{\partial{\dot{R}}}{ \partial{b_g} } $$ item in paper should not have transpose symbol, right? In code we approximate this right jacobin $$J_r$$ into identity matrix, the transpose symbol have very small effect.
  

• Similar question about lidar measurement wrt true state $$x_k$$ jacobin $$J^k$$, evaluated at current estimated value $$\hat{\mathbf{x}}^k_k$$, it should also not have transpose symbol, right ?
  

• $$\frac{\partial{\dot{R}}}{{\partial{R}}} $$ in paper it is $$E_{XP}(-\hat{\omega_i} \Delta t)$$, but in code it disapper, cov(3, 3) = d(\dot{R}) / dR = Exp(-omega * dt)

IKFoM/Sample_1/FAST_LIO/include/use-ikfom.hpp

Lines 110 to 126 in 59cfc09

	Eigen::Matrix<double, 24, 23> df_dx(state_ikfom &s, const input_ikfom &in)
	{
	Eigen::Matrix<double, 24, 23> cov = Eigen::Matrix<double, 24, 23>::Zero();
	cov.template block<3, 3>(0, 12) = Eigen::Matrix3d::Identity();
	vect3 acc_;
	in.acc.boxminus(acc_, s.ba);
	vect3 omega;
	in.gyro.boxminus(omega, s.bg);
	cov.template block<3, 3>(12, 3) = -s.rot.toRotationMatrix()*MTK::hat(acc_);
	cov.template block<3, 3>(12, 18) = -s.rot.toRotationMatrix();
	Eigen::Matrix<state_ikfom::scalar, 2, 1> vec = Eigen::Matrix<state_ikfom::scalar, 2, 1>::Zero();
	Eigen::Matrix<state_ikfom::scalar, 3, 2> grav_matrix;
	s.S2_Mx(grav_matrix, vec, 21);
	cov.template block<3, 2>(12, 21) = grav_matrix;
	cov.template block<3, 3>(3, 15) = -Eigen::Matrix3d::Identity();
	return cov;
	}

[zhh2005757]

Exp(-omega * dt) is almost near to identity matrix

[narutojxl]

yes, agree with you. BTW, @zhh2005757 , about Q2 and Q3, is there a typo in paper?

[Joanna-HE]

1. we calculate multiply delta t after calculating F_x, at the bottom line of the predict function. 2. There should be a transpose, since A as defined in the paper is left jacobian, not the right jacobian. 3. In theory, $$\frac{\partial{\dot{R}}}{{\partial{R}}} $$ in paper it is $$E_{XP}(-\hat{\omega_i} \Delta t)$$ should not disappear, it is calculated when there is a SO3 state. 获取 Outlook for iOS<https://aka.ms/o0ukef>

…

________________________________ 发件人: Xiaoliang Jiao ***@***.***> 发送时间: 星期五, 八月 23, 2024 11:41 上午 收件人: hku-mars/IKFoM ***@***.***> 抄送: ***@***.*** ***@***.***>; Mention ***@***.***> 主题: [hku-mars/IKFoM] typos in df_dx ? (Issue #19) This is an external email. Hello @Joanna-HE<https://github.com/Joanna-HE> Thanks for your excellent work to share this toolkit. I have some foolish questions to look for your help, thanks in advance! * I notice when calculating $$F_{\tilde{x}}$$, in pape some items have $\Delta t$, but in the code, it disapper. Did we when calculating propagated covariance consider consective imu time diff $\Delta t$ in somewhere? * $$\frac{\partial{\dot{R}}}{ \partial{b_g} } $$ item in paper should not have transpose symbol, right? In code we approximate this right jacobin $$J_r$$ into identity matrix, the transpose symbol have very small effect. [image]<https://github.com/user-attachments/assets/26578d8f-037b-4ad9-baea-12b2ee42ae15> * Similar question about lidar measurement wrt true state $$x_k$$ jacobin $$J^k$$, evaluated at current estimated value $$\hat{\mathbf{x}}^k_k$$, it should also not have transpose symbol, right ? [image]<https://github.com/user-attachments/assets/b6526137-3cc1-4ac5-b2a3-beb06d9eb65f> * $$\frac{\partial{\dot{R}}}{{\partial{R}}} $$ in paper it is $$E_{XP}(-\hat{\omega_i} \Delta t)$$, but in code it disapper, cov(3, 3) = d(\dot{R}) / dR = Exp(-omega * dt) https://github.com/hku-mars/IKFoM/blob/59cfc095ca74425f9b330c7c04a5d74f68c6dd62/Sample_1/FAST_LIO/include/use-ikfom.hpp#L110-L126 ― Reply to this email directly, view it on GitHub<#19>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ANJUIXVBGTENPKTRXQ32YQDZS2VOTAVCNFSM6AAAAABM7LPDJ2VHI2DSMVQWIX3LMV43ASLTON2WKOZSGQ4DEMJXGM4TCNI>. You are receiving this because you were mentioned.Message ID: ***@***.***>

[narutojxl]

@Joanna-HE, I'm really really thanks Dr. He kindly and detaily to solve my problem. Close it now!

[narutojxl]

@Joanna-HE , Dr. He, I'm so sorry to bother you again, i try to when fixing aboving typo get some troubles. Thanks for your kind help in advance!

• The items circled in blue in the picture all have a coefficient dt, in df_dx() function we don't have dt. As you mentioned above "1. we calculate multiply delta t after calculating F_x, at the bottom line of the predict function."

• The items circled in red in the picture do not have a coefficient dt in paper.

• For example, $$\dot(P)/P$$ is Identity, this item has no dt in paper, $$dot(P)/V$$ is identity* dt in paper.

• According to above, the red circled items in the picture should all be divided by dt in df_dx() function. But when i test with bag, for example, dot(Q)/Q = Exp(-omega_i * dt) / dt, lio will immediately diverge. But when i do not divided by dt to implement the red items, the lio's state is normal.

• Q1：The predict function is very complicated for me to carefully get the details. So i am here to seek your verification, when we implement the red items in df_dx() function, we must not divided by dt, as you have alreadly considered this in prediction function, right?

• Q2： I notice in paper, these items: dot(P) / P = I, dot(V) / V = I, dot(bg) / bg = I, dot(ba) / ba = I, dot(g^w) / (g^w) = I, are all zero in df_dx() function. Should these items be I, or I /dt, or zero in df_dx() func？

[narutojxl]

In predict func,

F_x1 = cov::Identity();
F_x1 += f_x_final * dt;
P_ = (F_x1)*P_ * (F_x1).transpose() + (dt * f_w_final) * Q * (dt * f_w_final).transpose();

So the red items should be zeros in df_dx() function.

[narutojxl]

date: 20241025.
I privately consulted Dr. He, she told me Fx in the fast-lio paper is the derivative of x_k+1 wrt x_k, while the df_dx() in the code is the derivative of the perturbation with respect to x_k. They are two different things.