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hku-mars / FAST_LIO

A computationally efficient and robust LiDAR-inertial odometry (LIO) package
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FASTLIO 中，状态方程的雅克比推导，A阵的推导求解惑 #163

Closed kahowang closed 1 year ago

kahowang commented 2 years ago

如下图1为高翔老师在简明ESKF中的状态方程F雅克比矩阵推导，图二为FASTLIO1 论文中的F阵推导，经比对，其他项的雅克比都是一样的，但是红色框的部分(delta_R 对 dleta_bg 求雅克比)，这里的A阵是一个小量吗，推导是怎样的，希望能解惑，谢谢。

image-20220523201256904

image-20220523201554370

Joanna-HE commented 2 years ago

kahowang @.***>于2022年5月23日 周一下午8:24写道：

如下图1为高翔老师在简明ESKF中的状态方程F雅克比矩阵推导，图二为FASTLIO1 论文中的F阵推导，经比对，其他项的雅克比都是一样的，但是红色框的部分(delta_R 对 dleta_bg 求雅克比)，这里的A阵是一个小量吗，推导是怎样的，希望能解惑，谢谢。

[image: image-20220523201256904] https://camo.githubusercontent.com/82cb2507050f8ca4f369c27bd370cb2ee8f62b3089d499ea4e38d31c48d934f9/68747470733a2f2f6b61686f2d7069632d313330373130363037342e636f732e61702d6775616e677a686f752e6d7971636c6f75642e636f6d2f4353444e5f50696374757265732f2545362542372542312545382539332539442545352541342539412545342542432541302545362538342539462545352539392541382545382539452538442545352539302538382545352541452539412545342542442538442f25453725414325414325453425424125384325453725414225413025453625424625383025453525383525383925453925383725384325453725413825384225453825414525413131696d6167652d32303232303532333230313235363930342e706e67

[image: image-20220523201554370] https://camo.githubusercontent.com/0e80ac8520c3eca8716c97d01ea11b20d4ed7ea65053f0ae93556d329bd7ae4d/68747470733a2f2f6b61686f2d7069632d313330373130363037342e636f732e61702d6775616e677a686f752e6d7971636c6f75642e636f6d2f4353444e5f50696374757265732f2545362542372542312545382539332539442545352541342539412545342542432541302545362538342539462545352539392541382545382539452538442545352539302538382545352541452539412545342542442538442f25453725414325414325453425424125384325453725414225413025453625424625383025453525383525383925453925383725384325453725413825384225453825414525413131696d6167652d32303232303532333230313535343337302e706e67

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Joanna-HE commented 2 years ago

当delta t趋近于零时，A（omega·delta t）等于单位阵

He, Dongjiao @.***>于2022年5月25日 周三上午1:19写道：

kahowang @.***>于2022年5月23日 周一下午8:24写道：

如下图1为高翔老师在简明ESKF中的状态方程F雅克比矩阵推导，图二为FASTLIO1 论文中的F阵推导，经比对，其他项的雅克比都是一样的，但是红色框的部分(delta_R 对 dleta_bg 求雅克比)，这里的A阵是一个小量吗，推导是怎样的，希望能解惑，谢谢。

[image: image-20220523201256904] https://camo.githubusercontent.com/82cb2507050f8ca4f369c27bd370cb2ee8f62b3089d499ea4e38d31c48d934f9/68747470733a2f2f6b61686f2d7069632d313330373130363037342e636f732e61702d6775616e677a686f752e6d7971636c6f75642e636f6d2f4353444e5f50696374757265732f2545362542372542312545382539332539442545352541342539412545342542432541302545362538342539462545352539392541382545382539452538442545352539302538382545352541452539412545342542442538442f25453725414325414325453425424125384325453725414225413025453625424625383025453525383525383925453925383725384325453725413825384225453825414525413131696d6167652d32303232303532333230313235363930342e706e67

[image: image-20220523201554370] https://camo.githubusercontent.com/0e80ac8520c3eca8716c97d01ea11b20d4ed7ea65053f0ae93556d329bd7ae4d/68747470733a2f2f6b61686f2d7069632d313330373130363037342e636f732e61702d6775616e677a686f752e6d7971636c6f75642e636f6d2f4353444e5f50696374757265732f2545362542372542312545382539332539442545352541342539412545342542432541302545362538342539462545352539392541382545382539452538442545352539302538382545352541452539412545342542442538442f25453725414325414325453425424125384325453725414225413025453625424625383025453525383525383925453925383725384325453725413825384225453825414525413131696d6167652d32303232303532333230313535343337302e706e67

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kahowang commented 2 years ago

当delta t趋近于零时，A（omega·delta t）等于单位阵 He, Dongjiao @.>于2022年5月25日 周三上午1:19写道： … kahowang @.>于2022年5月23日 周一下午8:24写道： > 如下图1为高翔老师在简明ESKF中的状态方程F雅克比矩阵推导，图二为FASTLIO1 > 论文中的F阵推导，经比对，其他项的雅克比都是一样的，但是红色框的部分(delta_R 对 dleta_bg > 求雅克比)，这里的A阵是一个小量吗，推导是怎样的，希望能解惑，谢谢。 > > [image: image-20220523201256904] > https://camo.githubusercontent.com/82cb2507050f8ca4f369c27bd370cb2ee8f62b3089d499ea4e38d31c48d934f9/68747470733a2f2f6b61686f2d7069632d313330373130363037342e636f732e61702d6775616e677a686f752e6d7971636c6f75642e636f6d2f4353444e5f50696374757265732f2545362542372542312545382539332539442545352541342539412545342542432541302545362538342539462545352539392541382545382539452538442545352539302538382545352541452539412545342542442538442f25453725414325414325453425424125384325453725414225413025453625424625383025453525383525383925453925383725384325453725413825384225453825414525413131696d6167652d32303232303532333230313235363930342e706e67 > > [image: image-20220523201554370] > https://camo.githubusercontent.com/0e80ac8520c3eca8716c97d01ea11b20d4ed7ea65053f0ae93556d329bd7ae4d/68747470733a2f2f6b61686f2d7069632d313330373130363037342e636f732e61702d6775616e677a686f752e6d7971636c6f75642e636f6d2f4353444e5f50696374757265732f2545362542372542312545382539332539442545352541342539412545342542432541302545362538342539462545352539392541382545382539452538442545352539302538382545352541452539412545342542442538442f25453725414325414325453425424125384325453725414225413025453625424625383025453525383525383925453925383725384325453725413825384225453825414525413131696d6167652d32303232303532333230313535343337302e706e67 > > — > Reply to this email directly, view it on GitHub > <#163>, or unsubscribe > https://github.com/notifications/unsubscribe-auth/ANJUIXT4NE4MNI5TFWLCFXLVLN2JJANCNFSM5WVVM75Q > . > You are receiving this because you are subscribed to this thread.Message > ID: @.***> >

非常感谢你的回复，想请问一下，这项是Jr吗？所以推导的运动模型也是和高博一样的是吗

Joanna-HE commented 2 years ago

是Jr，和高博一样。

kahowang @.***>于2022年5月25日 周三上午10:13写道：

当delta t趋近于零时，A（omega·delta t）等于单位阵 He, Dongjiao @.

>于2022年5月25日 周三上午1:19写道： … <#m8611080069083662337> kahowang @.>于2022年5月23日 周一下午8:24写道： > 如下图1为高翔老师在简明ESKF中的状态方程F雅克比矩阵推导，图二为FASTLIO1 > 论文中的F阵推导，经比对，其他项的雅克比都是一样的，但是红色框的部分(delta_R 对 dleta_bg > 求雅克比)，这里的A阵是一个小量吗，推导是怎样的，希望能解惑，谢谢。 > > [image: image-20220523201256904] > https://camo.githubusercontent.com/82cb2507050f8ca4f369c27bd370cb2ee8f62b3089d499ea4e38d31c48d934f9/68747470733a2f2f6b61686f2d7069632d313330373130363037342e636f732e61702d6775616e677a686f752e6d7971636c6f75642e636f6d2f4353444e5f50696374757265732f2545362542372542312545382539332539442545352541342539412545342542432541302545362538342539462545352539392541382545382539452538442545352539302538382545352541452539412545342542442538442f25453725414325414325453425424125384325453725414225413025453625424625383025453525383525383925453925383725384325453725413825384225453825414525413131696d6167652d32303232303532333230313235363930342e706e67

[image: image-20220523201554370] > https://camo.githubusercontent.com/0e80ac8520c3eca8716c97d01ea11b20d4ed7ea65053f0ae93556d329bd7ae4d/68747470733a2f2f6b61686f2d7069632d313330373130363037342e636f732e61702d6775616e677a686f752e6d7971636c6f75642e636f6d2f4353444e5f50696374757265732f2545362542372542312545382539332539442545352541342539412545342542432541302545362538342539462545352539392541382545382539452538442545352539302538382545352541452539412545342542442538442f25453725414325414325453425424125384325453725414225413025453625424625383025453525383525383925453925383725384325453725413825384225453825414525413131696d6167652d32303232303532333230313535343337302e706e67 — > Reply to this email directly, view it on GitHub > <#163 https://github.com/hku-mars/FAST_LIO/issues/163>, or unsubscribe > https://github.com/notifications/unsubscribe-auth/ANJUIXT4NE4MNI5TFWLCFXLVLN2JJANCNFSM5WVVM75Q . > You are receiving this because you are subscribed to this thread.Message > ID: @.***> >

非常感谢你的回复，想请问一下，这项是Jr吗？所以推导的运动模型也是和高博一样的是吗

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