From 755c75278215739d39b36fed689d3ae0b6ca79c5 Mon Sep 17 00:00:00 2001 From: Varun Agrawal Date: Tue, 21 Sep 2021 12:29:36 -0400 Subject: [PATCH] update ImuFactor doc --- doc/ImuFactor.lyx | 41 ++++++++++++++++++++++++++++++++++------- doc/ImuFactor.pdf | Bin 225325 -> 225898 bytes 2 files changed, 34 insertions(+), 7 deletions(-) diff --git a/doc/ImuFactor.lyx b/doc/ImuFactor.lyx index bba8f212a..c79a5f37a 100644 --- a/doc/ImuFactor.lyx +++ b/doc/ImuFactor.lyx @@ -1427,15 +1427,34 @@ pose/velocity/bias \begin_layout Standard We expand the state vector as -\begin_inset Formula $\zeta_{k}=[\theta_{k},p_{k},v_{k},a_{k}^{b}, \omega_{k}^{b}]$ +\begin_inset Formula $\zeta_{k}=[\theta_{k},p_{k},v_{k},b_{k}^{a},b_{k}^{\omega}]$ \end_inset -. - For the jacobian + to include the bias terms. + This gives the noise propagation equation as +\end_layout + +\begin_layout Standard +\begin_inset Formula +\begin{equation} +\Sigma_{k+1}=F_{k}\Sigma_{k}F_{k}^{T}+G_{k}\Sigma_{k}G_{k}\label{eq:prop-combined} +\end{equation} + +\end_inset + + +\end_layout + +\begin_layout Standard +where \begin_inset Formula $F_{k}$ \end_inset - of + is the +\begin_inset Formula $15\times15$ +\end_inset + + derivative of \begin_inset Formula $f$ \end_inset @@ -1443,13 +1462,21 @@ We expand the state vector as \begin_inset Formula $\zeta$ \end_inset -, we get a +, and +\begin_inset Formula $G_{k}$ +\end_inset + + is the \begin_inset Formula $15\times15$ \end_inset - matrix. + matrix for first order uncertainty propagation. The top-left \begin_inset Formula $9\times9$ +\end_inset + + of +\begin_inset Formula $F_{k}$ \end_inset is the same as @@ -1481,7 +1508,7 @@ derivation as matrices \begin_layout Standard \begin_inset Formula \[ -F_{k}=\left[\begin{array}{ccccc} +F_{k}\approx\left[\begin{array}{ccccc} I_{3\times3}-\frac{\Delta_{t}}{2}\Skew{\omega_{k}^{b}} & & & & H(\theta_{k})^{-1}\Delta_{t}\\ R_{k}\Skew{-a_{k}^{b}}H(\theta_{k})\frac{\Delta_{t}}{2}^{2} & I_{3\times3} & I_{3\times3}\Delta_{t} & R_{k}\frac{\Delta_{t}}{2}^{2}\\ R_{k}\Skew{-a_{k}^{b}}H(\theta_{k})\Delta_{t} & & I_{3\times3} & R_{k}\Delta_{t}\\ diff --git a/doc/ImuFactor.pdf b/doc/ImuFactor.pdf index 37badae9cc979302341b1dbac23e03b5be7445d9..933c71a749610b513627409ff903042378fbd989 100644 GIT binary patch delta 48287 zcmV(nK=Qw>;0@~J4UqaI!pjjxityai0V)|)#NN|*sas=V4M|64(Egp%ZJPc71)N0( zvmOEKO9L}DH))s60T4qCMat4{F5+;|=j)lC&erHW=t`>QpL|@v)MHDAgr@CYEjku=kT^|msPnATVL98W!>rAaR@_#n{XU3 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