diff --git a/doc/ImuFactor.lyx b/doc/ImuFactor.lyx index 55b7201e5..0922a3e9c 100644 --- a/doc/ImuFactor.lyx +++ b/doc/ImuFactor.lyx @@ -1,5 +1,5 @@ -#LyX 2.1 created this file. For more info see http://www.lyx.org/ -\lyxformat 474 +#LyX 2.0 created this file. For more info see http://www.lyx.org/ +\lyxformat 413 \begin_document \begin_header \textclass article @@ -12,13 +12,13 @@ \font_roman default \font_sans default \font_typewriter default -\font_math auto \font_default_family default \use_non_tex_fonts false \font_sc false \font_osf false \font_sf_scale 100 \font_tt_scale 100 + \graphics default \default_output_format default \output_sync 0 @@ -29,24 +29,15 @@ \use_hyperref false \papersize default \use_geometry true -\use_package amsmath 1 -\use_package amssymb 1 -\use_package cancel 1 -\use_package esint 1 -\use_package mathdots 1 -\use_package mathtools 1 -\use_package mhchem 1 -\use_package stackrel 1 -\use_package stmaryrd 1 -\use_package undertilde 1 +\use_amsmath 1 +\use_esint 1 +\use_mhchem 1 +\use_mathdots 1 \cite_engine basic -\cite_engine_type default -\biblio_style plain \use_bibtopic false \use_indices false \paperorientation portrait \suppress_date false -\justification true \use_refstyle 1 \index Index \shortcut idx @@ -253,7 +244,7 @@ X(t)=\left\{ R_{0},P_{0}+V_{0}t,V_{0}\right\} then the differential equation describing the trajectory is \begin_inset Formula \[ -\dot{X}(t)=\left[0_{3x3},V_{0},0_{3x1}\right],\,\,\,\,\,X(0)=\left\{ R_{0},P_{0},V_{0}\right\} +\dot{X}(t)=\left[0_{3x3},V_{0},0_{3x1}\right],\,\,\,\,\, X(0)=\left\{ R_{0},P_{0},V_{0}\right\} \] \end_inset @@ -611,7 +602,7 @@ key "Iserles00an" , \begin_inset Formula \begin{equation} -\dot{R}(t)=F(R,t),\,\,\,\,R(0)=R_{0}\label{eq:diffSo3} +\dot{R}(t)=F(R,t),\,\,\,\, R(0)=R_{0}\label{eq:diffSo3} \end{equation} \end_inset @@ -956,8 +947,8 @@ Or, as another way to state this, if we solve the differential equations \begin_inset Formula \begin{eqnarray*} \dot{\theta}(t) & = & H(\theta)^{-1}\,\omega^{b}(t)\\ -\dot{p}(t) & = & R_{0}^{T}\,V_{0}+v(t)\\ -\dot{v}(t) & = & R_{0}^{T}\,g+R_{b}^{0}(t)a^{b}(t) +\dot{p}(t) & = & R_{0}^{T}\, V_{0}+v(t)\\ +\dot{v}(t) & = & R_{0}^{T}\, g+R_{b}^{0}(t)a^{b}(t) \end{eqnarray*} \end_inset @@ -1024,7 +1015,7 @@ v(t)=v_{g}(t)+v_{a}(t) evolving as \begin_inset Formula \begin{eqnarray*} -\dot{v}_{g}(t) & = & R_{i}^{T}\,g\\ +\dot{v}_{g}(t) & = & R_{i}^{T}\, g\\ \dot{v}_{a}(t) & = & R_{b}^{i}(t)a^{b}(t) \end{eqnarray*} @@ -1050,7 +1041,7 @@ p(t)=p_{i}(t)+p_{g}(t)+p_{v}(t) evolving as \begin_inset Formula \begin{eqnarray*} -\dot{p}_{i}(t) & = & R_{i}^{T}\,V_{i}\\ +\dot{p}_{i}(t) & = & R_{i}^{T}\, V_{i}\\ \dot{p}_{g}(t) & = & v_{g}(t)=R_{i}^{T}gt\\ \dot{p}_{v}(t) & = & v_{a}(t) \end{eqnarray*} @@ -1105,7 +1096,7 @@ Predict the NavState from \begin_inset Formula \[ -X_{j}=\mathcal{R}_{X_{i}}(\zeta(t_{ij}))=\left\{ \Phi_{R_{0}}\left(\theta(t_{ij})\right),P_{i}+V_{i}t_{ij}+\frac{gt_{ij}^{2}}{2}+R_{i}\,p_{v}(t_{ij}),V_{i}+gt_{ij}+R_{i}\,v_{a}(t_{ij})\right\} +X_{j}=\mathcal{R}_{X_{i}}(\zeta(t_{ij}))=\left\{ \Phi_{R_{0}}\left(\theta(t_{ij})\right),P_{i}+V_{i}t_{ij}+\frac{gt_{ij}^{2}}{2}+R_{i}\, p_{v}(t_{ij}),V_{i}+gt_{ij}+R_{i}\, v_{a}(t_{ij})\right\} \] \end_inset @@ -1381,7 +1372,7 @@ B_{k}=\left[\begin{array}{c} 0_{3\times3}\\ R_{k}\frac{\Delta_{t}}{2}^{2}\\ R_{k}\Delta_{t} -\end{array}\right],\,\,\,\,C_{k}=\left[\begin{array}{c} +\end{array}\right],\,\,\,\, C_{k}=\left[\begin{array}{c} H(\theta_{k})^{-1}\Delta_{t}\\ 0_{3\times3}\\ 0_{3\times3} @@ -1391,147 +1382,6 @@ H(\theta_{k})^{-1}\Delta_{t}\\ \end_inset -\end_layout - -\begin_layout Subsubsection* -Units -\end_layout - -\begin_layout Standard -The units of the IMU are as follows: -\end_layout - -\begin_layout Standard -\begin_inset Tabular - - - - - - -\begin_inset Text - -\begin_layout Plain Layout -Parameter -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -Units -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -gyro_noise_sigma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $rad/s/\sqrt{Hz}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -accel_noise_sigma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $m/s^{2}/\sqrt{Hz}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -gyro_bias_rw_sigma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $rad/s$ -\end_inset - - or -\begin_inset Formula $rad\sqrt{Hz}/s$ -\end_inset - - -\end_layout - -\end_inset - - - - -\begin_inset Text - -\begin_layout Plain Layout -accel_bias_rw_sigma -\end_layout - -\end_inset - - -\begin_inset Text - -\begin_layout Plain Layout -\begin_inset Formula $m/s^{2}$ -\end_inset - -or -\begin_inset Formula $m\sqrt{Hz}/s^{2}$ -\end_inset - - -\end_layout - -\end_inset - - - - -\end_inset - - \end_layout \begin_layout Standard diff --git a/doc/ImuFactor.pdf b/doc/ImuFactor.pdf index adec08aa3..0b13c1f59 100644 Binary files a/doc/ImuFactor.pdf and b/doc/ImuFactor.pdf differ