diff --git a/doc/ImuFactor.lyx b/doc/ImuFactor.lyx index 0922a3e9c..55b7201e5 100644 --- a/doc/ImuFactor.lyx +++ b/doc/ImuFactor.lyx @@ -1,5 +1,5 @@ -#LyX 2.0 created this file. For more info see http://www.lyx.org/ -\lyxformat 413 +#LyX 2.1 created this file. For more info see http://www.lyx.org/ +\lyxformat 474 \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 @@ -29,15 +29,24 @@ \use_hyperref false \papersize default \use_geometry true -\use_amsmath 1 -\use_esint 1 -\use_mhchem 1 -\use_mathdots 1 +\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 \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 @@ -244,7 +253,7 @@ 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 @@ -602,7 +611,7 @@ 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 @@ -947,8 +956,8 @@ 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 @@ -1015,7 +1024,7 @@ 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*} @@ -1041,7 +1050,7 @@ 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*} @@ -1096,7 +1105,7 @@ 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 @@ -1372,7 +1381,7 @@ 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} @@ -1382,6 +1391,147 @@ 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 0b13c1f59..adec08aa3 100644 Binary files a/doc/ImuFactor.pdf and b/doc/ImuFactor.pdf differ