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IMU Parameters Documentation #624

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merged 5 commits into from
Dec 2, 2020
+8 −4
Merged

IMU Parameters Documentation #624

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845b6c5
added Imu parameter units to doc
varunagrawal Dec 1, 2020
31bf4b3
formatting
varunagrawal Dec 1, 2020
1bf7588
Revert "added Imu parameter units to doc"
varunagrawal Dec 1, 2020
63fc7b5
Revert "formatting"
varunagrawal Dec 1, 2020
a4d443e
Added units for imu noise and bias sigmas
varunagrawal Dec 1, 2020
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2 changes: 1 addition & 1 deletion cmake/GtsamTesting.cmake
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Original file line number Diff line number Diff line change
Expand Up @@ -88,7 +88,7 @@ enable_testing()

option(GTSAM_BUILD_TESTS "Enable/Disable building of tests" ON)
option(GTSAM_BUILD_EXAMPLES_ALWAYS "Build examples with 'make all' (build with 'make examples' if not)" ON)
option(GTSAM_BUILD_TIMING_ALWAYS "Build timing scripts with 'make all' (build with 'make timing' if not" OFF)
option(GTSAM_BUILD_TIMING_ALWAYS "Build timing scripts with 'make all' (build with 'make timing' if not" OFF)
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remove this from diff

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Aye aye


# Add option for combining unit tests
if(MSVC OR XCODE_VERSION)
Expand Down
180 changes: 165 additions & 15 deletions doc/ImuFactor.lyx
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Original file line number Diff line number Diff line change
@@ -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
Expand All @@ -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
Expand All @@ -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
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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*}

Expand All @@ -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*}
Expand Down Expand Up @@ -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
Expand Down Expand Up @@ -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}
Expand All @@ -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
<lyxtabular version="3" rows="5" columns="2">
<features rotate="0" tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Parameter
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
Units
\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
gyro_noise_sigma
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $rad/s/\sqrt{Hz}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
accel_noise_sigma
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
\begin_inset Formula $m/s^{2}/\sqrt{Hz}$
\end_inset


\end_layout

\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
gyro_bias_rw_sigma
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\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
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text

\begin_layout Plain Layout
accel_bias_rw_sigma
\end_layout

\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\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
</cell>
</row>
</lyxtabular>

\end_inset


\end_layout

\begin_layout Standard
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