added Imu parameter units to doc
Varun Agrawal
parent
0b045fdc59
commit
845b6c55b3
|
|
@ -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
|
||||
<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
|
||||
|
|
|
|||
Binary file not shown.
Loading…
Reference in New Issue