Add lyx document

doc/ImuFactor.lyx

@@ -0,0 +1,109 @@
+#LyX 2.0 created this file. For more info see http://www.lyx.org/
+\lyxformat 413
+\begin_document
+\begin_header
+\textclass article
+\use_default_options true
+\maintain_unincluded_children false
+\language english
+\language_package default
+\inputencoding auto
+\fontencoding global
+\font_roman default
+\font_sans default
+\font_typewriter default
+\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
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\use_hyperref false
+\papersize default
+\use_geometry false
+\use_amsmath 1
+\use_esint 1
+\use_mhchem 1
+\use_mathdots 1
+\cite_engine basic
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\use_refstyle 1
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Title
+The new IMU Factor
+\end_layout
+
+\begin_layout Author
+Frank Dellaert
+\end_layout
+
+\begin_layout Standard
+Let us assume a setup where frames with measurements are processed at some
+ fairly low rate, e.g., 10 Hz.
+ We define the state of the vehicle at those times as attitude, position,
+ and velocity.
+ These three quantities are referred to as a NavState, defining a 9-dimensional
+ manifold.
+\end_layout
+
+\begin_layout Standard
+The goal of the IMU factor is to integrate IMU measurement between two successiv
+e frames and create a binary factor between two NavStates.
+\end_layout
+
+\begin_layout Standard
+The binary factor is set up as a prediction:
+\begin_inset Formula 
+\[
+X_{j}\approx X_{i}\oplus dX_{ij}
+\]
+
+\end_inset
+
+where 
+\begin_inset Formula $dX_{ij}$
+\end_inset
+
+ is a tangent vector in the tangent space 
+\begin_inset Formula $T_{i}$
+\end_inset
+
+ to the manifold at 
+\begin_inset Formula $X_{i}$
+\end_inset
+
+.
+\end_layout
+
+\end_body
+\end_document