From f6200f4a2bba50b46e2be07d81cd52f9f0ce84ac Mon Sep 17 00:00:00 2001
From: Frank Dellaert <frank@skyd.io>
Date: Sat, 10 Oct 2015 13:48:52 -0700
Subject: [PATCH] Add lyx document

---
 doc/ImuFactor.lyx | 109 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 109 insertions(+)
 create mode 100644 doc/ImuFactor.lyx

diff --git a/doc/ImuFactor.lyx b/doc/ImuFactor.lyx
new file mode 100644
index 000000000..a1d33bf47
--- /dev/null
+++ b/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
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+\cite_engine basic
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+\index Index
+\shortcut idx
+\color #008000
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+\tocdepth 3
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+\tracking_changes false
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+\html_math_output 0
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+\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