Add lyx document
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#LyX 2.0 created this file. For more info see http://www.lyx.org/
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\lyxformat 413
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\begin_document
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\begin_header
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\textclass article
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\use_default_options true
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\language english
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\index Index
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\shortcut idx
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\color #008000
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\end_index
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\end_header
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\begin_body
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\begin_layout Title
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The new IMU Factor
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\end_layout
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\begin_layout Author
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Frank Dellaert
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\end_layout
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\begin_layout Standard
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Let us assume a setup where frames with measurements are processed at some
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fairly low rate, e.g., 10 Hz.
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We define the state of the vehicle at those times as attitude, position,
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and velocity.
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These three quantities are referred to as a NavState, defining a 9-dimensional
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manifold.
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\end_layout
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\begin_layout Standard
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The goal of the IMU factor is to integrate IMU measurement between two successiv
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e frames and create a binary factor between two NavStates.
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\end_layout
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\begin_layout Standard
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The binary factor is set up as a prediction:
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\begin_inset Formula
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\[
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X_{j}\approx X_{i}\oplus dX_{ij}
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\]
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\end_inset
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where
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\begin_inset Formula $dX_{ij}$
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\end_inset
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is a tangent vector in the tangent space
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\begin_inset Formula $T_{i}$
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\end_inset
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to the manifold at
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\begin_inset Formula $X_{i}$
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\end_inset
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.
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\end_layout
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\end_body
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\end_document
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