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| #LyX 2.0 created this file. For more info see http://www.lyx.org/ | ||||
| \lyxformat 413 | ||||
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| 
 | ||||
| \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 | ||||
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