This is the kinetic model for the MIT Draper X-Cell 90 developed by Rudolph van der Merwe in his dissertation on Sigma Point Kalman Filtering.

This is a 6DOF (Degrees of Freedom) rocket process model with 3D movement (translation and rotation) and has no modeling of forces on moments that act on the rocket. It uses the IMU (inertial measurement unit, that is the linear accelerations and the rotational velocities) to drive the 6DOF differential equations for this model.

An 18 dimension state vector would be used since we have an additional accelerometer q.

Variable |
Description |
Variable |
Description |
---|---|---|---|

x | north position | a,,b,,,,x,, | IMU x accelerometer bias |

y | east position | a,,b,,,,y,, | IMU y accelerometer bias |

z | down position | a,,b,,,,z,, | IMU z accelerometer bias |

q | ??? position | a,,b,,,,q,, | IMU q accelerometer bias |

v,,x,, | north velocity | w,,b,,,,x,, | (roll) gyro rate bias |

v,,y,, | east velocity | w,,b,,,,y,, | (pitch) gyro rate bias |

v,,z,, | down velocity | w,,b,,,,z,, | (yaw) gyro rate bias |

e,,0,, | attitude quaternion 1st component | e,,1,, | attitude quaternion 2nd component |

e,,2,, | attitude quaternion 3rd component | e,,3,, | attitude quaternion 4th component |

The models for PSAS would be something equivalent but in addition needs to account for all the Inertial Navigation System (INS) Error Equations.