## Applied Mathematics in Integrated Navigation Systems, Volume 1Intended for those directly involved with the design, integration, and test and evaluation of navigation systems, this text/CD-ROM presents elements of basic mathematics, kinematics, equations describing navigation systems and their error models, and Kalman filtering. Detailed derivations are presen |

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### Contents

Introduction | 3 |

Coordinate Systems and Transformations | 41 |

Earth Models | 59 |

Terrestrial Navigation | 73 |

Navigation Sensor Models | 101 |

Navigation Aids | 117 |

Kalman Filtering | 141 |

StrapDown Inertial Sensor Laboratory Calibration | 173 |

Inertial Navigation System Ground Alignment | 215 |

Global Positioning | 229 |

InMotion Alignment | 245 |

Integrated Differential Global Positioning | 267 |

Attitude Determination and Estimation | 279 |

Summary | 299 |

Appendix B Global Positioning System Position Velocity | 313 |

Fine Alignment Error Equations | 321 |

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### Common terms and phrases

acceleration accelerometer and gyro aircraft assumed attitude error vector axis azimuth error ballute body referenced coarse alignment components coordinate frame corresponding covariance matrix defined developed DGPS differential equation direction cosine matrix Doppler dynamic equations Earth ECEF ECEF frame elements error dynamic model error equations error representation estimation error Euler angle expressed following equation geodetic geographic frame given in Eq Global Positioning System GPS receiver gravity illustrated inertial navigation system inertial sensor initial integrated navigation systems ISBN Kalman filter algorithm latitude least-squares linear longitude measurement matrix measurement update navigation equations navigation frame navigation solution navigation state data navigation system error obtained outputs partial derivative perturbation position error position vector process noise pseudorange radar reference frame satellite sensor errors shown in Fig simulation strap-down symmetric matrix system error model TACAN terrestrial navigation tilt error transformation matrix variance wander azimuth frame zero

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