Basic Navigational Mathematics, Reference Frames and the Earth’s Geometry

  • Aboelmagd Noureldin
  • Tashfeen B. Karamat
  • Jacques Georgy


Navigation algorithms involve various coordinate frames and the transformation of coordinates between them. For example, inertial sensors measure motion with respect to an inertial frame which is resolved in the host platform’s body frame. This information is further transformed to a navigation frame. A GPS receiver initially estimates the position and velocity of the satellite in an inertial orbital frame. Since the user wants the navigational information with respect to the Earth, the satellite’s position and velocity are transformed to an appropriate Earth-fixed frame. Since measured quantities are required to be transformed between various reference frames during the solution of navigation equations, it is important to know about the reference frames and the transformation of coordinates between them. But first we will review some of the basic mathematical techniques.


Transformation Matrix Coordinate Frame Inertial Frame Body Frame Orthometric Height 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Aboelmagd Noureldin
    • 1
  • Tashfeen B. Karamat
    • 2
  • Jacques Georgy
    • 3
  1. 1.Department of Electrical and Computer EngineeringRoyal Military College of Canada/Queen’s UniversityKingstonCanada
  2. 2.Department of Electrical and Computer EngineeringQueen’s UniversityKingstonCanada
  3. 3.Trusted Positioning Inc.CalgaryCanada

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