Time reference and gps time
Outline 1. Global coordinate systems 

2. Time reference and GPS time 3. GPS orbits and satellite position computations
4. Ground track of satellite orbits
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Coordinate system definition
To define a Cartesian coordinate system, we need to
dimensions.
The
in 3 the plane.
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CTRS is also known as EarthCentre EarthFixed Realisation of a CTRS
Example of a CTRS realisation
INB/INB353 2009 7
Conventional inertial reference system (CIRS)
The equatorial plane with the plane of the earth’s orbit around the sun 

Definition of a CIRS Definition of a CIRS is as follows Origin a the centre of mass of the earth 

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Transformation from Inertial Space to Terrestrial Frame 

To account for the variations in Earth rotation parameters, as standard matrix rotation is
r    x   ECF  ECI   x   ECI  ,  r    x   ECF 

R  ECI   x   e  y  



 y    y    y    y  x   
e  
  ECF      ECF    
z  z  z  z  
        
 sin  0   
RECI ECF  ( )     sin   cos 

0   
  
0  0  1  
 
where ω e is the rotation rate of the earth (7.2921158553 x 105 rad/sec


The limitations of Cartesian coordinates: x,y,z: not
straightforward, not suitable for mapping Geodetic coordinates:
latitude, longitude and height that is defined on an oblate ellipsoid
also known as geographic or ellipsoid
coordinates
It is different from geocentric coordinates
Given a=6378137.0 m, the reciprocal flattening 1/f=298.257223563,
prove b=6356752.314m Solution:
From, f=(ab)/a, we have
a/(ab)=1/f
Then
b=a(1f)=a(1f)=6356752.314
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Heights Conventionally heights are measured
above an equalpotential surface
corresponding approximately to mean sea level (MSL) called the geoid
Ellipsoidal heights (e.g. from GPS) are measured above the ellipsoid
The difference is called the geoidal height See the next slide for the relationship