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

1

Coordinate system definition

 To define a Cartesian coordinate system, we need to

dimensions.

The
in 3 the plane.

4

 CTRS is also known as Earth-Centre Earth-Fixed 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

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		ECI
			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 10-5 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=(a-b)/a, we have
a/(a-b)=1/f
Then
b=a(1-f)=a(1-f)=6356752.314

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Heights  Conventionally heights are measured

above an equal-potential 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