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Path: SCPro/ProSensors
% Position and velocity of a GPS satellite in the earth-fixed reference frame.
The input data structure is data found in the GPS navigation message.
The GPS message has 5 subframes. The first contains the GPS week number,
a prediction of the user range accuracy, indicators of satellite health
and of the age of the data, an estimation of ths signal group delay, the
clock reference time and three coefficients for a quadratic polynomial
to model the satellite clock correction.
Each subframe consists of 10 30 bit words. Each has a header with the
telemetry word containing a synchronization pattern, and diagnostic
messages. The second word is the handover word containing the
time-of-week count for the epoch at the start of the next subframe.
The time-of-week count is a multiple of 1.5 second intervals since the
beginning of the current GPS week.
The second and third subframes transmit the broadcast ephemerides used in
this function.
It takes 30 seconds to transmit all five subframes, thus the broadcast
ephemerides are updated every 30 seconds.
The fourth and fifth subframes are change every message and have a
repetition rate of 25. Thus the total information takes 25 pages. The
fourth and fifth subframes contain the low-precision almanac for all of
the satellites in the GPS constellation. Thus every 12.5 minutes the
satellite gets an update for all 24 GPS satellites.
This routine can handle either the broadcast ephemerides or almanac.
The almanac angles are in semicircles (e.g. 0.1 = 18 deg.)
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Form:
[r, v, delta] = GPSOrbit( d, t )
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Inputs
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d (1,1) GPS Ephemerides
.tC (1,1) Satellite clock reference epoch
.a0 (1,1) Satellite clock offset
.a1 (1,1) Satellite clock drift
.a2 (1,1) Satellite clock frequency drift
.tE (1,1) Ephemerides reference epoch
.t0 (1,1) Sidereal time reference epoch
.e (1,1) Eccentricity
.sqrtA (1,1) Square root of semimajor axis (sqrt(m))
.m0 (1,1) Mean anomaly at reference epoch (rad)
.w0 (1,1) Argument of perigee (rad)
.i0 (1,1) Inclination (rad)
.l0 (1,1) Longitude of the node at the weekly epoch (rad)
.deltaN (1,1) Mean motion difference
.iDot (1,1) Rate of inclination angle (rad/s)
.omegaDot (1,1) Rate of note's right ascension
.cUC (1,1) Correction coefficient (argument of perigee)
.cUS (1,1) Correction coefficient (argument of perigee)
.cRC (1,1) Correction coefficient (radius)
.cRS (1,1) Correction coefficient (radius)
.cIC (1,1) Correction coefficient (inclination)
.cIS (1,1) Correction coefficient (inclination)
or
d (1,1) GPS Almanac
.e (1,1) Eccentricity
.tA (1,1) Ephemerides reference epoch
.t0 (1,1) Sidereal time reference epoch
.sqrtA (1,1) Square root of semimajor axis (sqrt(m))
.m0 (1,1) Mean anomaly at reference epoch (semicircles)
.w (1,1) Argument of perigee (semicircles)
.deltaI (1,1) Inclination delta (semicircles)
.l0 (1,1) Longitude of the node at the weekly epoch (semicircles)
.deltaN (1,1) Mean motion difference
.omegaDot (1,1) Rate of note's right ascension (semicircles/sec)
.a0 (1,1) Satellite clock offset
.a1 (1,1) Satellite clock drift
t (1,:) Observation epoch (sec)
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Outputs
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r (3,:) Earth-fixed Position vector (m)
v (3,:) Earth-fixed Velocity vector (m/s)
delta (1,:) Clock error
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Reference: Hofmann-Wellenhof, B., Lichtenegger, H. and J. Collins, "GPS:
Theory and Practice 4th Edition," Springer-Verlag.
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Common: Graphics/Plot2D SC: BasicOrbit/CP2I SC: BasicOrbit/M2Nu
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