RNAV Training Manual - Keilir

How does GPS work?
7. The GPS Receiver: Calculation of time and position
Stage 1: The pseudorange Stage 2: The accurate fix
Wh When th the GPS receiver i is i started-up, t t d it its iinternal t l or llocal l clock l k will ill be b Th The Receiver R i th then uses th the ephemeris h i (orbital) ( bit l) ddata t iin each h
inaccurate by an unknown error, called clock bias or offset, compared to
the reference GPS Time
A modern quartz clock may be accurate to one part in a million (ie. drift by one
microsecond every second). This means that after only 1s, the internal clock error can be
th the equivalent i l t of f hundreds h d d of f metres t (1 (1µs = ~300m 300 at t th the speed d of f li light). ht) A unit it th that t s
been switched off for a week or two could be inaccurate by ~1s or hundreds of thousands
of km.
The first stage of the navigation problem is to calculate pseudoranges
from the visible satellites to the GPS, ignoring the local clock offset.
Th These ranges are pseudo d because b they th are all ll kknown tto bbe wrong by b
the same (unknown) local clock error
For any given satellite, the Receiver generates the satellite s PRN code
internally, based on its code book , and starts the code sequence at the
time t e its ts local oca cclock oc says the t e sate satellite te sshould ou d have a e sta started ted its ts PRN
transmission. The internal PRN code is then time-shifted until it matches
(locks-on) to the PRN code signal from the satellite. This time-shift, or
offset, is the (pseudo) elapsed time between transmission and the
reception Time of Arrival (TOA)
Th The Pseudorange P d iis dderived i d ffrom the th TOA, TOA assuming i a given i speed d ffor
radio wave travel and the decoded time of transmission from the satellite
The 1023 bit PRN code is transmitted at 1000 times per second, and the Receiver can
judge the start of a bit to about 1%, so the maximum accuracy of the C/A code is ~3m
By y decoding g the Navigation g Message, g , the Receiver gets g data that allows it to correct
Pseudorange for the following errors
The SV (Satellite Vehicle) time offset from GPS time
Basic ionospheric corrections from the Almanac
Relativistic effects and receiver noise
The Receiver calculates pseudoranges from different satellites
simultaneously, so they are all subject an identical local clock error
satellite s Navigation Message to establish the satellite s position in
space at the time of the Pseudorange calculation
It requires a minimum of 4 satellite pseudoranges to determine a 3D
navigational a gat o a fix for o tthe e Receiver. ece e
The GPS system specification is that 5 satellites should always be available above
a mask (elevation) angle of 7.5 degrees (usually it is 6 or more)
With 4 satellite positions known and 4 pseudo ranges calculated,
the navigation problem can be expressed as 4 equations with 4
unknowns ( (the unknowns being the x,y,z position of f the receiver
and t, the clock bias error)
The Receiver calculates a solution to these equations and
establishes a position fix
With true t (rather ( th than th pseudo) d ) ranges, it would ld only l require i 3 satellite t llit position iti
spheres to determine a fix intersect. However, with pseudoranges, a 3 sphere
solution would give the wrong range. 4 pseudoranges spheres won t intersect at a
point because the ranges are not true and consistent with a single point in space.
The receiver, in effect, solves the equations to determine which value of local clock
error creates the best intersect of the 4 spheres
The receiver also calculates a Geometric Dilution of Precision (GDOP), based on
the relative position of the satellites (satellites close together provide a weaker fix)
When more than 4 satellites are available, modern receivers use
various other algorithms to provide a better fix
Fi Finally, ll th the x,y,z position iti ffrom th the centre t of f th the earth th iis translated t l t d
into latitude, longitude and altitude using the WGS84 datum, and
GPS Time is converted into UTC. (See later pages on WGS84)
Velocity (ie. ground speed and ground track) is calculated using a
combination of rate of change of position and Doppler shift
measurement of the L1 carrier frequency of different satellites,
compared to the receiver s L1 oscillator frequency
P A
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