GPS receivers which record carrier phase, measure the fraction of one wavelength (i.e. fraction of 19 cm for the L1 carrier) when the receiver first locks onto a satellite and continuously measure the carrier phase from that time.
Number of cycles between the satellite and receiver at initial start up (known as the ambiguity ) and the measured carrier phase together represent the satellite-receiver range. A simplified carrier phase model can be given as:
measured carrier phase = range + (ambiguity ´ wavelength) + errors Φ = r + N λ + errors
Φ measured carrier phase in meters
r satellite-receiver range in meters
N ambiguity (i.e. number of cycles)
λ carrier wavelength in meters.
A general carrier phase equation with different errors is (Leick, 2004):
Difference between received phase at receiver i and transmitted phase from satellite p
Nominal carrier frequency
Ionospheric phase advance at L1, depends on ionospheric conditions along the path and on frequency, always negative since the phase is advanced by ionosphere
Tropospheric delay, depends on tropospheric conditions along path but independent of carrier frequency. Hence, no subscript to identify it, always positive
Hardware delays and multipath effects on L1 carrier phase
L1 phase measurement noise (< 0.01 cycles).
Integer ambiguity. Refers to the first epoch of observations and remains constant during period of observation unless any cycle slip occurs after which it may continue with a new constant integer value of N.
Carrier based measurements can be converted from cycle units to length units by multiplying both sides with λ1 = c / f1
A typical example of conversion from cycle units to length units.
A typical example of conversion from cycle units to length units.
