Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos

proportional to the rate of change of the total electron content of the ionosphere.
The upper limit for the frequency measurement error due to the ionosphere is
0.085 Hz. This value corresponds to the error of 1.6 cm/s in the delta range
measurement[Parkinson & Spilker, p. 495].
The frequency shift due to the ionosphere is a function of transmitted frequency.
Consequently, the users receivingtwo different frequencies can correct for the first
order ionospheric errors.
5.1.2 Receiver Noise
Even if the frequency of the GPS signal managed to penetrate the ionosphere
without disturbance, the actual measurement would still cause errors. The properties
of the measurement errors depend heavily on the receiver architecture. The
largest receiver error in the frequency measurement is the clock drift error d. Its
effect on the delta range measurement can be of the order of 10 m/s. Fortunately,
the clock drift error can be taken as an extra variable that is solved for, as was
done in Chapter 4. The order of magnitude of the remaining receiver noise is
hard to estimate theoretically.
5.1.3 Unknown User Velocity
In Subsection 4.3.3 we assumed that the satellite relative velocity vectors vi are
known. With the equation 4.2, vi was defined as wi − wu, wherewi is the
satellite velocity vector and wu is the user velocity vector. The satellite velocity
vector wi can be calculated from the current ephemeris if one knows the current
time. By contrast, the user velocity vector wu is unknown unless one has some
extra information. The most common form of extra information is probably the
knowledge that the user is stationary.
Takingthe vector wu as a variable to be solved for means that we have three
more unknowns, since wu ∈ R 3 . Thus, the number of required satellites for the
positioningincreases from four to the usually unrealistic number of seven. Solving
for wu is not considered any further here.
Let us consider the error that the unknown user velocity causes. Assume that
the user velocity wu is replaced by a biased user velocity estimate wu + △wu.
Then, accordingto the equation 4.2, the satellite relative velocity vectors vi are
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