Global Positioning System Reference
In-Depth Information
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C
HAPTER 5
[Fir
PSEUDORANGE AND CARRIER PHASE
O
BSERVABLES
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—
0.0
——
Nor
PgE
Pseudoranges and carrier phases are the most important GPS observations (observ-
ables) used for positioning. Solutions are available that use pseudoranges only, carrier
phases only, or both types of observations. The early solutions for navigation relied
on pseudoranges. More recently, even point positioning often includes the carrier
phase observable. Carrier phases are always required for accurate surveying at the
centimeter level. Processing algorithms exist that use the (undifferenced) observa-
tions directly. However, one often uses certain linear combinations. Popular examples
are the double differences and the triple differences.
Measuring pseudoranges and carrier phases involves advanced techniques in elec-
tronics and digital signal processing. This chapter deals with the equations that di-
rectly apply to the pseudoranges and carrier phases as downloaded from the receiver.
The goal is to determine geocentric positions (point positioning) or relative positions
between co-observing stations (differential or relative positioning). These equations
are also the basis for estimating ionospheric and tropospheric parameters with GPS,
or the transfer of time.
In addition to deriving and discussing the basic pseudorange and carrier phase
equations and the double- and triple-difference functions, we address frequently
asked questions of novice GPS users. Examples include simultaneity of observations,
singularities, and a priori knowledge of initial station and ephemeris. The implications
of relativity for GPS observables have widely been addressed in the literature, e.g.,
Grafarend (1992), Hatch (1992), Ashby (1993), and Schwarze et al. (1993). In this
chapter, remarks on relativity are limited to Section 5.3.1, where a clock correction
term is given to account for satellite orbital eccentricity. The correction and the ad-
justment to the fundamental frequency of 10.23 MHz mentioned in Section 3.2.2 are
the only references to the applicability of relativity to GPS in this topic. In relative
positioning, most of the relativistic effects cancel or become negligible.
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