1. Introduction
The 3D coordinates of the GPS receiver position and the
receiver clock error can be estimated based on the trilateration
concept provided that at least four GPS satellites
are simultaneously tracked by the GPS receiver. Trilateration
is a geometric method used to determine the location
of a point using the geometry of spheres based on distance
measurements [1]. The position and velocity vectors of
each satellite can be acquired from the broadcast ephemerides.
Much precise ephemerides can be obtained from
the International GPS Services (IGS). The positioning
accuracy can be improved with more observations either
from other satellites that are simultaneously tracked or
from the same set of satellites with longer observing time.
The distance from a GPS receiver to a satellite (called
range) can be obtained from two GPS observables: 1)
pseudo ranges (from codes) and 2) phase ranges. The
pseudo range observable is a measure of the distance between
the satellite and the receiver’s antenna, referring to
the epoch of emission and reception of the codes [2]. The
range can be determined by multiplying the speed of light
and the total travel time, which is inferred from correlateing
the identical pseudo-random noise (PRN) of the received
codes to the receiver-generated replica. On the
other hand, the range can also be expressed by the total
number of waves, including the integer and the fractional
parts, multiplied by the wavelength of the carrier wave [3].
The phase observable is the fractional part of the phase
difference between the received wave and that of the internal
receiver oscillator. The integer part of the exact
number of carrier waves from each satellite to the antenna,
called the initial integer ambiguity, remains unknown and
needs to be solved for. The correct ambiguity solution is a
key to achieve higher accuracy in the kinematic GPS positioning.
It is common to use both code and phase observations,
provided that the receiver is equipped with
such capabilities. A typical single commercial GPS receiver
(non-geodetic grade) can estimate the user’s position
to within an average accuracy of about 12 meters,which is not satisfactory for many applications. In fact,
GPS can produce positions that are accurate to sub-centimeter
level. Many factors affect the accuracy of GPS positioning
including orbital errors, satellite and receiver
clock errors, signal propagation errors, measurement noise,
satellite geometry measures, tropospheric delay, ionospheric
delay, multipath errors, ect..
GPS positional accuracy can be improved by using
differential corrections obtained by using a technique
called Differential GPS (DGPS), which has been known
to provide the most accurate positioning results [4]. Differential
correction can be applied in real time at the data
collection phase or in the office, at the post-processing
phase. The simple setting of the Differential GPS (DGPS)
involves the cooperation of two receivers: one is referred
to the base or reference station (whose coordinates are
known with the associated variance and covariance); the
other is referred to the rover (whose coordinates are to be
determined while being either stationary or moving).
With both receivers collecting data simultaneously, the
common errors such as the clock synchronization errors
and the atmospheric range delays can be eliminated by
differencing the observations of both receivers with respect
to the same set of satellites. DGPS provides the
rover’s coordinates with respect to the reference station
due to the differencing; that is, the 3D coordinate components
of the relative position vector from the reference
station to the rover’s position. In addition, as the baseline
length between the reference station and the rover’s position
increases, the number of satellites simultaneously
tracked decreases, and therefore the atmospheric conditions
at the ends of the baseline start to de-correlate [5].
As a result, the differencing can no longer eliminate as
much atmospheric errors as it would in the case of shorter
baseline. Hence, the rover’s position accuracy depends
on that of the reference station’s coordinates as
well as the baseline length. The length of the baseline
between the base station and the location to be estimated
affects the positioning accuracy as shown below:
DGPS positioning accuracy = ±[0.5 cm + 1 ppm of the
baseline length]
This demonstrates that DGPS is largely dependent on
the length of the baseline. This limitation can be resolved
by using shorter baselines or by establishing a so-called
virtual reference station (VRS). The concept of VRS will
be covered later in the paper. Although DGPS reduces
atmospheric, ephemeris, and satellite clock errors; it
doesn’t reduce errors form satellite measurement geometry,
multipath, or the receiver. Nevertheless, networks of
points based on DGPS concept are being established by
governmental and nongovernmental organization around
the world for positioning and navigation purposes. These
DGPS networks whether used for positioning or navigation,
are commonly known as wide-area GNSS networks.