PRINCIPLES OF POSITIONING |
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I>positioning is meant the determination of the spatial location
of
objects:
With respect to a coordinate system whose origin is uniquely defined, and generally inaccessible. Positioning in this system is known as point positioning or absolute positioning.
In
this mode of positioning the reference system must be rigorously
defined
and maintained. No direct access to the origin, or the reference
axes,
is usually possible and total reliance is placed on the integrity
of the
coordinated points within the reference system. In general the origin
is
the geocentre, and the axes of the system are defined in a
conventional
manner. In classical geodesy, astronomic observations were the
only means
by which an absolute position (more correctly, the horizontal
components
of position) could be obtained.
In modern geodesy, satellite tracking offers the means by which 3-D position can be determined with varying degrees of accuracy. Satellite point positioning is the process by which:
(1) given the position vector of the satellite being tracked (in the global system);
(2) given the range vector from the ground tracking station to the satellite being tracked (in the same system);
(3) determine the position vector of the ground station.
This is conceptually illustrated in Figure 1 below. The following comments can be made:
Figure 1. Basic concept of
satellite point positioning.
R is the position vector of the antenna relative to the origin r is the position vector of the satellite relative to the origin is the range vector between the antenna and satellite
Some space geodesy technologies can
determine the absolute position of a
stationary object to a very high
accuracy, as for example the Satellite
Laser Ranging (SLR) technique. In
general, however, the coordinates of a
station in an absolute
sense are determined to a much lower accuracy
than the precision of
the measurements themselves.
This
is the mode used in conventional terrestrial geodesy.
Although
coordinates are expressed in terms of the three coordinate
components of
a global reference system, they are derived from
observations made
to nearby control points whose coordinates are
known.
In classical geodesy the absolute coordinates of an "origin" station in a geodetic datum are arbitrarily assigned, and their relation to the geocentre is therefore rather poorly defined. However, as a result of high precision geodetic survey operations, the coordinates of other stations are determined to a comparatively high accuracy, but only in a relative sense. An entire family of points can be fixed in this way to construct a network. A network is an efficient means of propagating position information, and given the many possible "pathways" in a network from one station to any other station, the "redundant" information can be utilised in a network "adjustment" to derive the best set of coordinates for all the network control points.
Since conventional terrestrial positioning technologies have in the past been used exclusively to determine the interstation vectors, the links between adjacent network points have been restricted to those which have the property of station intervisibility. It is usual to distinguish between a horizontal geodetic network, for which the latitudes and longitudes of control points are determined to a high (relative) accuracy, and a geodetic levelling (or vertical) network comprising points whose heights are known accurately. In general, the horizontal control points have only weakly determined heights, while level benchmarks do not have accurate horizontal position information.
In the case of GPS, absolute position is rather poorly defined (that is, the coordinates relative to the origin of the global satellite datum), but relative positioning of two or more stations can be performed to a very high precision. Conceptually, relative position is the difference between the two position vectors (in the global system), expressed in a local reference system with origin at one of the ground stations. Most errors in absolute position are common to both sets of coordinates, and hence largely cancel from the baseline components. In this case the positioning accuracy approaches that of the basic measurement precision itself, and this is therefore the standard GPS surveying mode (as well as for precise GPS navigation).
Ideally, to determine theposition vector of a station, or the baseline
vector between a pair of stations,
it is preferable to measure both
the length of
the range vector and its orientation. There is no one
system that can
provide all this information simultaneously, and to the
precision required
for surveying and navigation applications. The space
positioning techniques
that have been developed to date are generally based
on the following
observation technologies (Figure 2):
Figure 2. Extraterrestrial
geodetic positioning technologies.
It is beyond the scope of these lecture notes to describe the systems based on these measurement technologies and the reader is referred to textbooks such as SEEBER (1993), and the article by PARKINSON et al (1995), for details. The focus of these notes will be on microwave range and range-rate technologies, which are the basis of the GPS and TRANSIT Doppler satellite positioning systems.
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© Chris Rizos, SNAP-UNSW, 1999