8.3.1 Ambiguity
Resolution: The Key to Modern GPS
Surveying
Introductory Remarks: Modern GPS
Surveying Techniques
The basis of high precision GPS positioning is the double-differenced observable
(section 6.3.5 and section 7.2.6). Expressing eqn (7.2-4) in a form that highlights the
known quantities:
 |
(8.3-1) |
The coordinates of
receiver 1 are assumed known. The unknown parameters
consist of the
ambiguity parameters (which are constants for the entire
observation
session) and the coordinates of receiver 2 (embedded in the
2i
range quantities). The processing
of these observation equations in a conventional
Least Squares scheme
permits the values of the unknown parameters (and their
uncertainties) to
be estimated. This, of course, is the basis of the
double-difference
ambiguity-free solution. The evolution
of the uncertainties
of the coordinate parameters is illustrated in the
figure below.
The evolution in
quality of a baseline solution as ambiguities are
resolved.
With regard to Figure above there are
several comments that may be made:
- In region A the
precision (and accuracy) of the coordinates steadily
improves as more
data is collected.
- As soon as sufficient data is available to resolve
the ambiguities
(at epoch 15) a dramatic improvement in the coordinate
parameter precisions
is evident.
- In region B, when the unambiguous range
data (based on precise phase
measurements now converted to precise range
observations) are processed,
there is no improvement in the quality of
the coordinate solution, and in
effect there is no real justification for
continuing to collect data past
epoch 15.
- If enough data is collected over an observation session,
the precision
of the ambiguity-free baseline solution will steadily
improve, converging
to that obtained from an ambiguity-fixed
solution.
In conventional static GPS surveying the data is post-processed
and it is therefore not known apriori at what point (or even if) sufficient
data has been collected to ensure an ambiguity-fixed solution is obtained. Hence
conservative observation session lengths (not less than 30 minutes, and usually
60 minutes) are recommended (section 5.2.3).
The basis of all modern GPS surveying techniques has been the ability
to
address the following questions, that suggest themselves from an
inspection
of figure above and the comments made above:
- How
can the length of the observation span required to ensure ambiguity
resolution be made significantly shorter than for the case of conventional
GPS surveying?
- Arethere any "tricks" to improving ambiguity
resolution
efficiency, particularly when observation sessions are short?
- How can ambiguity resolution be made more reliable, particularly when
observation sessions are short?
- How can positioning using phase data
be best carried out after
ambiguities have
been resolved? That is, how to minimise the number
of times ambiguity
resolution must be carried out?
- How can the ambiguity resolution
procedure be made so "transparent"
that it may be carried out
automatically, even with the receiver in motion,
and whenever it is
required?
In response to GPS survey-user pressure for: (a) increased productivity (that
is, shorter observation sessions), and (b) increased operational flexibility
(particularly in order to address kinematic applications); manufacturers have
developed several modern GPS surveying techniques (section 5.5.1):
Rapid
static positioning techniques.
Reoccupation
techniques.
"Stop
&Go"techniques.
Kinematic
positioning
techniques.
Each technique has its
advantages, and disadvantages, as far as field
and office operations are
concerned. Furthermore, each technique addresses
the two issues of: (1)
ambiguity resolution for short observation sessions,
and (2)
"carrier-range" positioning (section
8.1.4),
in different ways, for example:
- Rapid
Static Procedure: employs a sophisticated
ambiguity search
procedure to test many sets of candidate ambiguity sets
and select the
(most likely) correct one, using only a small amount of
data. (Hence this
method strives to narrow the width of region A in figure
above, and to
predict the point at which ambiguity resolution occurs with
high
reliability.) If the ambiguity search procedure fails, the technique
gives poor baseline results because there is insufficient data to obtain
a good quality ambiguity-free solution. The method can only be
applied
on static baselines.
- Reoccupation Procedure: simulates a long
observation session via two short observation sessions over the same
baseline,
but separated in time by an hour or more. (It is not the length
of the
observation session but the change in satellite-baseline geometry
over
a session that is important for ambiguity resolution, hence the data
can
be "thinned" during the middle of the session, or deleted
entirely!)
It shares some of the advantages of conventional (long
observation session)
GPS surveying in that ambiguity resolution is
optional. Good quality baseline
results can be obtained from an
ambiguity-free solution. Obviously the
method can only be employed on
static baselines.
- "Stop &
Go" Procedure :
is a combination of static positioning (the
"stop" part), and
kinematic movement of the antenna (the
"go" part). The ambiguities
must be determined by some
initialisation process, so that all positioning
takes place with
carrier-range observations (that is, within region B of
figure above). There are several methods of ambiguity resolution, including
standard static bas
eline determination, observing a known baseline, "antenna
swap"
method, and determination of ambiguities "on-the-fly"
(that is,
as the antenna moves). Such ambiguity resolution (or initialisation)
takes place at the start of the survey (before moving to the first point
to be surveyed), and at any time loss-of-lock occurs.
- Kinematic Procedures: are those when the
entire
process of ambiguity resolution (or initialisation) and
"carrier-range"
positioning takes place while the antenna is in
motion. Otherwise it is
identical to the "stop & go"
procedure.
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© Chris Rizos, SNAP-UNSW, 1999