amic noise
ect to code
n vector is
31)
32)
33)
assumed.
ponents are
dentical in
ito the three
S:
4)
15, and j=1,
g and
uniformly,
completely
uniformly,
In other
asymptotic
I'he longer
e the state
itions (30)
nce of the
n X(j) can
olution X,
f filtering
n be seen
rate while
ble. This
mparison
moothing
ted to the
-hievable.
Figure 1 shows the convergence of the filtering variance
with filtering time and the effects of different noise levels of
the code solutions onto this resulting accuracy. However,
this theoretical accuracy model has only limited validity
because both code position vector X(k) and delta- position
vector X(k,k-1) are affected by systematic error sources such
as un-modelled troposphere errors, GPS orbital errors and
multipath. The magnitude of these effects depends on the
user's receiver and the measurement environment.
(3
10r
P
1
B sj
U
g
=
DOES
ù 0 20 40 60 80 100
€ i Filtering Time in Epochs(1-100)
5 T T T T
©
a
E 0.5} =
oO ae u...
€ ; U—— RS ——
E 0 500 1000 1500 2000 2500
Filtering Time in Epochs(100-2500)
Figure 1 The Convergence of Filtering Accuracy with
Time, where the standard deviations of the code position
are assumed as 10 m ( dot line ), 5 m (Solid line) and 2 m
(broken line).
From this figure we learn that this method allows under
good conditions for real-time positioning with decimetre
accuracy or better. Also, the method is suitable for any
ranges and dynamic environments as no assumptions where
necessary relating to the baseline length and receiver's
dynamics.
4. AIRBORNE TEST RESULTS AND ANALYSIS
4.1 Description Of The Long-Range Dynamic (LRD) GPS
Processing System
The LRD system processes the measurements from both
base and mobile receivers epoch by epoch. First, cycle slip
detection and removal for one-way phase measurements is
performed on the basis of combined phase measurements
Ni, and N.;s. Next, the accepted integer candidates are
used to compute the residuals of ionosphere-free double
69
difference measurements and then form a Fisher test
statistic for selecting correct integer cycle slips (Han, 1995).
After this, ionosphere-free double differenced phase and
code ranges are jointly used to create delta-position vectors
and position vectors, followed by the described on-line
filtering and off-line smoothing processes, which require
only 4 satellites for initialisation and maintenance and are
therefore suitable for the environments with large mask
angles; of course the use of more satellites are advantageous.
4.2 Testing Results For Cycle Slip Detection And Repair
Airborne DGPS kinematic data were collected on June 4
1992 from two Trimble Geodesist IIP GPS receivers. Ll
and L2 carrier phase and C/A code and P2 code data were
available for use. The base station was located some 57
meters from the take-off and touch-down site of the
aeroplane. The data were logged every second for 2.5 hours,
including static tracking periods of 4-5 minutes before take-
off and after landing. Figure 1 shows the 2D trajectory of
the aeroplane, whose height was 4500 metres during the en
route phase of the flight. To demonstrate our method's
efficiency for cycle slip detection and repair, the real-valued
cycle estimates of DN; and DN; of PRN 23 for the
airborne receiver are plotted in Figure 3a and b, where a
moving time window of ten seconds of data was used to fit
the ionosphere variation while the prediction time is set to
one second. It can be seen that the noise of DN, is
normally bounded within the range of +0.20cycles (1 cycle
= 14.653m), thus the integer CS;s can be uniquely
determined. The DN; noise sometimes exceeds 0.5 cycle
(1 cycle= .864m). The CS, variable may therefore have
two integer solutions, and the test procedure proposed in
Han (1995) is applied to select an unique integer candidate.
In order to test the method's ability for data gap removal,
the prediction time was set to 60 seconds and the moving
time window was set to 1 minute. Figure 4a,b show the
real-valued cycle estimates of DN, (k+60) and DN.
79(k+60) for the same satellite. The figure shows the
significant increase in the noise level of the DN(k+60)
estimates. Also in this example, correct integer cycles have
been determined by the same test procedure.
4.3 Experimental Results for the Filtering Solutions
Four types of positioning solutions were obtained: the phase
delta-position solution, the code position solution, the
filtered solution and smoothing solution. In addition, as the
initial baseline vector has been determined by an external
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996
