we arrive at
A comb
(sidelap
AED Ach 4f OM corner -
xi (AT PA) ! (AT PU & A- N)). (5) SE
Using a global term AN = 4- N for the improvement in Bi
direction to the satellites one yields m
16 +
xl- QA" P1+QA" P(AN). (6) “i
12 Fi
The design matrix contains the direction cosines of each
observed satellite (geometric information) and reflects
ambiguities and cycle slips.
To keep the number of additional ambiguity terms small,
only those, which could not be fixed reliable in the GPS
processing are improved. Therefore, coordinates with
‘improved’ ambiguities can be computed from a ‘forced’
coordinate estimation done by the GPS processing
software and improvements of the coordinate estimates
1000 me —
Figure 6: used satellites block Oesingen
horizontal lines: continuously used satellites
Figure 6 gives an overview about the used satellites in
the block Oesingen. 10 flight strips have been used. The
10 +
lo d ; satellites 1, 3, 4, 6 and 7 could be used without cycle slip Figure €
AN "from the combined bundle adjustment: over the whole flight time, satellite 9 was not used in the A wi
first flight strip. The other satellites have been used only B: col
S proved EE ed + Ey (7) in one flight strip. The satellite number in figure 6 does C: col
not correspond to the numbers of the GPS-satellites, they
For this GPS error model - some ambiguities already are only internal numbers. After a cycle slip the internal Figure
solved, some still not reliable fixed, but forced to integers —— Satellite number is changed. The satellite 14 is not used adjustm
- the corresponding design matrix is evaluated to be in the whole strip 8. In the traditional method of system
incorporated into a combined bundle adjustment. The combined block adjustment this can cause an hand si
new GPS model for remaining systematic GPS errors inhomogeneity of the solution, with the new approach photos
can be handled by the software packages GEONAP and also this satellite can be used. configu
BLUH. method
14 ; var cn traditio!
5. EMPIRICAL RESULTS NV) E distance in flight direction — samedi
ied | P^ WM the olc
The new approach was applied to the data set | | +9.5cm
‘Oesingen’. In a first processing of the GPS data all | The res
ambiguities and cycle slips are estimated and fixed, if the | | andas
ambiguity resolution algorithms have succeeded using iil | The ho
stochastic criterion's. One satellite was badly corrupted AE da A BS M J Bf both m
by cycle slips and rejected completely from the GPS cul | WMA / genera
processing. In total 18 ambiguities/cycle slips are present Br X is stabl
for the complete block. However, 4 ambiguities could be | = control
reliable fixed using the stochastic properties of the vd Mn ^ DX block v
GEONAP processing software. pe 0 10000 20000 20000 40000 50000 60000 70000 80000 mam | is not §
Te m combir
Figure 7: Differences GPS-positions against projection becaus
UU. nee Eg A "d dh centers determined by reference adjustment with BLUH ii ai
+ PE ar Hep. CE uk rcd The differences between the interpolated GPS-positions Is reac
co Ho ans ti este ull ie and the projection center coordinates determined by Improv
sre datei ar i A tao bundle block adjustment without GPS-data are shown in :
im ; ue figure 7. The offset of the GPS-antenna was not Beside
DE GEE Fi recorded, but it can be seen in figure 7 as -1.2m in X and calibra
et ee ES 0.15m in Y. In addition the typical changes depending introdu
PA A e Ek upon the flight strips are obvious. A fitting of the compo
3 o o differences individually for every flight strip by constant antenn
i As a aE Tor a tr values (shift) yields to RMSX=+9.1cm, RMSY=+9.2cm flown i
aT ar TE Eee and RMSZ-44.3cm. A linear regression (drift) reduces unkno
D eq iem eee m à the differences only to RMSX=+9.1cm, RMSY=+9.1cm :
3 E and RMSZ=+3.7cm. The differences are not only caused
Design Vue by the GPS-positioning, the root mean square of the
projection center accuracy determined by block The i
Figure 5: block Oesingen with control and check points adjustment is RMSXo=+5.2cm, RMSYo=+5.7cm and depo
140 photos, image scale 1 : 8000, f=153mm RMSZo=+2.8cm. ane.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
358