Full text: XVIIIth Congress (Part B4)

(12) 
, Guerra and 
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yaragraph 33. 
first iterations 
and for this 
ntain also the 
rst order, the 
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nction of the 
To solve this problem a constant diagonal matrix Q = yl, where 
= 0.1, is applied for the first 7 iterations, and the danish 
method is applied for the following ones. 
33. Numerical problems 
The analitycal model reported in (8) makes it possible to solve 
simultaneously two different problems: i.e. the cartographic 
georeference and the non-conventional photogrammetric survey. 
Furthermore for each phase a sort of specific problems are also 
solved. These are the plane transformations between the 
different map units and map layers and, for the photogram- 
metric survey, the updating of particulars not already reported 
in cartography. From the computational point of view a big 
difficulty is given by the fact that for the most of the unknown 
values to be estimated or predicted their approximative values 
are not available. 
For this purpose and for each group of unknowns contained in 
the subvectors X4, X2, X3, X4 and s different operational 
strategies have been identified. 
The working method followed considers the geometrical 
meaning of the different unknowns, and consists of a cascade 
process for the computation of the approximate values. 
The estimation of the parameters of an homologous 
transformation and the planimetric coordinates of the carto- 
graphic tie points, contained in the subvector x,, allows to 
estimate the planimetric coordinates of the cartographic- 
photogrammetric tie points X4. These values together with the 
orthometric height x, make it possible to compute the 
approximate values of the DLT parameteres contained in the 
subvector X2. . 
The increments of coordinates contained in the vector s and 
relative to cartographic and photogrammetric control points 
refer to approximate values which are more close to reality 
because they could come, for instance, from GPS measure- 
ments. 
3.4. Use of GPS in cartography 
Since the beginning, GPS has also been tried to determine the 
coordinates of the photogrammetric check points (Ackermann, 
1991). For this purpose it is useful to recall some of the aspects 
jointed to the instrumentation, the errors of the methods, the 
productivity and the cartographic applications. 
The instruments available today are technically better than 
those of some years ago, the receivers have a better signal to 
noise ratio and are less sensitive to systematic errors. This has 
permitted the obtaining of greater and greater precision, 
especially in the differential use of the code. Furthermore, the 
completion of the constellation has permitted, with a single 
code, that is, with receivers that cost of a few thousands dollars, 
the obtaining of sub metrical precision. These precisions are 
already sufficient for the support and updating of middle and 
small scale maps (1:10.000--1:100.000) but not yet for maps of 
larger scale. 
The use of the single code has the advantage of furnishing low 
cost coordinates that are free of momentary losses of signal, 
however, long sessions of measurements are necessary to obtain 
differential sub metrical precision because of multi-path errors 
(Yola and Kleusberg, 1991). 
The precision and the productivity increases with the use of 
single frequency receivers which, at the moment, have a cost 
that can be compared with that of a good total station. It is not 
necessary to use two frequencies for the support or the 
construction of large scale maps (1:1.000+1:5.000) up to a 
197 
distance of 10-15 km. In this extent the precision furnished by 
the construction companies varies from +(lcm+2ppm) for the 
static modality to +(2cm+2ppm) for the stop-and-go method. 
The most productive methods, in increasing order, are: the 
pseudo-static method which forces the reoccupation of site after 
about an hour, the stop-and-go method and the continuous 
kinematic method. 
The kinematic method can also be used for positioning in real 
time (RTK) with the use of transmitting station, a receiver and 
two radio modem (Allison, Griffioen and Talbot, 1994). 
The stop-and-go method forces the presence of a good 
constellation (at least 5 satellites). All the methods are suitable 
for a maximum distance of 10+15 km. 
The use of the single L1 frequency introduces "iono- 
deformations" on a ground network, which as a first approxi- 
mation, are assimilable to a scale factor, even though it is 
possible to recover 90% of the ionospheric delay with the diver- 
gence method in the C/A & L1 receivers. 
The use of the predicted ephemeris, which are indispensable for 
the RTK positioning technique, causes an error which is 
reflected on the baseline components, but only slightly on the 
slope distances. 
These and other errors increases for long distances of the fixed 
receiver, then is not possible to use data from a fixed station 
national service over the 15 km distance, but instead it is 
necessary to use a couple of L1 receivers. 
3.5. Transformation problems 
GPS cartographic surveying permits updating of a GIS database 
with new points or obtain the GPS coordinates from the already 
surveyed points. In this second case the proposed technique 
allows one both to obtain the transformation parameters from 
among the GPS coordinates, cartographic coordinates and 
orthometric heights and to improve the global precision of the 
map. This latter requirement is very useful if one uses the 
digital version of cartographic products or cadastral maps. 
It is known that the precision for long distances is poor for 
these maps, while instead in this case the GPS system furnishes 
the greatest precision. 
To obtain the (@,À,h), coordinates of a set of points referring 
to a local ellipsoid (n) by means of the (q,A,h),, of the same 
points referring to another ellipsoid (w) that is differently 
oriented, the well-known Molodensky formula is useful. Let's 
imagine that the first system is the national system, in which 
the cartography is referred, and the WGS84 geocentric system 
is the second. It is known in Italy, from experience, that the 
variations due to passage are of the order 100-200 m in 
planimetry and of about 50 m in altimetry. One can write 
(Pierozzi, 1989): 
ep 
A, 17] A, | - A($X9,9Y9,6Z9, 86,96, ,067,9a,00)! — ABT 
h h 
n w 
(14) 
The first six components of the 8 vector are the shift and 
rotation between the two systems, the last two are the semiaxis 
and the ellipsoidal flattering variations. The hypothesis that no 
scale factors exist between the systems has been assumed in the 
formula. The terms of matrix A are known non-linear functions 
of (@,A,h),, the & terms are "a priori" unknowns of the 
problem (apart from terms da and da). When, in a certain area, 
a certain number of points are available in both systems, 
equation (14) is useful to obtain by a least square solution these 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996 
 
	        
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