GROSS ERROR DETECTION OF CONTROL POINTS
WITH DIRECT ANALYTICAL METHOD
T. Jancso
Department of Photogrammetry and Remote Sensing, College of Geoinformatics, University of West Hungary
H-8000, Szekesfehervar, Pirosalma u. 1-8. , Hungary
e-mail: t.jancso@geo.info.hu
Commission III, WG III/8
KEY WORDS: Photogrammetry, Adjustment, Orientation, Algorithms, Error
ABSTRACT:
The paper demonstrates a new adjustment method together with a very effective gross-error detection in the space resection and in
the on-line aerial triangulation.
The basic concept is well known for more than one hundred years, the only problem was that the algorithm is very complex and the
implementation was very time consuming without modern computers. Now this barrier doesn't exist any more.
The adjusted value of the unknowns can be derived from the weighted mean value of solutions gained from minimally necessary
number of control points and it is done in every combination. For example if we have five control points to solve the space resection,
we can solve this task grouping three control points in every combination, and by this way we can calculate the orientation elements
in ten different combinations. In this case the adjusted value of the unknowns will be the weighted mean value following the
Jacobian Mean Theorem.
Why is it necessary to follow this way? Because we can pick up very effectively the points with a value of gross-error and it can be
done before getting the adjusted value, which is a very remarkable issue comparing with the least square method or the robust
estimators.
In practice, the first task is to determine the outer orientation elements, for this we usually use the collinear equations, which needs
initial values of unknowns and an iteration process. In this paper I present a direct solution to solve the space resection in
photogrammetry using geometrical considerations on the basis of three control points. The method doesn't need initial values and
iterations, however, it is proved, that using only three control points more than one solutions are probable. To get a unique solution
we need no less, than four control points. In this case we should do the resection in all possible combination and the differences
gained from every solution can be adjusted using the Jacobian Mean Theorem and in parallel the procedure of the gross error
detection can be done as well. I will illustrate by an example of calculation to check the validity of the presented method.
1. INTRODUCTION
1.1 Aims
To solve the space resection for one stereopair means a very
important topic in photogrammetry since after this we can start
to determine new ground points or together with a reliable
stereo-correlation method even we can build DTM models.
The usual start point to solve the space resection is the use of
collinear equations:
TRE nx Xen - vs Zs) |
: n,(X -Xo)*n(X- X,)*r ET E (D
y => (Ko) (PK) (2-2,)
: EG -Xu)er(x- Xr -x,)
where
x, y: image coordinates reduced to the principal point
X,Y,Z: ground coordinates
o» Y
y : elements of rotation matrix,
ÿ
x 7, coordinates of projection center
O0?
where every ns flp,œ,x)
c, : focal length
After the Taylor linearization with the iterative solution we can
face the following problems:
e It’s no possible in every case to give approximate
values of unknowns with such an accuracy which is
enough to have a convergent iterative process
(especially at terrestrial photogrammetry)
e To detect the points with gross errors is not so easy if
there are several points with gross errors. The least
square method distributes the gross errors to other
points (even to good ones); and the robust estimators
can become uncertain if the number of points with
gross error is more than one.
This paper gives an alternative solution to avoid the above
mentioned problems.
Internat
1.2 Th
First I |
three co
adjustec
(Gleins
three (c
necessai
21 Sp
As it is
sides. T
points, ^
known
determir
M1,
center c
calculate
Figu
Let's dei
values w
using the
geometry
If we tak
will diffe
only two
We can
AABC
