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Abstract 
ON THE DETECTION OF GROSS AND SYSTEMATIC ERRORS IN COMBINED 
ADJUSTMENT OF TERRESTRIAL AND PHOTOGRAMMETRIC DATA 
S.F. El-Hakim 
National Research Council of Canada 
Ottawa, Ontario, Canada KIA OR6 
Commission III 
A special bundle adjustment program which accepts terrestrial and 
photogrammetric data has been developed with self-calibration capability and a 
built-in gross-error detector with "data snooping". The program compu 
redundancy numbers as well as the external reliability factor for each 
adjusted image point. Using actual and simulated data, in the form of 
terrestrial observations between object points, 
tes the 
the effect of additional 
constraints on the ability of a photogrammetric system to detect gross and 
systematic errors has been studied. In the combined adjustment, the detection 
of gross errors was improved significantly, 
intersection of rays is geometrically weak. The detection of systemat 
errors did not improve, but their effect on the adjusted object coordinates 
(external reliability) was greatly reduced. 
Introduction 
particularly in areas where the 
ic 
Simultaneous adjustment of terrestrial and photogrammetric observations has 
been explored already for more than a decade (e.g., Wong and Elphingstone, 
1971; Kenefick et al, 1978; and El-Hakim and Faig, 1981). 
The main purpose of 
these applications has been to allow a reduction in the number of cotrol 
points especially in areas where available geodetic observations are 
insufficient for an adjustment of a complete geodetic network of control 
points for phototriangulation. 
Instead of using the usually required number 
of geodetically adjusted control points, therefore only available control 
points plus some terrestrial observations, replacing the remaining control 
points, are entered into a simultaneous adjustment with the photogrammetric 
measurements. 
Another benefit from the combined adjustment, discussed in the present paper, 
is an improvement in the ability of the photogrammetric system to detect gross 
and systematic errors. The terrestrial observations enforce certain 
relationships between the ground coordinates. 
Points connected by such 
observations have less freedom to move. Thus, if an error exists in an image 
coordinate it will appear, depending on the type of terrestrial observation, 
mainly in the image residual rather than in the ground coordinates, which 
means a higher reliability for these points. An earlier study [E1-Hak 
19815] showed that distance observations between points of low reliability, 
such as edge points, increase the reliability substantially (redundancy 
numbers for x increased from zero to about 0.8) when adjusted simultaneously 
with the photogrammetric data. 
The study is here expanded to include two types of systematic error: 
lens distortion and affine film deformation. Also included, in additi 
spatial distances between points, are observed height differences as 
terrestrial data. 
The program GEBAT (El-Hakim and Faig 1981), used in 
im, 
Only two distances at each point are needed. 
radial 
on to 
the 
following tests, has been extended to compute parameters such as redundancy 
numbers and external reliability factors. Three different types of da 
been employed: a simulated block with relatively dense netwrok of points and 
regular flight arrangement, a large-scale actual block, and a small close- 
range convergent photography block. The bulk of the research has been 
performed on the simulated block since it provides more flexibility and 
unlimited variation in its parameters. 
ta have 
The two actual blocks have only been