f the new 
servation 
nations 
(17) 
(18a) 
(18b) 
ck-substi- 
(19) 
exploited 
ns. 
je updated 
as for the 
ve it from 
in Gruen 
e addition 
lub (1969) 
1ethods fit 
roach. De- 
cing these 
S into the 
thmetic is 
ut the cor- 
and trans- 
form with 
r d is also 
gh explicit 
' residuals 
| approach 
son (1974, 
(20) 
the obser- 
  
   
GP'^[4, AJ] - | GP = 4 (21) 
2 
Hence 52 = Q2/r can easily be derived from the lower 
portion d» of the transformed right hand side of the (k - 
1)? stage of the system. 
The sequential updating of Q can be achieved by simply 
adding Q to d and updating Q with Givens transforma- 
tions (Gentleman, 1973). 
U Ü d d 
G0 1-]01l 6 0|-7]156]. (22) 
T 
a(x) 0 Hg) 0 
For blunder detection, which is particularly important in 
automated measurement systems, Baarda's data snooping 
has become standard. The computation of the related test 
criteria w; = —vj/0, , (12 1,... , n), requires the compu- 
tation of both the residual vector v and the diagonal ele- 
ments of the Qyy-Matrix. In Gruen (1985a) it has been 
shown how the full Q,,-matrix can be efficiently comput- 
ed or updated both with the Givens and the TFU ap- 
proach. In practical operations, we clearly prefer the 
method of “unit observation vector” (Gruen, 1982), be- 
cause in the process of on-line triangulation only a rela- 
tively small number of selected residuals have to be tested 
at any given stage. An operational procedure for blunder 
detection and deletion of gross erroneous observations in 
the case of non-diagonaldominant Q,,P-matrices and, if 
the suspicion exists that more than one blunder is in the 
data at a given time, was suggested in Gruen (1985b). Af- 
ter each deletion of an observation the remaining residuals 
and the estimated variance factor are updated in a recur- 
sive fashion and tested again in order to get rid of the in- 
fluence of the rejected observation. 
3. PRACTICAL EXAMPLE 
The software package OLTRIS (On-Line Triangulation 
System, see Kersten et al., 1992 for description), which 
  
  
  
was developed for the US DoD (Department of Defense), 
is used for the computation of the sequential estimation 
operations in the practical example of this section. 
Figures 1 and 2 show our 3-D laboratory testfield which 
served as the test object to be imaged by our (simulated) 
robot, equipped with one CCD-camera. In fact, instead of 
a robot, a human operator “filmed” an image sequence 
with a JVC video camera GR-S77E (S-VHS). 
  
  
  
  
  
Figure 1: 3-D testfield used for on-line triangulation 
   
  
  
  
  
  
  
  
  
(a) Dimensions of the testficld 
and camera path (planview) 
  
  
  
(b) Dimensions of the testficld and illustration of the used camera path for acquiring the test sequence 
Figure 2: Dimensions of the testfield and camera path