detection on-line, in order to provide error-free data and good 
approximate values for the final off-line adjustment. 
There may be some differences when dealing with close range 
photogrammetry, especially for production control. In addition to the 
important blunder detection aspect the need for final results without 
too much delay makes it desireable to treat the entire block in one 
piece. The ability to meet these requirements will depend on the 
successful development of adjustment algorithms, as well as the 
efficiency and price of computer hardware. 
SEQUENTIAL ADJUSTMENT ALGORITHMS AND PERFORMANCE 
With simultaneous adjustment the time for computing a new solution 
basicly increases by the third power of the number of parameters. 
Consequently the response time requirements would soon be violated, 
even for "block" adjustment of two or three photos. Sequential updating 
of the inverted or the decomposed normal equation matrix followed by 
back substitution will increase only by the second power of the number 
of parameters. 
Even with good sequential adjustment algorithms the response time will 
soon be too long when the number of photos and object points increases. 
Therefore it will always be interesting to find "the best" algorithm, - 
in order to be able to operate with the desired block sizes on-line. 
A number of algorithms for sequential adjustment have been suggested. 
Some of them are in use or have been tested. Others have merely been 
mathematicly described. 
In /11/ Mikhail and Helmering give algorithms for updating of the 
inverse. This approach has been adopted in several OLT systems, and is 
known as "Kalman-form". 
In /4/ Grün describes an algorithm called Triangular Factor Update 
(TFU), which updates the decomposed normals, based on Gauss 
decomposition. Taking care of the sparse matrix structure is an 
integral part of the algorithm. 
The procedures of TFU are described in more detail in /13/, which is 
related to an actual implementation of the algorithm. Furthermore, this 
reference describes a test where a Kalman-form algorithm is compared to 
the TFU algorithm. A block adjustment is carried out with 9 photos, 
with the addition of various numbers of new observations at different 
stages. The program also includes blunder detection according to a 
method shown in /4/, followed by deletion of observations pointed out. 
The conclusion is that the TFU algorithm is superior to the Kalman-form 
algorithm both concerning time consumption and storage requirement. 
The use of Givens transformations is suggested by Blais /1/. He also 
shows how the inverse may be updated along with the Cholesky factor of 
the normal equations, and indicates that matrix sparsity may be 
- 359.r