Full text: XVth ISPRS Congress (Part A3)

    
  
    
  
  
  
   
    
    
  
  
  
   
   
    
  
   
  
  
   
   
    
   
  
  
   
  
  
   
   
   
  
  
  
    
   
    
OPTIMIZATION OF LEAST-SQUARES COMPUTATIONS 
IN ON-LINE PHOTOGRAMMETRY 
Dr. J.A.R. Blais 
Division of Surveying Engineering 
The University of Calgary 
Calgary, Alberta, Canada T2N 1N4 
Commission III 
Abstract: 
Least-squares computations can be carried out in several different ways for 
adjustment, prediction, filtering and smoothing purposes. The orthogonal 
and square-root algorithms are especially advantageous for on-line computa- 
tions where computational efficiency, storage requirements and numerical 
accuracy are critical. Different algorithms for such least-squares compu- 
tations are briefly discussed with their principal characteristics in inter- 
active environments. Some aspects of the corresponding firmware implementa- 
tions are also mentioned for photogrammetric applications. 
1. INTRODUCTION 
Over the past decade, there has been much research and development in the 
field of least-squares computations for adjustment, prediction, filtering 
and smoothing purposes. A great deal of motivation for these efforts has 
been related to complex navigation problems in the space programme. The 
critical situations often encountered in real-time navigation require the 
best numerical techniques available. 
The estimation problems in the context of on-line photogrammetry are ob- 
viously much simpler than in space navigation. However in order to opti- 
mize the benefits of recursive least-squares computations with limited 
computer facilities and quality control requirements, it is imperative that 
proper attention be given to the computational algorithms and related numeri- 
cal matters. Otherwise the advantages of on-line computations can easily be 
eroded away to the point that their implementation becomes debatable in 
practical situations. 
The principal objective of the following discussion is to emphasize that 
least-squares computations can indeed be optimized in terms of computational 
efficiency, storage requirements and numerical accuracy without sacrificing 
any aspect of the mathematical rigour of the least-squares formulations. 
2. LEAST-SQUARES ESTIMATION PROBLEMS 
Photogrammetric estimation problems are quite varied in different applica- 
tion contexts. For the purposes of the following discussion, they are going 
to be classified as adjustment, prediction, filtering and smoothing problems 
of least-squares estimation. Appropriate linearizations of the mathematical 
models are also assumed for the sequel. 
Adjustment problems for orientation and triangulation purposes are definitely 
the most common least-squares problems in photogrammetry. The corresponding 
mathematical model consists in forming an overdetermined system of linear 
equations 
T 
Ax =f +e E[e] = 0 E[ee ] = Co 
    
	        
Waiting...

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.