v 
the normal equations. One fully general approach designed specifically to 
accomplish this is the method of augmented bordering derived in Brown (1974) . 
According to this method, new information implicit in the set of obser- 
vational equations 
(24) Av. + Bà s € 
can be merged into an already existing set of banded-bordered normal equations 
(25) NS = c 
through the following process of bordering: 
(26) 
  
Here, A denotes the covariance matrix of the observations appearing in the new 
system of observational equations (24) and 8 is a vector of 4 new parameters, 
where 4 denotes the number of new equations introduced by (24). Inasmuch as 
the matrix N is already postulated to be of banded-bordered form, it follows 
that the new system (26) is also of such form with the borderwidth of N being 
augmented by ^ new elements. Thus the method of augmented bordering permits 
one to introduce new information in a manner that preserves the banded- 
bordered characteristics of the basic system of normal equations. 
Through the method of augmented bordering and other strategems aimed 
at exploiting the border, it becomes possible to generate practical solutions 
to a variety of special photogrammetric problems that would otherwise be 
cumbersome or intractable. A number of these are specifically addressed in 
Brown (1974) and will only be mentioned here: 
(a) the rigorous simultaneous adjustment of both photogrammetric o 
and geodetic observations (two different approaches Leading 
to banded-bordered normal equations are developed); 
(b) the introduction of equal-elevation constraints arising from 
measurements along shorelines of Lakes, some of which may 
span many models (each Lake utilized adds one element to the 
border and has no effect on the bandwidth); 
(c) the introduction of orbital constraints into strips or blocks 
of photographs taken by a satellite borne camera (full 
details are to be found in Haag and Hodge (1972)); 
(d) accommodation of datum shifts between different geodetic 
nets connected by a common photogrammetric block; 
(e) accommodation of parameters of relative orientation of 
multiple cameras rigidly fixed with respect to one other 
(e.g., as with multispectral systems or with stellar-oriented 
terrain cameras); 
NO >vu0c >.» > DO SS tt co > UU) 'd tco fy zt kk CO >> I Xi CO © Fh c Ui. CO © OY NYS At bs > 
= Cg 
YD