Full text: Proceedings of the Symposium "From Analytical to Digital" (Part 3)

Starting with a system of linearized observation equations 
in a classical bundle block adjustment which can be writ- 
ten as equation (1) including photogrammetric observations 
and possibly control point coordinates, the least squares 
principle leads to a system of normal equations (2). 
General non-photogrammetric information can be formulated 
as linear or linearized condition equations (3) between 
observations and unknown parameters. In most practical 
cases these equations are observation equations, where B 
is a unit matrix, including the special case of coordinate 
"observations", where C is a negative unit matrix. 
A simultaneous adjustment of the observations generating 
(1) and (3), which are independent of each other, results 
in the normal equation system (4) or the normal equation 
system (5), where the Lagrange multipliers are eliminated. 
V4 HA +R = f B (1) 
The least squares adjustment of (1) leads to: 
T 
(C A'S.A ) "x *m AP f (29 
% ii 
B '* vo ^g * xs f P (3) 
The least squares adjustment of (1) and (3) leads to: 
ALB. A ci x | ATP, f | 
4 1 T * | = | 1 1| (4) 
6 -BP,B |k Et 
T T "121,71 * x Al T -iglj-1 
or (A P,À + C (BP, B^) *C) X A Pf, + C (BP, Bt) £, 
(5) 
In the equations f,,f, contain the observations, v ,V2 are 
the residuals of the observations, P,,P2 are the weight 
matrices, A,B,C are coefficient matrices based on partial 
derivatives, x is the vector of corrections to the initial 
values of the unknown parameters and k are Lagrange multi- 
pliers or correlates, equal to the number of condition 
equations in (3). 
In the following some aspects concerning the processing of 
non-photogrammetric data are discussed. 
Firstly, in those cases, where the addition of the term 
(cT (BP5iBT)-1 c) to the existing system (2) causes a deci- 
sive loss in the numerical rigour of the solution, the 
corresponding Lagrange multipliers should not be elimi- 
nated and the resulting system would be of type (4). The 
elimination of the correlates, however, can lead to an ill 
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