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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