ith
3. Significance testing of coordinate differences in deformation measurements
The determination of point movements requires repetitive object measurements to
various periods. If the observation program is exactly identical during the
different periods the multivariate concept is an appropriate model for point
estimation, interval estimation and hypotheses testing.
Generally the corresponding repetitive observations are not independent. In this
case the covariance matrix of these observations can be estimated immediatly - on
the contrary to the univariate adjustment, where usually only the variance of
unit weight is estimated.
For multivariate estimation problems and hypothesis testing see Anderson /1/,
Koch /14/. Statistically seen, the multivariate concept is the most general one,
but it requires design matrices which are identically for each observation period.
Since this is an essential practical restriction for photogrammetric problems -
observations can only be rejected if this is done for those belonging together
in all periods, the camera stations and the rotation elements are not allowed to
be changed - we use an univariate model, adapted to the special situation of
deformation measurements.
Without loss of generality we restrict on two observation periods I, II. Thus we
get the model
rm
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—
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N
>
—
>
4
+
hy il 2
2
wl ; =
© P ; E(e) 0
Model (54), which is an extension of model (28), permits various arrangements of
the unknowns. For example, the solution vector of the control points can be re-
garded as a joint vector for both periods. The same may yield for the vector of
additional parameters. If no common unknowns are used, system (54) can be divided
into two seperate adjustments.
According to the purpose of movement determination we set up the globel null -
hypothesis (with model (54) and the notation of (1)) to
H s B. GX. ..B AM , m = number of points (55)
° 3m,6m 6m,1 6m,l to be jointly tested
The structure of B depends on the sequence of the unknowns in model (54). If the
vector of point coordinates to be tested is arranged like
T
dx s (dX 11 > dX111° dYı1> dY114 > dZ11» dZ111° m dX im
then B is structured as
B = 0091 -1:0/ 60 (56)
3m , 6m : ut :
