VoSi - max $5.45 (5)
S £i
For example, additional parameters are selected by means of t-test,
that is to delete S; when
^
^
$1 € toy, Tolley (6)
and accept S4 otherwise, where Ve / 2 is the right side critical value
for t-test statistic corresponding to significance level&. In this
case, we have
^ ^ ^
= {Sı: 8i S ty, a ds; }
and
Toss = max By = (ty, + tg) Offa; = 8 Cafés - (M
S1€W
The Vos; given in Eq.(7) turns out to be the existing measure of
internal reliability /2/. It is just the maximum of the here
proposed posteriori measure for the-given procedure of parameter
selection. It gives only a superior limit but not the Supremum of
the non-detectable s, in the result. Vs, is fixed for a given
photogrammetric System. While the gross and systematic errors for
different realizations (or different sets observational data) of the
same System may be different. Therefore, as a measure of the
internal reliability of a concrete result, the posteriori measure is
more accurate than the existing measure.
The posteriori measure for the external reliability that describes
the biases for a function of the estimators influenced by the bias
for the deleted parameter s; can be derived by repeating the
procedure Forstner used in papers /2/ and /3/ with the TS; replacing
VoS; . Then the posteriori bound Ves f for the influence of the
py.
bias for sj on the linear (or linearized) function f is as follows:
—~ a €
Vif $ Vp,if - Og: di (8)
h = - : 1 1, v1,
where §; = Gi] T * 8/2) hiA(A A) A hids; (9)
A
Ty = 84/0, fasi (10)
^
Oe is the estimator of the stantard deviation of the estimator
of £f, hj is the column submatrix of H corresponding to s;, and
is actually the bound for the influence of Ys; on the length of the
estimator vector of the main unknown vector x.
Each $ is once used in the test for parameter selection, so is
ready-made for the assessment of the final result. Therefore,
using the posteriori reliability measures to assess the quality of
results increases little amount of eomputation. It is thus feasible.
4. POSTERIORI RELIABILITY IN THE CASE ADOPTING ROBUST METHODS
A characteristio for the robust methods is that they may be carried
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