Quality Control of DFHRS Database Computation
In both cases - the geometrical approach implemented in the DFHRS software version 4.2, as
well as the integrated geometrical–physical approach implemented in the DFHRS software
version 5.0 - the functional models (2a-f) and ((4d)-(6)) respectively, mean
and over-determined system of equations with respect to the parameters, and require
parameter-estimations for redundant equation systems. The DFHRS software version 4.3 and
version 5.0 solve the respective parameter estimation by a least squares adjustment
(also called L2-norm estimation). The L2-norm is optimal - in the sense of a
Maximum-Likelihood parameter estimation (M-estimation) – in the case of assumed
multivariate normal distributed errors v. Generally any other M-estimation, such
as e.g. the robust L1-Norm (M-optimal for multivariate Laplace distributed errors v),
can be applied as well. Based on any M-estimation the quality control and the quality
indicators, can be set up in the following way:
Statistical tests for all single observations, the so-called data-snooping.
“Reproduction values” ∇H for the fitting-points (B,L,h|H). The reproduction values
∇H give the fictive changes of the resulting local heights H - computed as
H = h – N(p|B,L,h) from of the DFHRS-database – for the case, that the respective
fitting point (B,L,h|H) would not have taken part in the DFHRS_DB computation.
Variance component estimations for all different observation groups, and the
Computation of the covariance matrix Cp of the parameters. From Cp
the variances of any function f(p) of the above polynomial parameters
p and the SCHA parameters (Cnm’,Snm’), respectively
can be computed. A characteristic function is the so-called “accuracy surface”
of the HRS, the Geoid N or quasi-geoid NQG. The accuracy surface
represents the position-dependent standard deviation of σN(B,L,h)
over a country. Fig. 4 shows the accuracy surface for the geoid N in the district
area of Windhuk, Namibia.
Fig.4. Accuracy surface σN
(B,L,h) for the < 3 cm DFHRS data-base
(geoid N) of Windhuk, Namibia.