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 (2af) and ((4d)(6)) respectively, mean
and overdetermined system of equations with respect to the parameters, and require
parameterestimations 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 L2norm estimation). The L2norm is optimal  in the sense of a
MaximumLikelihood parameter estimation (Mestimation) – in the case of assumed
multivariate normal distributed errors v. Generally any other Mestimation, such
as e.g. the robust L1Norm (Moptimal for multivariate Laplace distributed errors v),
can be applied as well. Based on any Mestimation the quality control and the quality
indicators, can be set up in the following way:

Statistical tests for all single observations, the socalled datasnooping.

“Reproduction values” ∇H for the fittingpoints (B,L,hH). The reproduction values
∇H give the fictive changes of the resulting local heights H  computed as
H = h – N(pB,L,h) from of the DFHRSdatabase – for the case, that the respective
fitting point (B,L,hH) 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 (C_{nm}’,S_{nm}’), respectively
can be computed. A characteristic function is the socalled “accuracy surface”
of the HRS, the Geoid N or quasigeoid N_{QG}. The accuracy surface
represents the positiondependent standard deviation of σ_{N}(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 σ
_{N}(B,L,h) for the < 3 cm DFHRS database
(geoid N) of Windhuk, Namibia.
Concept