International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004
INS/GPS observations are required for the dynamic ob-
servation equations. The general network model is made
up of the dynamic observation model —INS observation
equations— and the static observation model —GPS ob-
servation equations, ground control points and the pho-
togrammetric collinearity equations.
The geodetic monitoring network is a time dependent net-
work in that it is a network of observed and measured
points at given epochs and we want to know the situation
of the network points within the time observation epochs
and in future time epochs. We have the measured points at
epochs [fo, £1, ---. ty] and we want to determine the po-
sition of the network points at epoch £; + At. This is, in
principle, a stochastic process over [fo, --oc). This model
is made up ofthe static observation model —GPS static ob-
servation equations, known control point equations, known
constant 3D coordinate differences for points in a same tec-
tonic plates, etc.— and the dynamic observation model —
known variable coordinate differences according to some
geophysical deformation model.
7 AUNIFIED APPROACH
The implications of the definition of time dependent net-
works of the preceding section are obvious. However, for
the sake of clarity we underline them under the theoretical,
algorithmic, software and production viewpoints.
7.1 A unified theoretical approach
The classical network is a set of instruments, observations
and parameters. They are related through static observa-
tion models. The network approach is a procedure to es-
timate the parameters. The inputs are the values of ob-
servations and, if needed, the initial approximations of the
parameters. The outputs are the estimated values of the pa-
rameters. On demand, the network approach can generate
the covariance of the parameters and/or the auto-covariance
function.
The time dependent network concept that we propose in
this paper is a set of instruments, observations and time
dependent and independent parameters. They are related
through static and dynamic observation models. A time de-
pendent parameter generates a set of equations, one equa-
tion for every time epoch. Now, the network approach is a
procedure to estimate both time dependent and time inde-
pendent parameters. The inputs are the values of the obser-
vations and, if needed, initial approximations of the param-
eters (note that, in this case, initial approximations are for
time dependent and independent parameters). The outputs
are the estimated values of the parameters including the
stochastic processes. On demand, the network approach
can generate the covariance of the parameters and/or the
auto-covariance function. We insist on the parallelism of
the time dependent and time independent network con-
cepts.
We claim that the time dependent network concept pro-
posed provides a unified theoretical framework that cov-
182
ers the estimation of time dependent and time indepen-
dent parameters. The time dependent network is based on
static and dynamic observation models. The time indepen-
dent network is (solely) based on static observation mod-
els. Thus, the classical network can be seen as a particular
case of the new time dependent networks.
This unified approach is the basis for the reasonable de-
velopment of time dependent network determination soft-
ware, which is at the same time rigorous and simple. We
discuss this aspect in the next section.
7.2 A unified algorithmic and software approach
A modern well designed software system of the class we
are discussing here is based in the object-oriented paradigm.
Combining object-oriented design and the previous theory,
a simple and powerful time dependent network determi-
nation software can be generated. This software system
shall include these fundamental entity classes: observa-
tion, instrument, parameter and model. See (Colomina et
al., 1992) for a related discussion and modelling in time
independent networks.
The observations may have an associated time (time epoch
of the observation). We call them time-tagged observa-
tions. However, we emphasize that our observations, al-
though time dependent, are stochastically independent as
they are only subject to a white noise process. In principle,
it should not come as a surprise that for a time dependent
networks, all what we have to do is to generalize time de-
pendent parameters and dynamic observation models from
time independent parameters and static observation mod-
els, respectively.
NA SSA
common math and modelling base
Figure 1: Unified SW approach
Interestingly enough, in our unified software approach, the
mathematical foundation libraries are not much different
from the classical approach. This applies both to internal
software aspects and to interface aspects. Moreover, with
minor changes, most of the organizational parts and dis-
crete mathematical components of existing [well designed]
network adjustment packages can be kept. Even more in-
teresting is the fact that the NA and SSA computational
engines can share the same model libraries, as the estima-
tion engines work with the same models, their software im-
plementation and their external interfaces. In other words,
the parallel development and maintenance of an NA and an
SSA engine within the frame of a general system is possi-
ble.
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