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In the first section a numeration is given to the
name of all network points. Thus the points are
identified by the same integer number in the file
"misnrete.dat" (in which the tridimensional Carte
sian geocentric coordinates with the e.q.m. of the
I.G.S./A.S.I. and of the known local stations are
reported, if these must be assumed as observables,
and the GPS measured baseline vector compo
nents with the correspondent cofactor matrix), in the
file "xinirete.dat" (in which there are the Cartesian
coordinates of the permanent I.G.S./A.S.I., the
known local stations and the unknown points) and
the file "nppirete.dat" (where is reported the nume
ration, the name, the unknown parameters of the all
points, besides the unknown pointer array).
In the second section, there are other input data
files : the file "emisrete.dat" (which reports the initial
scale factors for the GPS vectors cofactor matrices)
and the file "parellis.dat" (in which there are the
geometric parameters of the reference ellipsoid). In
this section, it is performed the least-squares adjust
ment as in 3., the blunder detection as in 4. , and
finally the BIQUE estimates of the two variance
components of the prefixed stochastic model (14)
as in 5.
The input and output of both sections are reported
in the following Figure 1 :
Figure 1 : Input - Output flow chart of the files
MISPAR.for and PARPESI.for
The output of the section parpesi.for is the file
TEMP which contains all questioned in the file
parpesi.opz. Particularly, the output of the least-
squares adjustment can be the adjusted tridimen
sional Cartesian geocentric coordinates (X,Y,Z)
with the e.q.m., the geodetic coordinates (cp, X., h)
with the e.q.m. (c v , Ox, c?h) and (a e , a n , a h ) of the
points. The output of the internal reliability can be
the a posterior global variance factor, the norma
lised weighted LS residuals and the magnitude of
one gross error.
In the file "pesirete.dat" we have, for each iteration
in the BIQUE estimate, the value of the variance
factors of updating and the BIQUE of the variance
components.
In the file "xitprete.dat" we have, for each iteration
of the BIQUE estimate, the value adjusted tridimen
sional Cartesian geocentric coordinates (X, Y, Z).
Finally, in the output file TEMP, we can have for
each GPS vector: the names of station-forward
points, the final BIQUE of the variance components,
the length of the baseline and scale factor of the
cofactor matrix.
3. LEAST SQUARES ADJUSTMENT
3.1 Functional model
The functional model of Gauss-Markov is assu
med :
Ax = I + v (1)
where
A is the (n , u) design matrix of known coeffi
cients with rank(A) = u
x is the (u , 1) vector of the unknown tridimen
sional Cartesian geocentric coordinates ;
I is the (n, 1) random vector of the obser
vations ;
v is the (n , 1) vector of true errors of the obser
vations ;
£| the variance-covariance (n , n) matrix of the
observations.
The design (n , u) matrix A is a (3,3) block struc
tured matrix, as the (u , 1) vector I is partitioned in
(3,1) uncorrelated subvectors.
In this section, I denotes the (3,3) identity matrix.
The i-th block row of A is :
a i =[0 I ... o] (2)
- if the tridimensional Cartesian geocentric coor
dinates of a known (I.G.S./A.S.I. or local) station
are assumed as observables, then the corre
spondent (3,1) observation subvector is
