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A COMPUTER PROGRAM FOR THE VARIANCE-COVARIANCE ESTIMATION
OF GPS BASELINE VECTORS
N. Crocetto*, M. Gatti**, C. Materazzo*, L. Toscano’
* Second University of Naples, Italy
** University of Ferrara, Italy
*** University of Naples "Federico II", Italy
ISPRS Commission VI, Working Group 3
KEYWORDS : GPS, baseline vectors, I.G.S./A.S.I., variance factors, software, Fortran, BIQUE.
ABSTRACT
We present a computer program in FORTRAN 77S for the least-squares adjustment of geodetic networks
with GPS measured baseline vectors. The known tridimensional Cartesian geocentric coordinates of some
GPS points can be assumed as fixed with their variances or as observable. Furthermore, the Baarda test
can be performed on the normalised weighted least-squares residuals. Finally, the input covariance matrix
of the GPS measured baseline vectors can be assumed as cofactor matrix, thus the program performs the
BIQUE (Best Invariant Quadratic Unbiased Estimate) estimates of the two variance components of a
prefixed stochastic model. At the end we report an example of application of the program.
1. INTRODUCTION
The commercial software (i.e. the Trimble and the
Ashtech) don’t use to estimate the variance factors
of the a prefixed stochastic model regarding GPS
data.
In regard to the least-squares adjustment of geo
detic networks with GPS measured baseline vector
components, we have conceived a program written
in FORTRAN 77S. This program can assume the
tridimensional Cartesian geocentric coordinates of
some known GPS points (i.e. I.G.S./A.S.I. perma
nent GPS network and/or local stations) as fixed
with their variances or as observable.
Generally, the input covariance matrix of the GPS
measured baseline vectors are underestimated by
the commercial programs of the GPS carrier phase
data processing. Hence we have implemented, in
this program, the performance of the BIQUE (Best
Invariant Quadratic Unbiased Estimate) estimates
of the two variance components of a prefixed sto
chastic model.
Furthermore, the Baarda test can be performed on
the normalised weighted least-squares residuals, in
order to localise "gross" errors in the correlated ob
servations. This test is needed to ensure a correct
BIQUE estimate of the variance factors.
The program considers single-baseline vectors and
hence the weight matrix is diagonal block structured
with (3,3) full blocks. Hence we remark that the
program works on block structured matrices in all
the operations on the matrices and vectors involved
in all the following procedures. Thus we obtain a
larger gain in efficiency by the point of view of com
putational effort.
In the next sections we present the program struc
ture, the least-squares adjustment model, the blun
der detection method, the variance factors BIQUE
procedure, and finally an application a GPS network
in Po river Delta (Crocetto el al., 1998b).
2. PROGRAM STRUCTURE
The program has a modular structure which con
sists in two sections:
- MISPAR.for
- PARPESI.for
The options files, mispar.opz and parpesi.opz, of
both sections contain the network name "rete".
In the file "misrete.dat" it is possible to choose the
Trimble output data format, which gives the GPS
measured baseline vector components and their
variance-covariance matrices, or, alternatively, the
Ashtech output data format, which gives the GPS
measured baseline vector components, their e.q.m.
and correlation matrices.
The points are identified with their names in the file
"misrete.dat", in the files "elenfis.dat" and "xyzfrete.
dat" (containing the tridimensional Cartesian geo
centric coordinates with the e.q.m. respectively of
the I.G.S./A.S.I. and of the known local stations).
