201
¡.e. the GCP coordinates and the phase are assumed to
be not correlated,
al is the variance associated to the L th
u ParamL
pseudo-observation,
1
Parang
is the relative weight.
The weight associated to each pseudo-observation is
employed to select the appropriate set of model
parameters.
From equation (9) the LS solution can be computed
obtaining the adjusted values of unknown parameters and
observations (Sansò, 1991):
ii=N' , 'A T K‘ , '(D-Ç 0 -b)
C=5o-Q-d t -k- 1 .u 0
where:
Gens R., Van Genderen J.L., (1996). "SAR Interferometry
- Issues, Techniques, Applications", Int. J. Remote
Sensing, voi. 17, No. 10, pp. 1803-1835.
Goldstein R.M., Zebker H.A., Werner C.L., (1988).
"Satellite Radar Interferometry: Two Dimensional
Phase Unwrapping". Radio Science, voi. 23, No. 4,
pp.713-720.
Hanssen R., Feijt A., (1996). "A First Quantitative
Evaluation of Atmospheric Effects on SAR
Interferometry". Proceedings of ESA Fringe ‘96, Zurich
(Switzerland).Http://www.geo.unizh.ch/rsl/fringe96/pa-
pers/hanssen.
Hanssen R., (1998). "Atmospheric Heterogeneities in ERS
Tandem SAR Interferometry". DEOS Report, No. 98.1,
Delft University Press, Holland.
Koskinen J., (1995). "The ISAR-Interferogram Generator
Manual". ESA/ESRIN, Frascati, Italy.
Sansò F., (1991). "Il Trattamento Statistico dei Dati", (in
italian) Città Studi Edizioni, Torino, Italy.
K = DQD T
N = A T • K' 1 • A is the normal matrix,
U 0 =D ^o-A iî-b
Tannous I., Pikeroen B., (1994). "Parametric Modelling of
Spaceborne SAR Image Geometry. Application:
SAESAT/SPOT Image Registration". Photogr.
Engineering & Remote Sensing, vol. 60, No. 6, pp.
755-766.
So=yo -9
yo
y
- C yy
is the observation vector,
is the vector of the approximate
values of the observations,
is the cofactor matrix,
is the variance-covariance matrix,
Gq is sigma nought (variance of unit
weight).
The solution of the non-linear system is obtained
iteratively updating, at every iteration, the matrices A, D
and b.
The variance-covariance matrix of the solution, obtained
by variance propagation, is:
C n - n -=<îo 2 N- 1
where:
2 Uj-K-’Uo
°o =—r—
I is the number of equations,
m is the number of unknown parameters.
REFERENCES
Crippa B., Crosetto M., Mussio L., (1998). “The Use of
Interferometric SAR for Surface Reconstruction”. Proc.
of the ISPRS-Comm. I Symposium, Bangalore (India),
Int. Arch, of Phot, and RS, vol. XXXII, Part 1, pp. 172-
177.