TOPOGRAPHY AND DISPLACEMENT OF POLAR GLACIERS FROM
MULTI-TEMPORAL SAR INTERFEROGRAMS: POTENTIALS, ERROR ANALYSIS AND
VALIDATION
Franz Meyer
Remote Sensing Technology, TU Muenchen, Arcisstrasse 21, D-80333 Munich, Germany - franz.meyer@bv.tum.de
Commission III, WG III/3
KEY WORDS: SAR, Interferometer, Adjustment, Algorithms, Radar, Modelling, Multitemporal, Environment
ABSTRACT
This paper describes a new technique to simultaneously estimate topography and motion of polar glaciers from multi-temporal SAR
interferograms. The approach is based on a combination of several SAR interferograms in a least-squares adjustment using the Gauss-
Markov model. For connecting the multi-temporal data sets, a spatio-temporal model is proposed that describes the properties of the
surface and its temporal evolution. Rigorous mathematical modeling of functional and stochastic relations allows for a systematic
description of the processing chain. It also is an optimal tool to parameterize the statistics of every individual processing step, and the
propagation of errors into the final results. Within the paper theoretical standard deviations of the unknowns are calculated depending
on the configuration of the data sets. The influence of gross errors in the observations and the effect of non-modeled error sources on
the unknowns are estimated. À validation of the approach based on real data concludes the paper.
1 INTRODUCTION
The capability of SAR interferometry (InSAR) in terms of defor-
mation monitoring and topographic mapping has been proven by
various case studies during the last decades. In recent years, the
focus of investigations has changed towards a detailed analysis of
potential error sources, such as temporal and geometrical decor-
relation, atmospheric path delay, surface penetration and orbit un-
certainties. The analysis of stable targets, so called permanent
scatterers, identified from a number of interferograms enables
to minimize the effect of temporal and geometrical decorrelation
and to remove the influence of the atmospheric path delay. Based
on this technique, DEMs with meter accuracy and millimeter ter-
rain motion detection can be derived. However, due to the lack
of stable targets, this method can not be applied for the analysis
of glaciers and ice sheets, which is a well known application of
InSAR. Thus, the evaluation of possible error sources is still a
challenging problem in glacier monitoring.
This paper presents an estimation method to determine topogra-
phy and motion of polar ice masses from SAR interferograms.
The approach is focused on a systematic modeling of all process-
ing steps and their particular stochastic properties. The functional
and stochastic description of all influences on the interferometric
phase signal serves as basis for a detailed accuracy, robustness
and error analysis of the estimated results. Special emphasis is
put on the investigation of influences from topography and mo-
tion, as well as the effects of orbit errors, atmospheric path delays,
and the penetration depth of the signal into the surface.
2 METHOD
2.1 Adjustment model
The aim of all adjustment methods is to map a number of n er-
roneous observations b on a number of u « n unknown param-
eters x. To make this step possible it is indispensable to for-
mulate functional relations between observations and unknowns.
1004
The functional model of a least-squares adjustment based on er-
roneous observations is defined by
b-ésfu insi. fanf) (D
with é being the estimated values of residuals and the estimated
unknowns £;. If accuracy measures for the observations are avail-
able, weighting of the observations may be performed. Observa-
tions with high accuracy will get high weights and will therefore
have strong influence on the estimated parameters and vice versa.
The a priori information about the accuracy of the observations
is called stochastic model and is arranged in the so called covari-
ance matrix Kpp.
Using the Gauss-Markov theory the optimal solution of a over-
determined equation system as shown in Equation (1) is derived
by minimizing the objective function ó:
ö=E" Pu — min (2)
with Py, = Ky. Solving this minimization problem yields the
adjusted unknowns & as well as their theoretical accuracies ex-
pressed by the Q5 matrix
o = o nm —1 "mp o
QAAE = (A Peu) ATP b+ x (3)
m =]
Qui (A Peu À) (4)
I
. . . ~ . . o . .
with A comprising the functional relations and x containing ap-
proximate values for the unknowns (Mikhail, 1976).
2.2 Observations and unknowns
Based on observations derived from SAR data the unknown to-
pography h and motion v = A of polar glaciers are estimated.
Within the adjustment, only that component of the surface move-
ment that lies in the line of sight of the sensor can be determined.
Thus, v always corresponds to the line of sight component of sur-
face motion.
SAR SLC's of the ERS C-band SAR serve as primary data source.
From this data sets N SAR interferograms are formed. Unfortu-
nately, the temporal baseline At of the interferograms can not be
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