An Approach of Error Propagation Modelling of SAR Interferometric
|Rüdiger Gens||International Institute for Aerospace Survey and Earth Sciences (ITC), P.O. Box 6, 7500 AA Enschede, The Netherlands |
|John L. van Genderen||
||International Institute for Aerospace Survey and Earth Sciences (ITC), P.O. Box 6, 7500 AA Enschede, The Netherlands |
SAR interferometry has proved to be a promising technique for
a number of geoscientific applications by providing height information.
The theoretical aspects are basically understood and the current
research focuses on the potentials investigating the limitations
of the technique. In order to reach an operational status, it
is necessary to have a good quality assessment of the results.
One possible way to assess the accuracy and reliability of SAR
interferometric products is the development of an error propagation
model. This can provide information about the sensitivity of each
single input parameter or processing step as well as a quantitative
quality measure for the output, which is independent from additional
information introduced as reference data. The development and
implementation of this error propagation model is addressed in
- Keywords: Error propagation model, quality assessment
As user of any products based on a certain processing scheme it
is essential to have information on the reliability of the data
sets. Often the details of the different processing steps are
not available. This makes it even more difficult to estimate the
quality of the data set. A common approach for assessing the quality
of interferometric products is the comparison with a reference
data set. We will focus in this paper on the quality assessment
of digital elevation models (DEMs).
In order to be able to compare an interferometrically derived
DEM with a reference model, such a reference model needs to be
accessable. This can be a problem in remote areas where no additional
information is available. The use of a reference model for a comparison
is done assuming that this model is reliable and without any distortions.
From the statistical point of view, a reference DEM with an accuary,
which is one order better than the InSAR DEM, is required. The
result of the comparison of the DEMs gives a quantitative measure
how well the two elevation models fit together. Any systematic
errors remain undetected.
To overcome these problems, we estimate the quality of an InSAR
DEM using an error propagation model based on an empirical approach.
The theoretical background and the implementation of this error
propagation model is described in the following chapters.
Error propagation model
The error propagation model is implemented in an empirical way
because this needs only a limited knowledge about the software
used for the processing. The values of all input parameters as
well as their accuracies are needed in the model. A list of all
output parameters is also required. Each single processing step
needs to be estimated separately. On the other hand, it is possible
to perform the error propagation in a flexible way to different
stages of the processing.
The accuracy of the input parameters is sometimes difficult to
estimate. There are studies undertaken to assess the quality of
some parameters, e.g. baseline (Solaas, 1994). Using precise orbit
information for the processing also quality estimates are provided
(Massmann, 1995). Other values such as wavelength, bandwidth,
etc. vary slightly in the data sets and are difficult to calibrate.
The use of an error propagation model has also its limitations.
Errors caused by atmospheric effects (described by Tarayre and
Massonnet, 1994) or backscatter related influences are not considered
unless there are included in any of the processing steps.
Another aspect of discussion is the question how the final result
of the quality assessment is required. There are three different
levels for which the quality measure could be defined: the pixel
level, the feature level, and the whole image. The user might
be most interested in certain features.
In order to keep the approach as flexible as possible, the implementation
of the error propagation model is performed in an empirical way.
There is no information necessary how the software is actually
implemented. Figure 1 shows a general scheme of the error propagation.
Figure 1: General scheme of the error propagation
For each single processing step the values and the accuracies
of all input parameters as well as a list of output parameters
have to be known. The data set is then processed once with the
original values and afterwards each time with one slightly changed
input parameter. The accuracy of the output parameters is then
derived from the changes of the adapted and the original calculation.
This empirical approach also allows to estimate the sensitivity
of the different parameters on the processing step. In this early
stage of the implementation, the processing is performed with
full quarter scenes in order to investigate the influence of input
parameters on characteristics such as the terrain height, slope
direction, etc. Another aspect is to setup rules for choosing
areas for the quality assessment. The data processing can be performed
using the full scenes but the quality assessment should be limited
to a small representative area. As mentioned before, this also
depends on the final result of the quality assessment. The user
could choose an area, which is representative and where also features
of interest are included.
The development of the error propagation provides the opportunity
to assess the quality of interferometric data independently from
any reference data. It can be adapted to different software realisations
because it is independent from the actual calculation. This is
an advantage due to the fact that there is no standard method
in the processing of SAR interferometric data sets. It can also
be used for optimising the interferometric processing in terms
of accuracy. It is a promising tool but for a final evaluation
of the usefulness of this approach it needs to be further investigated.
The ITC research on SAR interferometry forms part of the CEC's
Human Capital and Mobility Programme Research Network "Synergy
of Remotely Sensed Data". Contract No. CHRX-CT93-0310.
It is also supported by the European Space Agency (AOT.NL 303).
- Massmann, F.-H., 1995:
- Information for ERS PRL/PRC Users, Technical Note,
German Processing and Archiving Facility (D-PAF).
- Solaas, G.A., 1994:
- ERS-1 Interferometric Baseline Algorithm Verification,
ESA report ES-TN-DPE-OM-GS02.
- Tarayre, H. and Massonnet, D., 1994:
- Effects of a Refractive Atmosphere on Interferometric Processing.
Proceedings of IGARSS '94, Pasadena, California, pp. 717-719.
Keywords: ESA European
Space Agency - Agence spatiale europeenne,
observation de la terre, earth observation,
satellite remote sensing,
teledetection, geophysique, altimetrie, radar,
chimique atmospherique, geophysics, altimetry, radar,