Conclusions and Outlook

the stochastic model, they remain completely unconsidered by the gridsearch estimator, which does not provide a stochastic model at all. The consequential result was an inconsistent network of baseline er-ror estimates. Nevertheless, the gridsearch method may be capable of producing more reliable results if the nonlinear atmospheric contribution at long wavelengths is either insignificant, mitigated before-hand or accounted for externally.

6.4.2. Potential Improvements

In spite of the basically promising results of the proposed approach, there are still some aspects that could be optimised by further research. One is the strategy of selecting phase observations that has to consider a trade-off between stochastical rigour and robustness. On the one hand, the observation quality is variable in space, and some parts of the interferogram might lack any reliable phase meas-urement. On the other hand, a quality-oriented selection or weighting of observations runs the risk that the estimates adjust to a local phase trend that is not representative for the whole interferogram.

Whereas the approach of using unweighted and homogeneously distributed observations is an acceptable compromise, there may be a more sophisticated way to find an optimal compromise by means of robust estimation techniques (see section 4.5.1).

A major deficiency of the proposed least squares estimator is the still imperfect stochastic model. Es-pecially the incidental violation of the stationarity assumption for the estimation of covariance functions and the neglect of algebraic correlations between interferograms are suspected to contribute significantly to the unsatisfactory performance. However, developing a more adequate model would be a complicated undertaking with uncertain benefit and thus not recommended in the first place. This is different for the gridsearch estimator, which does not involve a stochastic model at all. An adapted weighting scheme may have the potential to enable a more reliable outlier identification.

Regardless these conceivable enhancements, the greatest step forward in handling orbit errors could be made by applying the proposed methodology to a variety of data sets with different focusses of research.

Thus, the performance in everyday applications can be evaluated, weaknesses identified, and strategies for further fine-tuning developed. Additional benefit may also be drawn from the joint consideration of orbit errors together with other signal components. Especially the deficient atmospheric modelling has potential for improvement by exploiting numerical weather models.

6.4.3. Embedding into the Processing Chain

There are several concepts on how to enhance the performance of InSAR processing by integration of orbit error estimation.

1. A priori orbit correction. Orbit errors are estimated without any consideration of deformation or atmosphere, and the predicted orbital signals are subtracted from the interferograms in a pre-processing step. This is the simplest approach and has been pursued within the scope of this thesis.

Leakage of the long wavelength deformation component can be mitigated by temporal high-pass filtering of the orbit error estimates.

2. Support of phase unwrapping. Extraordinarily large orbit errors and the resulting spatial phase gradients between PS candidates can complicate or even impede phase unwrapping. As a rem-edy, approximate orbital error signals can be estimated, subtracted before and restored after the unwrapping step.

6.4. Conclusions and Outlook

3. Joint estimation with deformation and/or atmosphere. The most elaborate methodology would be a joint estimation of all signal components, whereas the mathematical model for the orbital component could be based on the methodology presented here. As a joint estimation requires processing the data from all interferograms at a time, it involves a considerable computational load and is only practicable if the spatial dimension is reduced by hierarchical partitioning or pixel-wise estimation.

4. Iteratively-alternating estimation with deformation and/or atmosphere. Another option to reduce the complexity of the joint estimation (3.) is to alternatingly estimate the individual contributions and iterate towards converging parameters for deformation, orbit errors and eventually the atmo-spheric contribution. For the estimation of the orbital component, the methodology presented here can be used without adaption.

To facilitate the application of this methodology and related follow-up research, the estimators from chapter 4.3 have been integrated into the DORIS InSAR processor as an optional step (http://doris.

tudelft.nl, version 4.04, stepESTORBITS, see alsoM MORBITS and S MORBITS).

6.4.4. General Applicability

Seeing the recent quality enhancements of orbit products, the need for orbit error estimation and correc-tion is indeed becoming quescorrec-tionable. The trajectories for the latest SAR satellites have reached a level of accuracy at which the effect of residual orbit errors on interferograms is hardly significant. Moreover, modern InSAR processors are capable to filter out small orbital contributions by their spatio-temporal correlation properties, not requiring an explicit estimation (Hooper, 2008;Ketelaar, 2009;Ferretti et al., 2011). Nevertheless, there are a number of scenarios in which explicit orbit error correction will still be useful in the future.

1. Radarsat. With Radarsat-1 and Radarsat-2 there are two operational SAR satellites, the orbit accuracy of which is still far from meeting InSAR requirements. As strong Radarsat orbit errors may significantly complicate 3D phase unwrapping in PS processing, orbit error correction techniques are very relevant for processing Radarsat data. At least Radarsat-2 can be expected to operate for another couple of years, filling the gap in the series of C-band SAR missions between Envisat and Sentinel-1a.

2. Historical missions. Monitoring of long-term deformation processes always requires measurements spanning several years. At least during the next decade, there will still be considerable interest in acquisitions before 2010 or even from the 1990s to trace back the effects of anthropogenic activities or to maximise the temporal basis for the estimation of slowly creeping tectonic processes.

3. Single interferograms or short time series. If the data coverage is too poor to adequately support a temporal filtering, a simple orbit error correction may be reasonable if large-scale deformation signals are beyond the focus of research.

4. Implicit temporal filtering. Besides conventional filtering in the spatial or frequency domain, which is inherent to PS approaches, a distinction between deformation and orbit errors is alternatively feas-ible by a joint or iteratively-alternating estimation of both components with an adequate stochastic modelling. For the orbital component, the methodology proposed here can be used.

5. Temporarily underperforming GPS.The outstanding performance of GPS tracking cannot be guar-anteed for any time in the future. An increase of ionospheric activity due to geomagnetic storms or

the general variations of the solar cycle may cause degradations in the quality of orbit products. It is also possible that GPS signals are artificially deteriorated at any time due to military considerations of the United States of America. This would entail a serious degradation of orbit determination performance as long as on-board receivers are not designed to complementarily treat signals of other GNSS. And though very unlikely, it cannot be excluded that the on-board GPS receiver of a SAR satellite fails, and orbits have to be determined with relatively imprecise backup systems.

6. Near real-time applications. The computation of precise ephemerides requires tracking data from both before and after an event as well as auxiliary data supporting various correction models.

As acquisition, processing and gathering of these data takes some time, the more accurate orbit solutions are only available with a delay of some hours, days or even weeks. However, to support time-critical decisions in disaster management, it is not acceptable to postpone InSAR processing until high-quality orbit data are available. Hence, orbit error estimation techniques can be used to predict a precise trajectory based on interferometry with older images.

7. Quality assurance. Even with the expectable high quality orbits in the future, it will still be valuable to have a methodology in place to continuously check if the actual orbit accuracy meets the requirements.

6.4.5. Separability from other Signal Components

The interferometric signal can generally be decomposed into three contributions: deformation, atmo-spheric propagation delay and residual errors in the geometric phase, whereas the long wavelength com-ponent of the latter is dominated by orbit errors. For the estimation of either deformation, atmosphere or orbit errors, all three contributions have to be accommodated by either the functional or the stochastic model. Any imperfection in modelling may cause leakage from the interferometric signal of one com-ponent into the estimate of another comcom-ponent.

In order to assess the severity of leakage, the signal of interest has to be defined. In deformation analysis, deformation is the signal of interest. Estimating deformation parameters, leakage from the orbital con-tribution can be mitigated by estimating and subsequently subtracting the orbital error signal. Leakage can never be prevented completely, since it is infeasible to model the deformation signal both functionally and stochastically at an ultimate level of detail. Concrete strategies to distinguish the contributions of orbital errors and deformation have been outlined in section 4.2.2.

As the atmospheric contribution does not follow a characteristic pattern, it cannot be modelled func-tionally. A rigorous consideration in the stochastic model is only straightforward for the short scale component. The linear part of the large scale component is only separable from the orbital contribution by integrating complementary meteorological measurements and otherwise leaks into the orbit error es-timates. Since deformation and not atmosphere is the signal of interest, this type of leakage is tolerable.

However, a learning from section 6.2 is that large scale nonlinear atmospheric artefacts still can signific-antly bias the orbit error estimates and generate an inconsistent set of parameters, which is definitely not tolerable. Hence, consistent orbit error estimation can only go along with consistent atmospheric model-ling, and the impact of leakage has to be assessed in context of the respective mathematical model.