An RKHS approach to modelling and inference for spatiotemporal geodetic data with applications to terrestrial radar interferometry
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Author
Date
2019Type
- Doctoral Thesis
ETH Bibliography
yes
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Abstract
Reproducing kernel Hilbert spaces (RKHS) are interpretable as normed spaces of functions furnished with a probability distribution and as such are especially suitable for modelling and inference of spatial, temporal, or spatiotemporal phenomena exhibiting a large degree of randomness. Since the set of RKHS is in one-to-one correspondence with the set of positive definite kernels that in turn completely determine a unique RKHS and can be interpreted as a comprehensive description of the associated stochastic processes correlation structure, the choice of an appropriate kernel is essential to ensure the performance of estimators derived within the RKHS framework. We investigate the spectral decomposition of positive definite kernels and their associated compact kernel operators and find that it leads not only to insights linking functional calculus and signal separation but also suggests a new stochastic model for reproducing kernels that enables their inference from observational data. Solving the inference problem requires the development of numerical methods that parallel the ones employed in semidefinite programming. The resulting algorithm proves to be extendable to allow for the inclusion of affine constraints making it applicable for a wide variety of problems and we subsequently employ RKHS based separation of signal and noise to data originating from terrestrial radar interferometry. Show more
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https://doi.org/10.3929/ethz-b-000346619Publication status
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ETH ZurichSubject
Reproducing kernel Hilbert spaces, Geostatistics, Radar interferometry, AdjustmentOrganisational unit
03964 - Wieser, Andreas / Wieser, Andreas
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ETH Bibliography
yes
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