Atmospheric Phase Screen Retrieval in a GeoSAR Simulation Using Data Assimilation

Abstract: This report presents a data assimilation method to retrieve the atmospheric phase screen (APS) using a sequence of coarse resolution images produced by a geosynchronous synthetic aperture radar (GEO SAR). Since there are presently no such radars in geosynchronous orbit, the simulations in this report will use or be informed by a GEO SAR simulator developed at Cranfield University. A geosynchronous radar is used to retrieve the APS for two reasons. Firstly, a radar in this orbit, as opposed to low earth orbit, provides a raw measurement of the time rate of change of the APS at a certain point. This measurement is the azimuth shift of a target feature in the image from its true position that can be used even when the target features are not coherent between images. Secondly, the almost permanent view of such a radar can only be exploited to produce high spatial resolution images integrated over a long time period if the time varying phase distortion introduced by the atmosphere can be subtracted. Even if this is not the intended use of the APS, its retrieval would also be valuable in its own right.
A data assimilation algorithm, the Kalman filter, is used for the APS retrieval. Two possibilities for propagation models and three variants of a measurement model are developed. These are used together in different combinations to study the differences in performance that they yield. The intention is to demonstrate that under certain simplified conditions, an APS retrieval can be performed that preserves the physical character of the APS and that is superior to a retrieval using only the measurements and no propagation model, or using a persistence model. The results of the simulations vindicate this intention, and reveal that additional techniques could be used to mitigate some of the significant obstacles to such a retrieval, such as techniques used to reduce measurement bias and certain adaptive filtering techniques.