Robust Signal Processing with Applications to Positioning and Imaging

This dissertation investigates robust signal processing and machine learning techniques, with the objective of improving the robustness of two applications against various threats, namely Global Navigation Satellite System (GNSS) based positioning and satellite imaging. GNSS technology is widely used in different fields, such as autonomous navigation, asset tracking, or smartphone positioning, while the satellite imaging plays a central role in monitoring, detecting and estimating the intensity of key natural phenomena, such as flooding prediction and earthquake detection. Considering the use of both GNSS positioning and satellite imaging in critical and safety-of-life applications, it is necessary to protect those two technologies from either intentional or unintentional threats. In the real world, the common threats to GNSS technology include multipath propagation and intentional/unintentional interferences. This thesis investigates methods to mitigate the influence of such sources of error, with the final objective of designing secure and resilient GNSS receivers for robust GNSS positioning. Generally speaking, there are two kinds of positioning technology in GNSS receiver: two-step (2SP) and Direct Position Estimation (DPE) methods. The 2SP method is the conventional positioning method, where 3 blocks are typically required: acquisition block, tracking block and navigation solution block. To improve robustness against common threats mentioned above, this thesis built robust signal processing methods in each block: 1) the use of robust statistics to design enhanced correlation schemes that are resilient to jamming interferences in acquisition and tracking blocks, named as Robust Interference Mitigation (RIM); 2) the use of Deep Learning to learn signal correlation in tracking block in multipath-rich environments, where propagation channel models are too complex to be of practical use; and 3) the design of a variational-based Robust Kalman Filter that can mitigate outliers and provide Position, Velocity, and Time (PVT) estimates in challenging environments. The DPE method is a new positioning technique, aiming to acquire PVT solution directly instead of using Doppler-shift and time-delay of satellite signal as intermediate variables. However, given that the input to DPE is still the received satellite signal, the influence of the three kinds of aforementioned threats is still relevant. This thesis therefore investigates the use of robust statistics to mitigate jamming signals in DPE receivers, similarly as done for the 2SP method earlier. To evaluate the loss of efficiency of using RIM in DPE schemes, the Cram?er?Rao Bound (CRB) is considered, showing a bounded loss. Regarding the application to satellite imaging technology, this thesis investigates two problems in multispectral and hyperspectral imaging, respectively. In terms of multispectral imaging, the low frequency of high-resolution spatial image occurrence is a common drawback that many researchers aimed at solving. This thesis proposes a Bayesian filtering method to fuse multi-temporal and multi-spectral images (from high-resolution/low-availability and low-resolution/high-availability images) for high resolution spatial estimates to extend the availability of high-resolution imaging. The novelty of this method is to consider historical high spatial resolution images and, to address the computational cost increase due to high-dimensional state-space model resulting from multi-spectral images. To cope with the high-dimensionality, the state space is partitioned into several low dimensional subspaces, with one filter or smoother dealing with the low-dimensional subspaces and interacting among them. The parallel processing is also introduced to speed up the whole processing under the assumption that all pixels in the coarse spatial resolution images are independent. As a result of this work, the fusing method improved robustness against low temporal frequency of high-resolution spatial images, while maintaining an affordable computational complexity. As a use case, this thesis considered Land Remote-Sensing Satellite 8 (Landsat 8) images as high-resolution spatial images and Moderate Resolution Imaging Spectroradiometer (MODIS) images as coarse-resolution images, with the objective of water and flood monitoring. In terms of hyperspectral imaging, this thesis focuses on improving Hyperspectral Unmixing (HU) method. In HU, the most common model due to its tractability is the linear mixing model, however, it might fail in modeling the nonlinear interactions between different materials. This drawback is addressed in this thesis by considering an Auto-encoder (AEC) based model. This thesis proposed an AEC based method, imposing a particular structure to both the encoder and the decoder networks in order to account for the physical properties of the problem, that is the fact that the encoder should invert the mixing process. Overall, this thesis leverages and develops new tools in robust statistics and Bayesian filtering to effectively and efficiently deal with model mismatches and, ultimately, provide improved data fusion methodologies that are applicable to a variety of problems, such as GNSS or remote sensing.