Numerous methods have been proposed for global navigation satellite system (GNSS) receivers to detect faulty GNSS signals. One such fault detection and exclusion (FDE) method is based on the mathematical concept of Euclidean distance matrices (EDMs). This paper outlines a greedy approach that uses an improved Euclidean distance matrix-based fault detection and exclusion algorithm. The novel greedy EDM FDE method implements a new fault detection test statistic and fault exclusion strategy that drastically simplifies the complexity of the algorithm over previous work. To validate the novel greedy EDM FDE algorithm, we created a simulated dataset using receiver locations from around the globe. The simulated dataset allows us to verify our results on 2,601 different satellite geometries. Additionally, we tested the greedy EDM FDE algorithm using a real-world dataset from seven different android phones. Across both the simulated and real-world datasets, the Python implementation of the greedy EDM FDE algorithm is shown to be computed an order of magnitude more rapidly than a comparable greedy residual FDE method while obtaining similar fault exclusion accuracy. We provide discussion on the comparative time complexities of greedy EDM FDE, greedy residual FDE, and solution separation. We also explain potential modifications to greedy residual FDE that can be added to alter performance characteristics.

Learning hydrologic models for accurate riverine flood prediction at scale is a challenge of great importance. One of the key difficulties is the need to rely on in-situ river discharge measurements, which can be quite scarce and unreliable, particularly in regions where floods cause the most damage every year. Accordingly, in this work we tackle the problem of river discharge estimation at different river locations. A core characteristic of the data at hand (e.g. satellite measurements) is that we have few measurements for many locations, all sharing the same physics that underlie the water discharge. We capture this scenario in a simple but powerful common mechanism regression (CMR) model with a local component as well as a shared one which captures the global discharge mechanism. The resulting learning objective is non-convex, but we show that we can find its global optimum by leveraging the power of joining local measurements across sites. In particular, using a spectral initialization with provable near-optimal accuracy, we can find the optimum using standard descent methods. We demonstrate the efficacy of our approach for the problem of discharge estimation using simulations.

Accurately measuring the aerosol optical depth (AOD) is essential for our understanding of the climate. Currently, AOD can be measured by (i) satellite instruments, which operate on a global scale but have limited accuracies; and (ii) ground-based instruments, which are more accurate but not widely available. Recent approaches focus on integrating measurements from these two sources to complement each other. In this paper, we further improve the prediction accuracy by using the observation that the AOD varies slowly in the spatial domain. Using a probabilistic approach, we impose this smoothness constraint by a Gaussian random field on the Earth's surface, which can be considered as a two-dimensional manifold. The proposed integration approach is computationally simple, and experimental results on both synthetic and real-world data sets show that it significantly outperforms the state-of-the-art.