Daniel Neamati

Daniel Neamati, Sriramya Bhamidipati, Grace Gao

Risk-aware urban localization with the Global Navigation Satellite System (GNSS) remains an unsolved problem with frequent misdetection of the user's street or side of the street. Significant advances in 3D map-aided GNSS use grid-based GNSS shadow matching alongside AI-driven line-of-sight (LOS) classifiers and server-based processing to improve localization accuracy, especially in the cross-street direction. Our prior work introduces a new paradigm for shadow matching that proposes set-valued localization with computationally efficient zonotope set representations. While existing literature improved accuracy and efficiency, the current state of shadow matching theory does not address the needs of risk-aware autonomous systems. We extend our prior work to propose Mosaic Zonotope Shadow Matching (MZSM) that employs a classifier-agnostic polytope mosaic architecture to provide risk-awareness and certifiable guarantees on urban positioning. We formulate a recursively expanding binary tree that refines an initial location estimate with set operations into smaller polytopes. Together, the smaller polytopes form a mosaic. We weight the tree branches with the probability that the user is in line of sight of the satellite and expand the tree with each new satellite observation. Our method yields an exact shadow matching distribution from which we guarantee uncertainty bounds on the user localization. We perform high-fidelity simulations using a 3D building map of San Francisco to validate our algorithm's risk-aware improvements. We demonstrate that MZSM provides certifiable guarantees across varied data-driven LOS classifier accuracies and yields a more precise understanding of the uncertainty over existing methods. We validate that our tree-based construction is efficient and tractable, computing a mosaic from 14 satellites in 0.63 seconds and growing quadratically in the satellite number.

Keidai Iiyama, Daniel Neamati, Grace Gao

To address the need for robust positioning, navigation, and timing services in lunar environments, this paper proposes a novel onboard clock phase jump detection framework for satellite constellations using range measurements obtained from dual one-way inter-satellite links. Our approach leverages vertex redundantly rigid graphs to detect faults without relying on prior knowledge of satellite positions or clock biases, providing flexibility for lunar satellite networks with diverse satellite types and operators. We model satellite constellations as graphs, where satellites are vertices and inter-satellite links are edges. The proposed algorithm detects and identifies satellites with clock jumps by monitoring the singular values of the geometric-centered Euclidean distance matrix (GCEDM) of 5-clique sub-graphs. The proposed method is validated through simulations of a GPS constellation and a notional constellation around the Moon, demonstrating its effectiveness in various configurations.

Lance Legel, Qin Huang, Brandon Voelker et al.

We present DeepEarth, a self-supervised multi-modal world model with Earth4D, a novel planetary-scale 4D space-time positional encoder. Earth4D extends 3D multi-resolution hash encoding to include time, efficiently scaling across the planet over centuries with sub-meter, sub-second precision. Multi-modal encoders (e.g. vision-language models) are fused with Earth4D embeddings and trained via masked reconstruction. We demonstrate Earth4D's expressive power by achieving state-of-the-art performance on an ecological forecasting benchmark. Earth4D with learnable hash probing surpasses a multi-modal foundation model pre-trained on substantially more data. Access open source code and download models at: https://github.com/legel/deepearth

Daniel Neamati, Yashwanth Kumar Nakka, Soon-Jo Chung

Accurate gravity field models are essential for safe proximity operations around small bodies. State-of-the-art techniques use spherical harmonics or high-fidelity polyhedron shape models. Unfortunately, these techniques can become inaccurate near the surface of the small body or have high computational costs, especially for binary or heterogeneous small bodies. New learning-based techniques do not encode a predefined structure and are more versatile. In exchange for versatility, learning-based techniques can be less robust outside the training data domain. In deployment, the spacecraft trajectory is the primary source of dynamics data. Therefore, the training data domain should include spacecraft trajectories to accurately evaluate the learned model's safety and robustness. We have developed a novel method for learning-based gravity models that directly uses the spacecraft's past trajectories. We further introduce a method to evaluate the safety and robustness of learning-based techniques via comparing accuracy within and outside of the training domain. We demonstrate this safety and robustness method for two learning-based frameworks: Gaussian processes and neural networks. Along with the detailed analysis provided, we empirically establish the need for robustness verification of learned gravity models when used for proximity operations.