arXiv subjects

Grace Gao

Publications and source records attributed to Grace Gao.

31 records · Page 2Linked to original sources

arXiv2024

A Survey of Machine Learning Techniques for Improving Global Navigation Satellite Systems

Global Navigation Satellite Systems (GNSS)-based positioning plays a crucial role in various applications, including navigation, transportation, logistics, mapping, and emergency services. Traditional GNSS positioning methods are model-based and they utilize satellite geometry and the known properties of satellite signals. However, model-based methods have limitations in challenging environments and often lack adaptability to uncertain noise models. This paper highlights recent advances in Machine Learning (ML) and its potential to address these limitations. It covers a broad range of ML methods, including supervised learning, unsupervised learning, deep learning, and hybrid approaches. The survey provides insights into positioning applications related to GNSS such as signal analysis, anomaly detection, multi-sensor integration, prediction, and accuracy enhancement using ML. It discusses the strengths, limitations, and challenges of current ML-based approaches for GNSS positioning, providing a comprehensive overview of the field.

eess.SP↗

arXiv2023

Spoofing-Resilient LiDAR-GPS Factor Graph Localization with Chimera Authentication

Many vehicle platforms typically use sensors such as LiDAR or camera for locally-referenced navigation with GPS for globally-referenced navigation. However, due to the unencrypted nature of GPS signals, all civilian users are vulner-able to spoofing attacks, where a malicious spoofer broadcasts fabricated signals and causes the user to track a false position fix. To protect against such GPS spoofing attacks, Chips-Message Robust Authentication (Chimera) has been developed and will be tested on the Navigation Technology Satellite 3 (NTS-3) satellite being launched later this year. However, Chimera authentication is not continuously available and may not provide sufficient protection for vehicles which rely on more frequent GPS measurements. In this paper, we propose a factor graph-based state estimation framework which integrates LiDAR and GPS while simultaneously detecting and mitigating spoofing attacks experienced between consecutive Chimera authentications. Our proposed framework combines GPS pseudorange measurements with LiDAR odometry to provide a robust navigation solution. A chi-squared detector, based on pseudorange residuals, is used to detect and mitigate any potential GPS spoofing attacks. We evaluate our method using real-world LiDAR data from the KITTI dataset and simulated GPS measurements, both nominal and with spoofing. Across multiple trajectories and Monte Carlo runs, our method consistently achieves position errors under 5 m during nominal conditions, and successfully bounds positioning error to within odometry drift levels during spoofed conditions.

eess.SP↗

arXiv2023

Binary sequence set optimization for CDMA applications via mixed-integer quadratic programming

Finding sets of binary sequences with low auto- and cross-correlation properties is a hard combinatorial optimization problem with numerous applications, including multiple-input-multiple-output (MIMO) radar and global navigation satellite systems (GNSS). The sum of squared correlations, sometimes referred to as the integrated sidelobe level (ISL), is a quartic function in the variables and is a commonly-used metric of sequence set quality. In this paper, we show that the ISL minimization problem may be formulated as a mixed-integer quadratic program (MIQP). We then present a block coordinate descent (BCD) algorithm that iteratively optimizes over subsets of variables. The subset optimization subproblems are also MIQPs which may be handled more efficiently using specialized solvers than using exhaustive search; this allows us to perform BCD over larger variable subsets than previously possible. Our approach was used to find sets of four binary sequences of lengths up to 1023 with better ISL performance than Gold codes and sequence sets found using existing BCD methods.

eess.SP↗

arXiv2022

A Deep Reinforcement Learning Approach to Rare Event Estimation

An important step in the design of autonomous systems is to evaluate the probability that a failure will occur. In safety-critical domains, the failure probability is extremely small so that the evaluation of a policy through Monte Carlo sampling is inefficient. Adaptive importance sampling approaches have been developed for rare event estimation but do not scale well to sequential systems with long horizons. In this work, we develop two adaptive importance sampling algorithms that can efficiently estimate the probability of rare events for sequential decision making systems. The basis for these algorithms is the minimization of the Kullback-Leibler divergence between a state-dependent proposal distribution and a target distribution over trajectories, but the resulting algorithms resemble policy gradient and value-based reinforcement learning. We apply multiple importance sampling to reduce the variance of our estimate and to address the issue of multi-modality in the optimal proposal distribution. We demonstrate our approach on a control task with both continuous and discrete actions spaces and show accuracy improvements over several baselines.

cs.LG↗

arXiv2022

Safe Reinforcement Learning Using Black-Box Reachability Analysis

Reinforcement learning (RL) is capable of sophisticated motion planning and control for robots in uncertain environments. However, state-of-the-art deep RL approaches typically lack safety guarantees, especially when the robot and environment models are unknown. To justify widespread deployment, robots must respect safety constraints without sacrificing performance. Thus, we propose a Black-box Reachability-based Safety Layer (BRSL) with three main components: (1) data-driven reachability analysis for a black-box robot model, (2) a trajectory rollout planner that predicts future actions and observations using an ensemble of neural networks trained online, and (3) a differentiable polytope collision check between the reachable set and obstacles that enables correcting unsafe actions. In simulation, BRSL outperforms other state-of-the-art safe RL methods on a Turtlebot 3, a quadrotor, a trajectory-tracking point mass, and a hexarotor in wind with an unsafe set adjacent to the area of highest reward.

cs.RO↗

arXiv2022

PlaneSLAM: Plane-based LiDAR SLAM for Motion Planning in Structured 3D Environments

LiDAR sensors are a powerful tool for robot simultaneous localization and mapping (SLAM) in unknown environments, but the raw point clouds they produce are dense, computationally expensive to store, and unsuited for direct use by downstream autonomy tasks, such as motion planning. For integration with motion planning, it is desirable for SLAM pipelines to generate lightweight geometric map representations. Such representations are also particularly well-suited for man-made environments, which can often be viewed as a so-called "Manhattan world" built on a Cartesian grid. In this work we present a 3D LiDAR SLAM algorithm for Manhattan world environments which extracts planar features from point clouds to achieve lightweight, real-time localization and mapping. Our approach generates plane-based maps which occupy significantly less memory than their point cloud equivalents, and are suited towards fast collision checking for motion planning. By leveraging the Manhattan world assumption, we target extraction of orthogonal planes to generate maps which are more structured and organized than those of existing plane-based LiDAR SLAM approaches. We demonstrate our approach in the high-fidelity AirSim simulator and in real-world experiments with a ground rover equipped with a Velodyne LiDAR. For both cases, we are able to generate high quality maps and trajectory estimates at a rate matching the sensor rate of 10 Hz.

cs.RO↗

arXiv2022

Set-Valued Shadow Matching Using Zonotopes for 3-D Map-Aided GNSS Localization

Unlike many urban localization methods that return point-valued estimates, a set-valued representation enables robustness by ensuring that a continuum of possible positions obeys safety constraints. One strategy with the potential for set-valued estimation is GNSS-based shadow matching~(SM), where one uses a three-dimensional (3-D) map to compute GNSS shadows (where line-of-sight is blocked). However, SM requires a point-valued grid for computational tractability, with accuracy limited by grid resolution. We propose zonotope shadow matching (ZSM) for set-valued 3-D map-aided GNSS localization. ZSM represents buildings and GNSS shadows using constrained zonotopes, a convex polytope representation that enables propagating set-valued estimates using fast vector concatenation operations. Starting from a coarse set-valued position, ZSM refines the estimate depending on the receiver being inside or outside each shadow as judged by received carrier-to-noise density. We demonstrated our algorithm's performance using simulated experiments on a simple 3-D example map and on a dense 3-D map of San Francisco.

cs.RO↗

arXiv2022

Decentralized Connectivity Maintenance for Multi-robot Systems Under Motion and Sensing Uncertainties

Communication connectivity is desirable for safe and efficient operation of multi-robot systems. While decentralized algorithms for connectivity maintenance have been explored in recent literature, the majority of these works do not account for robot motion and sensing uncertainties. These uncertainties are inherent in practical robots and result in robots deviating from their desired positions which could potentially result in a loss of connectivity. In this paper we present a Decentralized Connectivity Maintenance algorithm accounting for robot motion and sensing Uncertainties (DCMU). We first propose a novel weighted graph definition for the multi-robot system that accounts for the aforementioned uncertainties along with realistic connectivity constraints such as line-of-sight connectivity and collision avoidance. Next we design a decentralized gradient-based controller for connectivity maintenance where we derive the gradients of our weighted graph edge weights required for computing the control. Finally, we perform multiple simulations to validate the connectivity maintenance performance of our DCMU algorithm under robot motion and sensing uncertainties and show an improvement compared to previous work.

cs.RO↗

arXiv2022

Ellipsotopes: Combining Ellipsoids and Zonotopes for Reachability Analysis and Fault Detection

Ellipsoids are a common representation for reachability analysis, because they can be transformed efficiently under affine maps, and allow conservative approximation of Minkowski sums, which let one incorporate uncertainty and linearization error in a dynamical system by expanding the size of the reachable set. Zonotopes, a type of symmetric, convex polytope, are similarly frequently used due to efficient numerical implementation of affine maps and exact Minkowski sums. Both of these representations also enable efficient, convex collision detection for fault detection or formal verification tasks, wherein one checks if the reachable set of a system collides (i.e., intersects) with an unsafe set. However, both representations often result in conservative representations for reachable sets of arbitrary systems, and neither is closed under intersection. Recently, representations such as constrained zonotopes and constrained polynomial zonotopes have been shown to overcome some of these conservativeness challenges, and are closed under intersection. However, constrained zonotopes can not represent shapes with smooth boundaries such as ellipsoids, and constrained polynomial zonotopes can require solving a non-convex program for collision checking or fault detection. This paper introduces ellipsotopes, a set representation that is closed under affine maps, Minkowski sums, and intersections. Ellipsotopes combine the advantages of ellipsoids and zonotopes while ensuring convex collision checking. The utility of this representation is demonstrated on several examples.

eess.SY↗

arXiv2022

Improving GNSS Positioning using Neural Network-based Corrections

Deep Neural Networks (DNNs) are a promising tool for Global Navigation Satellite System (GNSS) positioning in the presence of multipath and non-line-of-sight errors, owing to their ability to model complex errors using data. However, developing a DNN for GNSS positioning presents various challenges, such as 1) poor numerical conditioning caused by large variations in measurements and position values across the globe, 2) varying number and order within the set of measurements due to changing satellite visibility, and 3) overfitting to available data. In this work, we address the aforementioned challenges and propose an approach for GNSS positioning by applying DNN-based corrections to an initial position guess. Our DNN learns to output the position correction using the set of pseudorange residuals and satellite line-of-sight vectors as inputs. The limited variation in these input and output values improves the numerical conditioning for our DNN. We design our DNN architecture to combine information from the available GNSS measurements, which vary both in number and order, by leveraging recent advancements in set-based deep learning methods. Furthermore, we present a data augmentation strategy for reducing overfitting in the DNN by randomizing the initial position guesses. We first perform simulations and show an improvement in the initial positioning error when our DNN-based corrections are applied. After this, we demonstrate that our approach outperforms a WLS baseline on real-world data. Our implementation is available at github.com/Stanford-NavLab/deep_gnss.

cs.RO↗

arXiv2022

Mosaic Zonotope Shadow Matching for Risk-Aware Autonomous Localization in Harsh Urban Environments

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.

cs.AI↗

arXiv2022

A Case Study Analysis for Designing a Lunar Navigation Satellite System with Time-Transfer from Earth-GPS

Recently, there has been a growing interest in the use of a SmallSat platform for the future Lunar Navigation Satellite System (LNSS) to allow for cost-effectiveness and rapid deployment. However, many design choices are yet to be finalized for the SmallSat-based LNSS, including the onboard clock and the orbit type. As compared to the legacy Earth-GPS, designing an LNSS poses unique challenges: (a) restricted Size, Weight, and Power (SWaP) of the onboard clock, which limits the timing stability; (b) limited lunar ground monitoring stations, which engenders a greater preference toward stable LNSS satellite orbits. In this current work, we analyze the trade-off between different design considerations related to the onboard clock and the lunar orbit type for designing an LNSS with time-transfer from Earth-GPS. Our proposed time-transfer architecture combines the intermittently available Earth-GPS signals in a timing filter to alleviate the cost and SWaP requirements of the onboard clocks. Specifically, we conduct multiple case studies with different grades of low-SWaP clocks and various previously studied lunar orbit types. We estimate the lunar User Equivalent Range Error (UERE) metric to characterize the ranging accuracy of signals transmitted from an LNSS satellite. Using the Systems Tool Kit (STK)-based simulation setup from Analytical Graphics, Inc. (AGI), we evaluate the lunar UERE across various case studies of the LNSS design to demonstrate comparable performance as that of the legacy Earth-GPS, even while using a low-SWaP onboard clock. We further perform sensitivity analysis to investigate the variation in the lunar UERE metric across different case studies as the Earth-GPS measurement update rates are varied.

cs.RO↗

arXiv2014

Navigating Robot Swarms Using Collective Intelligence Learned from Golden Shiner Fish

Navigating networked robot swarms often requires knowing where to go, sensing the environment, and path-planning based on the destination and barriers in the environment. Such a process is computationally intensive. Moreover, as the network scales up, the computational load increases quadratically, or even exponentially. Unlike these man-made systems, most biological systems scale linearly in complexity. Furthermore, the scale of a biological swarm can even enable collective intelligence. One example comes from observations of golden shiner fish. Golden shiners naturally prefer darkness and school together. Each individual golden shiner does not know where the darkness is. Neither does it sense the light gradients in the environment. However, by moving together as a school, they always end up in the shady area. We apply such collective intelligence learned from golden shiner fish to navigating robot swarms. Each individual robot's dynamic is based on the gold shiners' movement strategy---a random walk with its speed modulated by the light intensity and its direction affected by its neighbors. The theoretical analysis and simulation results show that our method 1) promises to navigate a robot swarm with little situational knowledge, 2) simplifies control and decision-making for each individual robot, 3) requires minimal or even no information exchange within the swarm, and 4) is highly distributed, adaptive, and robust.

cs.NE↗