Publications

This technical report is the more formal report associated with the previously approved IR request 1713115 (SAND No.SAND2023-06044O). This document will be shared with the confidence assessment executive working group that came out of ATRWG.

We study the problem of designing a distributed observer for an LTI system over a time-varying communication graph. The limited existing work on this topic imposes various restrictions either on the observation model or on the sequence of communication graphs. In contrast, we propose a single-time-scale distributed observer that works under mild assumptions. Specifically, our communication model only requires strong-connectivity to be preserved over nonoverlapping, contiguous intervals that are even allowed to grow unbounded over time. We show that under suitable conditions that bound the growth of such intervals, joint observability is sufficient to track the state of any discrete-time LTI system exponentially fast, at any desired rate. We also develop a variant of our algorithm that is provably robust to worst-case adversarial attacks, provided the sequence of graphs is sufficiently connected over time. The key to our approach is the notion of a 'freshness-index' that keeps track of the age-of-information being diffused across the network. Such indices enable nodes to reject stale estimates of the state, and, in turn, contribute to stability of the error dynamics.

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We consider the problem of distributed inference where agents in a network observe a stream of private signals generated by an unknown state, and aim to uniquely identify this state from a finite set of hypotheses. We focus on scenarios where communication between agents is costly, and takes place over channels with finite bandwidth. To reduce the frequency of communication, we develop a novel event-triggered distributed learning rule that is based on the principle of diffusing low beliefs on each false hypothesis. Building on this principle, we design a trigger condition under which an agent broadcasts only those components of its belief vector that have adequate innovation, to only those neighbors that require such information. We prove that our rule guarantees convergence to the true state exponentially fast almost surely despite sparse communication, and that it has the potential to significantly reduce information flow from uninformative agents to informative agents. Next, to deal with finite-precision communication channels, we propose a distributed learning rule that leverages the idea of adaptive quantization. We show that by sequentially refining the range of the quantizers, every agent can learn the truth exponentially fast almost surely, while using just 1 bit to encode its belief on each hypothesis. For both our proposed algorithms, we rigorously characterize the trade-offs between communication-efficiency and the learning rate.

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Here, we study a setting where a group of agents, each receiving partially informative private signals, seek to collaboratively learn the true underlying state of the world (from a finite set of hypotheses) that generates their joint observation profiles. To solve this problem, we propose a distributed learning rule that differs fundamentally from existing approaches, in that it does not employ any form of “belief-averaging”. Instead, agents update their beliefs based on a min-rule. Under standard assumptions on the observation model and the network structure, we establish that each agent learns the truth asymptotically almost surely. As our main contribution, we prove that with probability 1, each false hypothesis is ruled out by every agent exponentially fast, at a network-independent rate that is strictly larger than existing rates. We then develop a computationally-efficient variant of our learning rule that is provably resilient to agents who do not behave as expected (as represented by a Byzantine adversary model) and deliberately try to spread misinformation.

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We address the problem of simultaneous coverage control and stochastic, multi-target tracking with a single pursuer. We presume linear dynamics for the pursuer and linear stochastic dynamics for the targets. The pursuer is equipped with two sensors of varying fidelity: broad-range and narrow-range. We seek the optimal trajectory for the pursuer, as well as optimal sensor selection, over a finite time horizon. We formulate the problem as a mixed-integer program with quadratic constraints, and exploit a convex relaxation method to enable fast solution of local minima. We demonstrate our approach on several simulated scenarios.

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We study the problem of collaboratively estimating the state of a discrete-time LTI process by a network of sensor nodes interacting over a time-varying directed communication graph. Existing approaches to this problem either (i) make restrictive assumptions on the dynamical model, or (ii) make restrictive assumptions on the sequence of communication graphs, or (iii) require multiple consensus iterations between consecutive time-steps of the dynamics, or (iv) require higher-dimensional observers. In this paper, we develop a distributed observer that operates on a single time-scale, is of the same dimension as that of the state, and works under mild assumptions of joint observability of the sensing model, and joint strong-connectivity of the sequence of communication graphs. Our approach is based on the notion of a novel 'freshness-index' that keeps track of the age-of-information being diffused across the network. In particular, such indices enable nodes to reject stale information regarding the state of the system, and in turn, help achieve stability of the estimation error dynamics. Based on the proposed approach, the estimate of each node can be made to converge to the true state exponentially fast, at any desired convergence rate. In fact, we argue that finite-time convergence can also be achieved through a suitable selection of the observer gains. Our proof of convergence is self-contained, and employs simple arguments from linear system theory and graph theory.

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We study a setting where a group of agents, each receiving partially informative private observations, seek to collaboratively learn the true state (among a set of hypotheses) that explains their joint observation profiles over time. To solve this problem, we propose a distributed learning rule that differs fundamentally from existing approaches, in the sense that it does not employ any form of 'belief-averaging'. Specifically, every agent maintains a local belief on each hypothesis that is updated in a Bayesian manner without any network influence, and an actual belief that is updated (up to normalization) as the minimum of its own local belief and the actual beliefs of its neighbors. Under minimal requirements on the signal structures of the agents and the underlying communication graph, we establish consistency of the proposed belief update rule, i.e., we show that the actual beliefs of the agents asymptotically concentrate on the true state almost surely. As one of the key benefits of our approach, we show that our learning rule can be extended to scenarios that capture misbehavior on the part of certain agents in the network, modeled via the Byzantine adversary model. In particular, we prove that each non-adversarial agent can asymptotically learn the true state of the world almost surely, under appropriate conditions on the observation model and the network topology.

A small, consumable-free, low-power, ultra-high-speed comprehensive GC×GC system consisting of microfabricated columns, nanoelectromechanical system (NEMS) cantilever resonators for detection, and a valve-based stop-flow modulator is demonstrated. The separation of a highly polar 29-component mixture covering a boiling point range of 46 to 253 °C on a pair of microfabricated columns using a Staiger valve manifold in less than 7 seconds, and just over 4 seconds after the ensemble holdup time is demonstrated with a downstream FID. The analysis time of the second dimension was 160 ms, and peak widths in the second dimension range from 10-60 ms. A peak capacity of just over 300 was calculated for a separation of just over 6 s. Data from a continuous operation testing over 40 days and 20000 runs of the GC×GC columns with the NEMS resonators using a 4-component test set is presented. The GC×GC-NEMS resonator system generated second-dimension peak widths as narrow as 8 ms with no discernable peak distortion due to under-sampling from the detector.

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Applications in environmental monitoring, surveillance and patrolling typically require a network of mobile agents to collectively gain information regarding the state of a static or dynamical process evolving over a region. However, these networks of mobile agents also introduce various challenges, including intermittent observations of the dynamical process, loss of communication links due to mobility and packet drops, and the potential for malicious or faulty behavior by some of the agents. The main contribution of this paper is the development of resilient, fully-distributed, and provably correct state estimation algorithms that simultaneously account for each of the above considerations, and in turn, offer a general framework for reasoning about state estimation problems in dynamic, failure-prone and adversarial environments. Specifically, we develop a simple switched linear observer for dealing with the issue of time-varying measurement models, and resilient filtering techniques for dealing with worst-case adversarial behavior subject to time-varying communication patterns among the agents. Our approach considers both communication patterns that recur in a deterministic manner, and patterns that are induced by random packet drops. For each scenario, we identify conditions on the dynamical system, the patrols, the nominal communication network topology, and the failure models that guarantee applicability of our proposed techniques. Finally, we complement our theoretical results with detailed simulations that illustrate the efficacy of our algorithms in the presence of the technical challenges described above.

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Minimum detectable velocity (MDV) is a fundamental consideration for the design, implementation, and exploitation of ground moving-target indication (GMTI) radar imaging modes. All single-phase-center air-to-ground radars are characterized by an MDV, or a minimum radial velocity below which motion of a discrete nonstationary target is indistinguishable from the relative motion between the platform and the ground. Targets with radial velocities less than MDV are typically overwhelmed by endoclutter ground returns, and are thus not generally detectable. Targets with radial velocities greater than MDV typically produce distinct returns falling outside of the endoclutter ground returns, and are thus generally discernible using straightforward detection algorithms. This document provides a straightforward derivation of MDV for an air-to-ground single-phase-center GMTI radar operating in an arbitrary geometry.

Synthetic aperture radar (SAR) images exhibit a fundamental inverse relationship between image quality and collection range: various metrics and visual inspection clearly indicate that SAR image quality deteriorates as collection range increases. Standoff constraints typically dictate long-range imaging geometries for operational use of fielded SAR sensors. At the same time, system validation and data volume considerations typically dictate short-range imaging geometries for non-operational SAR data collections. This presents a conundrum for the developers of SAR exploitation applications: despite the fact that a sensor may be used exclusively at long ranges in operational settings, most or all of the data available for application development and testing may have been collected at short range. The lack of long-range imagery for development and testing can lead to a variety of problems, potentially including not only poor robustness to range-induced image-quality degradation, but even total failure if longer-range imagery invalidates fundamental algorithmic assumptions. We propose a method for simulating the effects of longer-range collection using shorter-range SAR images. This method incorporates the predominant contributing factors to range-induced image-quality degradation, including various signal-attenuation and aperture-decoherence effects. We present examples demonstrating our approach. © 2009 SPIE.