arXiv subjects

Daniel J. Stilwell

Publications and source records attributed to Daniel J. Stilwell.

17 recordsLinked to original sources

arXiv2025

Robust Sensor Placement for Poisson Arrivals with False Alarm Aware Spatiotemporal Sensing

This paper studies sensor placement when detection performance varies stochastically due to environmental factors over space and time and false alarms are present, but a filter is used to attenuate the effect. We introduce a unified model that couples detection and false alarms through an availability function, which captures how false alarms reduce effective sensing and filtering responses to the disturbance. Building on this model, we give a sufficient condition under which filtering improves detection. In addition, we derive a coverage-based lower bound on the void probability. Furthermore, we prove robustness guarantees showing that performance remains stable when detection probabilities are learned from limited data. We validate the approach with numerical studies using AIS vessel-traffic data and synthetic maritime scenarios. Together, these results provide theory and practical guidance for deploying sensors in dynamic, uncertain environments.

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arXiv2025

Decentralized Gaussian Process Classification and an Application in Subsea Robotics

Teams of cooperating autonomous underwater vehicles (AUVs) rely on acoustic communication for coordination, yet this communication medium is constrained by limited range, multi-path effects, and low bandwidth. One way to address the uncertainty associated with acoustic communication is to learn the communication environment in real-time. We address the challenge of a team of robots building a map of the probability of communication success from one location to another in real-time. This is a decentralized classification problem -- communication events are either successful or unsuccessful -- where AUVs share a subset of their communication measurements to build the map. The main contribution of this work is a rigorously derived data sharing policy that selects measurements to be shared among AUVs. We experimentally validate our proposed sharing policy using real acoustic communication data collected from teams of Virginia Tech 690 AUVs, demonstrating its effectiveness in underwater environments.

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arXiv2025

Near-optimal Sensor Placement for Detecting Stochastic Target Trajectories in Barrier Coverage Systems

This paper addresses the deployment of sensors for a 2-D barrier coverage system. The challenge is to compute near-optimal sensor placements for detecting targets whose trajectories follow a log-Gaussian Cox line process. We explore sensor deployment in a transformed space, where linear target trajectories are represented as points. While this space simplifies handling the line process, the spatial functions representing sensor performance (i.e. probability of detection) become less intuitive. To illustrate our approach, we focus on positioning sensors of the barrier coverage system on the seafloor to detect passing ships. Through numerical experiments using historical ship data, we compute sensor locations that maximize the probability all ship passing over the barrier coverage system are detected.

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arXiv2025

Improved Approximation of Sensor Network Performance for Seabed Acoustic Sensors

Sensor locations to detect Poisson-distributed targets, such as seabed sensors that detect shipping traffic, can be selected to maximize the so-called void probability, which is the probability of detecting all targets. Because evaluation of void probability is computationally expensive, we propose a new approximation of void probability that can greatly reduce the computational cost of selecting locations for a network of sensors. We build upon prior work that approximates void probability using Jensen's inequality. Our new approach better accommodates uncertainty in the (Poisson) target model and yields a sharper error bound. The proposed method is evaluated using historical ship traffic data from the Hampton Roads Channel, Virginia, demonstrating a reduction in the approximation error compared to the previous approach. The results validate the effectiveness of the improved approximation for maritime surveillance applications.

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arXiv2024

Efficient Feature Mapping Using a Collaborative Team of AUVs

We present the results of experiments performed using a team of small autonomous underwater vehicles (AUVs) to determine the location of an isobath. The primary contributions of this work are (1) the development of a novel objective function for level set estimation that utilizes a rigorous assessment of uncertainty, and (2) a description of the practical challenges and corresponding solutions needed to implement our approach in the field using a team of AUVs. We combine path planning techniques and an approach to decentralization from prior work that yields theoretical performance guarantees. Experimentation with a team of AUVs provides empirical evidence that the desirable performance guarantees can be preserved in practice even in the presence of limitations that commonly arise in underwater robotics, including slow and intermittent acoustic communications and limited computational resources.

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arXiv2024

Prediction of Acoustic Communication Performance for AUVs using Gaussian Process Classification

Cooperating autonomous underwater vehicles (AUVs) often rely on acoustic communication to coordinate their actions effectively. However, the reliability of underwater acoustic communication decreases as the communication range between vehicles increases. Consequently, teams of cooperating AUVs typically make conservative assumptions about the maximum range at which they can communicate reliably. To address this limitation, we propose a novel approach that involves learning a map representing the probability of successful communication based on the locations of the transmitting and receiving vehicles. This probabilistic communication map accounts for factors such as the range between vehicles, environmental noise, and multi-path effects at a given location. In pursuit of this goal, we investigate the application of Gaussian process binary classification to generate the desired communication map. We specialize existing results to this specific binary classification problem and explore methods to incorporate uncertainty in vehicle location into the mapping process. Furthermore, we compare the prediction performance of the probability communication map generated using binary classification with that of a signal-to-noise ratio (SNR) communication map generated using Gaussian process regression. Our approach is experimentally validated using communication and navigation data collected during trials with a pair of Virginia Tech 690 AUVs.

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arXiv2023

Use of a low-cost forward-looking sonar for collision avoidance in small AUVs, analysis and experimental results

In this paper, we seek to evaluate the effectiveness of a novel forward-looking sonar system with a limited number of beams for collision avoidance for small autonomous underwater vehicles (AUVs). We present a collision avoidance strategy specifically designed for a novel forward-looking sonar system based on posterior expected loss, explicitly coupling the obstacle detection, collision avoidance, and planning. We demonstrate the strategy with field trials using the 690 AUV, built by the Center for Marine Autonomy and Robotics at Virginia Tech, and verify the forward-looking sonar system using a prototype sonar with nine beams. Post-processed simulations are performed while changing parameters in the sensitivity of the system to demonstrate the trade-off between the detection and false alarm rates.

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arXiv2023

Toward optimal placement of spatial sensors

This paper addresses the challenges of optimally placing a finite number of sensors to detect Poisson-distributed targets in a bounded domain. We seek to rigorously account for uncertainty in the target arrival model throughout the problem. Sensor locations are selected to maximize the probability that no targets are missed. While this objective function is well-suited to applications where failure to detect targets is highly undesirable, it does not lead to a computationally efficient optimization problem. We propose an approximation of the objective function that is non-negative, submodular, and monotone and for which greedy selection of sensor locations works well. We also characterize the gap between the desired objective function and our approximation. For numerical illustrations, we consider the case of the detection of ship traffic using sensors mounted on the seafloor.

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arXiv2022

Non-Submodular Maximization via the Greedy Algorithm and the Effects of Limited Information in Multi-Agent Execution

We provide theoretical bounds on the worst case performance of the greedy algorithm in seeking to maximize a normalized, monotone, but not necessarily submodular objective function under a simple partition matroid constraint. We also provide worst case bounds on the performance of the greedy algorithm in the case that limited information is available at each planning step. We specifically consider limited information as a result of unreliable communications during distributed execution of the greedy algorithm. We utilize notions of curvature for normalized, monotone set functions to develop the bounds provided in this work. To demonstrate the value of the bounds provided in this work, we analyze a variant of the benefit of search objective function and show, using real-world data collected by an autonomous underwater vehicle, that theoretical approximation guarantees are achieved despite non-submodularity of the objective function.

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arXiv2022

Unscented Kalman Filtering on Manifolds for AUV Navigation -- Experimental Results

In this work, we present an aided inertial navigation system for an autonomous underwater vehicle (AUV) using an unscented Kalman filter on manifolds (UKF-M). The inertial navigation estimate is aided by a Doppler velocity log (DVL), depth sensor, acoustic range and, while on the surface, GPS. The sensor model for each navigation sensor on the AUV is explicitly described, including compensation for lever arm offsets between the IMU and each sensor. Additionally, an outlier rejection step is proposed to reject measurement outliers that would degrade navigation performance. The UKF-M for AUV navigation is implemented for real-time navigation on the Virginia Tech 690 AUV and validated in the field. Finally, by post-processing the navigation sensor data, we show experimentally that the UKF-M is able to converge to the correct heading in the presence of arbitrarily large initial heading error.

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arXiv2022

Evaluating the Benefit of Using Multiple Low-Cost Forward-Looking Sonar Beams for Collision Avoidance in Small AUVs

We seek to rigorously evaluate the benefit of using a few beams rather than a single beam for a low-cost obstacle avoidance sonar for small AUVs. For a small low-cost AUV, the complexity, cost, and volume required for a multi-beam forward looking sonar are prohibitive. In contrast, a single-beam system is relatively easy to integrate into a small AUV, but does not provide the performance of a multi-beam solution. To better understand this trade-off, we seek to rigorously quantify the improvement with respect to obstacle avoidance performance of adding just a few beams to a single-beam forward looking sonar relative to the performance of the single-beam system. Our work fundamentally supports the goal of using small low-cost AUV systems in cluttered and unstructured environments. Specifically, we investigate the benefit of incorporating a port and starboard beam to a single-beam sonar system for collision avoidance. A methodology for collision avoidance is developed to obtain a fair comparison between a single-beam and multi-beam system, explicitly incorporating the geometry of the beam patterns from forward-looking sonars with large beam angles, and simulated using a high-fidelity representation of acoustic signal propagation.

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arXiv2022

Development of a Simulation Environment for Evaluation of a Forward Looking Sonar System for Small AUVs

This paper describes a high-fidelity sonar model and a simulation environment that implements the model. The model and simulation environment have been developed to aid in the design of a forward looking sonar for autonomous underwater vehicles (AUVs). The simulator achieves real-time visualization through ray tracing and approximation. The simulator facilitates the assessment of sonar design choices, such as beam pattern and beam location, and assessment of obstacle detection and tracking algorithms. An obstacle detection model is proposed for which the null hypothesis is estimated from the environmental model. Sonar data is generated from the simulator and compared to the expected results from the detection model demonstrating the benefits and limitations of the proposed approach.

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arXiv2022

Experiments in Underwater Feature Tracking with Performance Guarantees Using a Small AUV

We present the results of experiments performed using a small autonomous underwater vehicle to determine the location of an isobath within a bounded area. The primary contribution of this work is to implement and integrate several recent developments real-time planning for environmental mapping, and to demonstrate their utility in a challenging practical example. We model the bathymetry within the operational area using a Gaussian process and propose a reward function that represents the task of mapping a desired isobath. As is common in applications where plans must be continually updated based on real-time sensor measurements, we adopt a receding horizon framework where the vehicle continually computes near-optimal paths. The sequence of paths does not, in general, inherit the optimality properties of each individual path. Our real-time planning implementation incorporates recent results that lead to performance guarantees for receding-horizon planning.

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arXiv2022

Fully Decentralized, Scalable Gaussian Processes for Multi-Agent Federated Learning

In this paper, we propose decentralized and scalable algorithms for Gaussian process (GP) training and prediction in multi-agent systems. To decentralize the implementation of GP training optimization algorithms, we employ the alternating direction method of multipliers (ADMM). A closed-form solution of the decentralized proximal ADMM is provided for the case of GP hyper-parameter training with maximum likelihood estimation. Multiple aggregation techniques for GP prediction are decentralized with the use of iterative and consensus methods. In addition, we propose a covariance-based nearest neighbor selection strategy that enables a subset of agents to perform predictions. The efficacy of the proposed methods is illustrated with numerical experiments on synthetic and real data.

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arXiv2021

Wasserstein-Splitting Gaussian Process Regression for Heterogeneous Online Bayesian Inference

Gaussian processes (GPs) are a well-known nonparametric Bayesian inference technique, but they suffer from scalability problems for large sample sizes, and their performance can degrade for non-stationary or spatially heterogeneous data. In this work, we seek to overcome these issues through (i) employing variational free energy approximations of GPs operating in tandem with online expectation propagation steps; and (ii) introducing a local splitting step which instantiates a new GP whenever the posterior distribution changes significantly as quantified by the Wasserstein metric over posterior distributions. Over time, then, this yields an ensemble of sparse GPs which may be updated incrementally, and adapts to locality, heterogeneity, and non-stationarity in training data.

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arXiv2021

Strictly Decentralized Adaptive Estimation of External Fields using Reproducing Kernels

This paper describes an adaptive method in continuous time for the estimation of external fields by a team of $N$ agents. The agents $i$ each explore subdomains $Ω^i$ of a bounded subset of interest $Ω\subset X := \mathbb{R}^d$. Ideal adaptive estimates $\hat{g}^i_t$ are derived for each agent from a distributed parameter system (DPS) that takes values in the scalar-valued reproducing kernel Hilbert space $H_X$ of functions over $X$. Approximations of the evolution of the ideal local estimate $\hat{g}^i_t$ of agent $i$ is constructed solely using observations made by agent $i$ on a fine time scale. Since the local estimates on the fine time scale are constructed independently for each agent, we say that the method is strictly decentralized. On a coarse time scale, the individual local estimates $\hat{g}^i_t$ are fused via the expression $\hat{g}_t:=\sum_{i=1}^NΨ^i \hat{g}^i_t$ that uses a partition of unity $\{Ψ^i\}_{1\leq i\leq N}$ subordinate to the cover $\{Ω^i\}_{i=1,\ldots,N}$ of $Ω$. Realizable algorithms are obtained by constructing finite dimensional approximations of the DPS in terms of scattered bases defined by each agent from samples along their trajectories. Rates of convergence of the error in the finite dimensional approximations are derived in terms of the fill distance of the samples that define the scattered centers in each subdomain. The qualitative performance of the convergence rates for the decentralized estimation method is illustrated via numerical simulations.

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arXiv2014

Stability and disturbance attenuation for a switched Markov jump linear system

We address a class of Markov jump linear systems that are characterized by the underlying Markov process being time-inhomogeneous with a priori unknown transition probabilities. Necessary and sufficient conditions for uniform stochastic stability and uniform stochastic disturbance attenuation are reported. In both cases, conditions are expressed as a set of finite-dimensional linear matrix inequalities that can be solved efficiently.

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