Daniel J. Stilwell

George P. Kontoudis, Daniel J. Stilwell

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.

Yifei Gao, Harun Yetkin, McMahon James et al.

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.

Mingyu Kim, Daniel Stilwell, Jorge Jimenez

This paper presents a framework for classifying and detecting spatial commission outliers in maritime environments using seabed acoustic sensor networks and log Gaussian Cox processes (LGCPs). By modeling target arrivals as a mixture of normal and outlier processes, we estimate the probability that a newly observed event is an outlier. We propose a second-order approximation of this probability that incorporates both the mean and variance of the normal intensity function, providing improved classification accuracy compared to mean-only approaches. We analytically show that our method yields a tighter bound to the true probability using Jensen's inequality. To enhance detection, we integrate a real-time, near-optimal sensor placement strategy that dynamically adjusts sensor locations based on the evolving outlier intensity. The proposed framework is validated using real ship traffic data near Norfolk, Virginia, where numerical results demonstrate the effectiveness of our approach in improving both classification performance and outlier detection through sensor deployment.

Michael E. Kepler, Alec Koppel, Amrit Singh Bedi et al.

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.

Harun Yetkin, Collin Lutz, Daniel Stilwell

We address the problem where a mobile search agent seeks to find an unknown number of stationary objects distributed in a bounded search domain, and the search mission is subject to time/distance constraint. Our work accounts for false positives, false negatives and environmental uncertainty. We consider the case that the performance of a search sensor is dependent on the environment (e.g., clutter density), and therefore sensor performance is better in some locations than in others. We specifically consider applications where environmental information can be acquired either by a separate vehicle or by the same vehicle that performs the search task. Our main contribution in this study is to formally derive a decision-theoretic cost function to compute the locations where the environmental information should be acquired. For the cases where computing the optimal locations to sample the environment is computationally expensive, we offer an approximation approach that yields provable near-optimal paths. We show that our decision-theoretic cost function outperforms the information-maximization approach, which is often employed in similar applications.

Collin C. Lutz, Daniel J. Stilwell

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.