We develop a decision-theoretic framework for distributed Bayesian experimental design in which local agents evaluate candidate experiments using expected information gain and transmit their local design decisions to a fusion center. Unlike centralized Bayesian design, where all likelihood components and information-gain values are available to a single planner, the fusion center in the distributed setting chooses a global experiment from compressed local recommendations. We derive the Bayes-optimal fusion rule, which selects the experiment with largest conditional expected centralized information gain given the observed local design decisions. This rule is analogous in spirit to optimal fusion rules in distributed detection, but differs fundamentally because the underlying utility is expected information gain and the resulting loss is information-gain regret rather than classification error. We also establish information-loss bounds and identify conditions under which the decision-only fusion rule is asymptotically equivalent to the centralized design. Numerical experiments show that Bayes-optimal fusion closely approximates the centralized oracle, whereas majority voting can be highly suboptimal when a minority of sites carry disproportionate information.

In this article, multitarget tracking and scanning are considered in a radar system operating in the track-while-scan mode. Specifically, time allocation for radar scanning and tracking of multiple maneuvering targets under a time budget constraint is addressed, aiming to jointly optimize the performance of both tracking and scanning in a cognitive radar. We first present the details of the model for tracking and scanning and formulate the time management task as a constrained optimization problem. Subsequently, we design a constrained deep reinforcement learning (CDRL) framework to find the time allocation strategy for the problem. In the proposed CDRL framework, the parameters of the neural networks and the dual variable are learned simultaneously. The deep deterministic policy gradient (DDPG) algorithm is introduced to tackle continuous action space and its performance is compared with deep Q-learning (DQL), heuristic approaches, and an optimization-based approach. Numerical results show that the radar with the proposed CDRL framework can autonomously allocate more time to the tracking task that requires greater attention while providing time for scanning and also constraining the total time budget below the predefined threshold.

Change detection (CD) in heterogeneous remote sensing images plays a crucial role in earth observation tasks, such as disaster monitoring and destruction assessment. Recent advancements in heterogeneous CD studies have substantially enhanced the capability to detect changes, but existing methodologies frequently lack effective control mechanisms for increasing false alarms when facing different heterogeneous scenes. Consequently, even with a high detection rate for changes, the real changes co-exist with lots of false alarms, thereby reducing the reliability and practical utility of the CD results. To address this issue, inspired by the insight of adaptive thresholding for false alarm control in constant false alarm rate (CFAR) detection, we propose a copula theory-based CD framework, named FAR-Aware-Copula-CD, to control false alarm rate (FAR) in heterogeneous CD. In the proposed FAR-Aware-Copula-CD, the heterogeneous CD problem is represented as a binary hypothesis testing problem. Then, the binary hypothesis testing problem is solved by a generalized likelihood ratio test based on copula theory, which effectively characterizes change statistics based on superpixel-level dependence within various heterogeneous image pairs. Finally, the decision thresholds of the copula-based change statistics are determined so as to satisfy the FAR constraint and ensure that the final CD result approaches a prespecified false alarm rate. Our FAR-Aware-Copula-CD provides a new approach for implementing controllable false alarms in heterogeneous CD tasks. Experimental results on four real-world datasets demonstrate the effectiveness of our proposed method.

This paper extends the widely used probability hypothesis density (PHD) and cardinalized PHD (CPHD) filters to non-standard observation models (NSOMs), such as pixelized track-before-detect and superpositional sensor models. Classical (C)PHD filters are computationally attractive but are derived under the standard point-object observation model. Existing (C)PHD variants for specific NSOMs typically rely on simplified assumptions, such as independent object-generated observations, to obtain closed-form solutions. These assumptions can fail in practical scenarios, such as closely spaced or merged-observation objects, resulting in severe performance degradation. To address this issue, we adapt (C)PHD filtering to the generic observation model (GOM), where the update step directly uses a generic multi-object likelihood. The Bayesian posterior under the GOM is projected back onto the Poisson and independently and identically distributed cluster families via Kullback-Leibler divergence minimization, yielding the proposed GOM-PHD and GOM-CPHD filters. We further show that the proposed filters reduce to existing (C)PHD variants under specific model assumptions and analyze the posterior-projection error. Furthermore, we develop a fast sequential Monte Carlo implementation of the proposed filters that avoids the combinatorial explosion, reduces the number of likelihood evaluations, and includes its convergence analysis. Finally, simulation results, including one diagnostic posterior-projection analysis scenario and two NSOM tracking scenarios, show regimes in which the posterior-projection error is smaller than the error induced by a mismatched likelihood and that the proposed filters improve tracking accuracy over representative NSOM-specific baselines with lower computational cost than labeled random finite set GOM baselines.

We address the problem of target detection using spatially distributed two-channel passive radars. The transmitter is assumed to be an unknown illuminator-of-opportunity (IO), which transmits a waveform lying in a known low-dimensional subspace (e.g., OFDM). Each receiver transforms its reference and surveillance signals into the IO-subspace, to obtain cross-correlation (CC) measurements. To save bandwidth, receivers collaboratively exchange and linearly combine the CC outputs, after which only a subset of the receivers transmit to a fusion center (FC), over a multiple-access channel (MAC). The collaboration weights are designed to enhance detection performance. Simulation results are provided to illustrate the performance of the proposed framework.

Distributed detection, which fuses the preprocessed observations of the same area from local sensors, can generally improve target detection performance. For scenarios in practical applications where sensors cannot obtain the target signal-to-noise ratio (SNR) parameters in advance, non-coherent integration is mostly used for distributed detection. However, this detector is equivalent to the optimal detector only under the condition that the target SNRs of all the sensors are exactly the same. This condition is quite stringent for the observation of non-cooperative targets. This paper first compares the performance of traditional optimal detectors, the non-coherent integration (NCI) detector, and the single-sensor detector from a unified perspective based on the concept of Pareto optimality. Then, from the perspective of multi-objective optimization, the fusion rule and corresponding parameter learning method are designed. Theoretical analysis shows that the proposed non-identical SNR detection fusion rule possesses weak Pareto optimality. Simulation experiments demonstrate that the proposed method effectively achieves a trade-off between the optimal detection performance across sensors with multiple SNRs. Compared to the optimal detector in the presence of mismatch between the assumed and actual SNR of the target, the proposed method can achieve a significant improvement in detection performance. Additionally, the proposed method outperforms the NCI detector in scenarios where the SNR distributions of target observations across different sensors exhibit greater diversity.

In this paper, scanning for target detection, and multi-target tracking in a cognitive radar system are considered, and adaptive radar resource management is investigated. In particular, time management for radar scanning and tracking of multiple maneuvering targets subject to budget constraints is studied with the goal to jointly maximize the tracking and scanning performances of a cognitive radar. We tackle the constrained optimization problem of allocating the dwell time to track individual targets by employing a deep deterministic policy gradient (DDPG) based reinforcement learning approach. We propose a constrained deep reinforcement learning (CDRL) algorithm that updates the DDPG neural networks and dual variables simultaneously. Numerical results show that the radar can autonomously allocate time appropriately so as to maximize the reward function without exceeding the time constraint.

This work studies distributed multiple testing with false discovery rate (FDR) control in the presence of Byzantine attacks, where an adversary captures a fraction of the nodes and corrupts their reported p-values. We focus on two baseline attack models: an oracle model with the full knowledge of which hypotheses are true nulls, and a practical attack model that leverages the Benjamini-Hochberg (BH) procedure locally to classify which p-values follow the true null hypotheses. We provide a thorough characterization of how both attack models affect the global FDR, which in turn motivates counter-attack strategies and stronger attack models. Our extensive simulation studies confirm the theoretical results, highlight key design trade-offs under attacks and countermeasures, and provide insights into more sophisticated attacks.

The ellipsoidal extended target estimation fusion problem is challenging due to the need to consider the target extension. Current methods consider the Wasserstein barycenter, which incorporates the underlying geometry of the Gaussian distributions measure space. However, these methods do not optimize the weights for each sensor. In this paper, we propose the Wasserstein Barycentric Coordinates Fusion (WBCF) method which can adaptively select fusion weights by utilizing prior information about the target extension. While the theory of Wasserstein barycentric coordinates is well-established for discrete distributions with identical supports, the general case involving arbitrary probability distributions presents a significant challenge due to the computational complexity arising from solving a non-convex and non-concave optimization problem. In the context of Gaussian distributions, this paper derives closed-form expressions for the derivatives of the objective function. Moreover, by reformulating the problem as a bi-level optimization problem, we propose practical algorithms for WBCF with minimal computational overhead. Finally, we demonstrate the performance of WBCF in simulated extended target tracking scenarios. By utilizing the optimization method, numerical results showcase the efficiency of the proposed method in terms of estimation accuracy and computational time.

Change detection (CD) in heterogeneous remote sensing images is a practical and challenging issue for real-life emergencies. In the past decade, the heterogeneous CD problem has significantly benefited from the development of deep neural networks (DNN). However, the data-driven DNNs always perform like a black box where the lack of interpretability limits the trustworthiness and controllability of DNNs in most practical CD applications. As a strong knowledge-driven tool to measure correlation between random variables, Copula theory has been introduced into CD, yet it suffers from non-robust CD performance without manual prior selection for Copula functions. To address the above issues, we propose a knowledge-data-driven heterogeneous CD method (NN-Copula-CD) based on the Copula-guided interpretable neural network. In our NN-Copula-CD, the mathematical characteristics of Copula are designed as the losses to supervise a simple fully connected neural network to learn the correlation between bi-temporal image patches, and then the changed regions are identified via binary classification for the correlation coefficients of all image patch pairs of the bi-temporal images. We conduct in-depth experiments on three datasets with multimodal images (e.g., Optical, SAR, and NIR), where the quantitative results and visualized analysis demonstrate both the effectiveness and interpretability of the proposed NN-Copula-CD.

The problem of scalar parameter estimation in a distributed wireless sensor network (WSN), in the presence of communication failures, is considered in this work. When sensors obtain measurements and attempt to transmit their measurements to the fusion center (FC) for parameter estimation, the transmissions to the FC may be unsuccessful due to various reasons such as poor communication channels, large distance between the sensors and FC or insufficient transmit power. To overcome the degradation of estimation performance due to missing data, we consider linear inter-sensor collaboration, where sensors exchange measurements with neighboring sensors, before transmitting to the FC. We consider two objectives: 1) maximize the estimation accuracy subject to collaboration power constraints and 2) minimize the collaboration power subject to the required estimation accuracy. We consider linear estimators for the parameter inference task, and propose methods for designing the collaboration scheme (collaboration weights). The performances of the estimators and collaboration design are compared using numerical results and simulations.

The time allocation problem in multi-function cognitive radar systems focuses on the trade-off between scanning for newly emerging targets and tracking the previously detected targets. We formulate this as a multi-objective optimization problem and employ deep reinforcement learning to find Pareto-optimal solutions and compare deep deterministic policy gradient (DDPG) and soft actor-critic (SAC) algorithms. Our results demonstrate the effectiveness of both algorithms in adapting to various scenarios, with SAC showing improved stability and sample efficiency compared to DDPG. We further employ the NSGA-II algorithm to estimate an upper bound on the Pareto front of the considered problem. This work contributes to the development of more efficient and adaptive cognitive radar systems capable of balancing multiple competing objectives in dynamic environments.

Cooperative and non-cooperative localization frequently arise together in wireless sensor networks, particularly when sensor positions are uncertain and targets are unable to communicate with the network. While joint processing can eliminate the delay in target estimation found in sequential approaches, it introduces complex variable coupling, posing challenges in both modeling and optimization. This paper presents a joint modeling approach that formulates cooperative and non-cooperative localization as a single optimization problem. To address the resulting coupling, we introduce auxiliary variables that enable structural decoupling and distributed computation. Building on this formulation, we develop the Scaled Proximal Alternating Direction Method of Multipliers for Joint Cooperative and Non-Cooperative Localization (SP-ADMM-JCNL). Leveraging the problem's structured design, we provide theoretical guarantees that the algorithm generates a sequence converging globally to the Karush-Kuhn-Tucker (KKT) point of the reformulated problem and further to a critical point of the original non-convex objective function, with a sublinear rate of O(1/T). Experiments on both synthetic and benchmark datasets demonstrate that SP-ADMM-JCNL achieves accurate and reliable localization performance.

In this work, we present distributed clustering algorithms that can handle large-scale data across multiple machines in the presence of faulty machines. These faulty machines can either be straggling machines that fail to respond within a stipulated time or Byzantines that send arbitrary responses. We propose redundant data assignment schemes that enable us to obtain clustering solutions based on the entire dataset, even when some machines are stragglers or adversarial in nature. Our proposed robust clustering algorithms generate a constant factor approximate solution in the presence of stragglers or Byzantines. We also provide various constructions of the data assignment scheme that provide resilience against a large fraction of faulty machines. Simulation results show that the distributed algorithms based on the proposed assignment scheme provide good-quality solutions for a variety of clustering problems.

Classic direct localization techniques have been shown to offer better localization performance and robustness in low signal-to-noise ratio (SNR) conditions. However, they require the transmission of complete baseband signals to the fusion center (FC), resulting in significant data transmission and storage burdens. To address the high data communication load in direct localization within wireless sensor networks, we propose a one-bit direct localization method. In particular, we account for the potential realistic channel effects between sensors and the FC, modeling them as Rayleigh fading channels incorporated into the position inference process. Subsequently, at the FC, we propose two one-bit direct localization methods corresponding to coherent and noncoherent reception decoding strategies. Since the localization process involves non-convex optimization of high-dimensional coupled parameters, we present an efficient solution based on the Majorization-Minimization (MM) method, which transforms the position estimation problem into a low-dimensional iterative search. We derive the Cram & eacute;r-Rao lower bound (CRLB) for the proposed methods under both decoding strategies and provide a quantizer design aimed at optimizing the system's localization performance. Due to the fading channel's impact, the constructed quantization threshold optimization problem is a combination of highly nonlinear and non-convex functions, making it difficult to solve directly. We further provide a computationally feasible solution based on the modified Barzilai-Borwein-based gradient descent (MBB-GD) method, which is a polynomial time algorithm. Numerical simulations validate the effectiveness of the proposed method in reducing the network communication load, mitigating the impact of fading channels, and ensuring the localization performance.

This survey paper examines recent advancements in low-resolution signal processing, emphasizing quantized compressed sensing. Rising costs and power demands of high-sampling-rate data acquisition drive the interest in quantized signal processing, particularly in wireless communication systems and Internet of Things sensor networks, as 6G aims to integrate sensing and communication within cost-effective hardware. Motivated by this urgency, this paper covers novel signal processing algorithms designed to address practical challenges arising from quantization and modulo operations, as well as their impact on system performance. We begin by introducing the framework of one-bit compressed sensing and discuss relevant theories and algorithms. We explore the application of quantized compressed sensing algorithms to sensor networks, radar, cognitive radio, and wireless channel estimation. We highlight how generic methods can be tailored to an application using specific examples from wireless channel estimation. Additionally, we review other low-resolution techniques beyond one-bit compressed sensing along with their applications. We also provide a brief overview of the emerging concept of unlimited sampling. While this paper does not aim to be exhaustive, it selectively highlights results to inspire readers to appreciate the diverse algorithmic tools (convex optimization, greedy methods, and Bayesian approaches) and sampling techniques (task-based quantization and unlimited sampling).

In multisensor state estimation, existing posterior Cram & eacute;r-Rao lower bounds (PCRLBs) are generally derived under the measurement independence assumption. When correlations among measurements are unknown, the true PCRLB cannot be computed due to the inability to compute the likelihood function corresponding to the local measurements. Motivated by the random-variables-based arithmetic average (RV-AA) fusion rule, which combines the local variables with unknown correlations as a linear mixture variable (LMV), an LMV-based approximation to the performance lower bound (LMV-A-LB) on RV-AA is derived in this article to provide a more refined performance indicator for it. This approximation uses the posterior obtained from the LMV along with the Bayes' rule to estimate the true but unavailable likelihood function. We show that the LMV-A-LB generally lacks a closed-form solution, so it is approximated using sequential Monte Carlo approaches. Furthermore, by limiting the system model to the commonly used additive Gaussian noise case, we compute the exact expression of the derived bound with the aid of the Kalman filters. Numerical simulation experiments demonstrate that the LMV-A-LB obtains a tighter performance lower bound for RV-AA fusion by comparing with existing bounds.

Deep reinforcement learning has been extensively studied in decision-making processes and has demonstrated superior performance over conventional approaches in various fields, including radar resource management (RRM). However, a notable limitation of neural networks is their ``black box" nature and recent research work has increasingly focused on explainable AI (XAI) techniques to describe the rationale behind neural network decisions. One promising XAI method is local interpretable model-agnostic explanations (LIME). However, the sampling process in LIME ignores the correlations between features. In this paper, we propose a modified LIME approach that integrates deep learning (DL) into the sampling process, which we refer to as DL-LIME. We employ DL-LIME within deep reinforcement learning for radar resource management. Numerical results show that DL-LIME outperforms conventional LIME in terms of both fidelity and task performance, demonstrating superior performance with both metrics. DL-LIME also provides insights on which factors are more important in decision making for radar resource management.

In this paper, an effective collaborative trajectory optimization (CTO) strategy is proposed for multitarget tracking in airborne radar networks with missing data. Missing data may occur during data exchange between radar nodes and a fusion center (FC) due to unreliability of communication channels. The CTO strategy aims to enhance the overall multi-target tracking performance by collaboratively optimizing the trajectories of airborne radars and the FC. In this paper, we derive the posterior Cram & eacute;r-Rao lower bound (PCRLB) with missing data to evaluate the target tracking performance. On this basis, to maximize the target tracking performance while considering dynamics, collision avoidance, and communication distance constraints, we formulate the CTO optimization problem. The formulated problem is non-convex and internally coupled, which is challenging to solve directly. We decompose the CTO problem into two subproblems and devise an alternating optimization method. Specifically, approximation, and successive convex approximation are applied to make the subproblems solvable. Then, the two subproblems are solved alternately to realize the collaborative trajectory optimization of radars and the FC. Simulation results demonstrate that the proposed CTO strategy achieves better target tracking performance as compared with other benchmark strategies.