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.

This paper introduces a representative-based approach for distributed learning that transforms multiple raw data points into a virtual representation. Unlike traditional distributed learning methods such as Federated Learning, which do not offer human interpretability, our method makes complex machine learning processes accessible and comprehensible. It achieves this by condensing extensive datasets into digestible formats, thus fostering intuitive human-machine interactions. Additionally, this approach maintains privacy and communication efficiency, and it matches the training performance of models using raw data. Simulation results show that our approach is competitive with or outperforms traditional Federated Learning in accuracy and convergence, especially in scenarios with complex models and a higher number of clients. This framework marks a step forward in integrating human intuition with machine intelligence, which potentially enhances human-machine learning interfaces and collaborative efforts.

This article considers the Wasserstein barycentric coordinates problem for Gaussian distributions which is the inverse problem of the Wasserstein barycenter problem. These coordinates take into account the underlying geometry of the measure space of Gaussian distributions and are thus meaningful for applications such as diffusion analysis and distributed information fusion. When the probability supports are discrete and identical, the theory of Wasserstein barycentric coordinates is well developed. However, for general probability distributions, the computation of Wasserstein barycentric coordinates is intractable since the technical hurdles involve solving a non-convex and non-concave optimization problem. For Gaussian distributions, we derive the closed-form expression of the derivatives for the objective function and propose a projected gradient descent method to solve the problem. Finally, we illustrate its application in diffusion tensor image (DTI) denoising including simulated DTI with different noise levels and DTI of the human brain.

Traditional centralized direct localization methods require the transmission of the complete baseband signal to the fusion center (FC) for target localization. Due to the limited communication bandwidth as well as energy required in transmission, this centralized framework is not suitable for largescale sensor networks. This paper proposes an information-driven decentralized direct localization framework. Firstly, a maximum-likelihood position estimator, based on the Gauss-Newton method, is derived. Then, a decentralized implementation framework is constructed. At its core, there is no dedicated FC while the sensors transmit information to their neighboring nodes only through single hops, achieving target localization through iterative processes based on the concept of consensus. Simulation results confirm the stability and robustness of the proposed method in different scenarios.

This paper addresses the localization challenge in cooperative multi-agent wireless sensor networks, specifically focusing on range-based localization. To enhance robustness against outliers in range measurements, we employ the Huber function, leading to the formulation of a robust yet nonconvex optimization problem with coupled agent variables. Confronted with this nonconvex optimization challenge, particularly in largescale networks, we reformulate the problem using Lagrange duality and conjugate theory. This restructuring yields subproblems characterized by smooth strong convexity for dual variables and a simplified form for primal variables, thereby facilitating an efficient solution. Building upon this reformulation, we introduce a novel distributed primal-dual algorithm that employs coordinate descent and proximal minimization techniques within an iterative framework. This approach furnishes closed-form solutions for both primal and dual variables. Theoretically, our method ensures not only the convergence of the sequence of objective function values but also, by leveraging the KurdykaŁojasiewicz property, we establish the guaranteed global convergence of the location estimates sequence to a critical point of the original objective function. Notably, our proposed approach exhibits lower computational complexity, communication cost, and storage space compared to existing methods. Numerical experiments underscore the superiority of the proposed method in terms of robustness and localization accuracy when compared to the other methods in the literature.

In this work, we consider a binary hypothesis testing problem involving human decision-makers. Due to the nature of human behavior, human decision-makers observe the phenomenon of interest sequentially up to a random length of time. The humans use a belief model to accumulate the log-likelihood ratios until they cease observing the phenomenon. The belief model is used to characterize the perception of the human decision-maker towards observations at different instants of time, i.e., some decision-makers may assign greater importance to observations that were observed earlier, rather than later and vice-versa. We further consider the performance of a group of humans using a global decision-maker that fuses human decisions using the Chair-Varshney rule. When the number of observations that were used by the humans to arrive at their respective decisions are available to the fusion center (FC), the weights in the Chair-Varshney rule are modified to include this information in the decision fusion rule. Numerical and simulation results are presented to corroborate and validate theoretical results.

Gibbs sampling is one of the most popular Markov chain Monte Carlo algorithms because of its simplicity, scalability, and wide applicability within many fields of statistics, science, and engineering. In the labeled random finite sets literature, Gibbs sampling procedures have recently been applied to efficiently truncate the single-sensor and multi-sensor $\delta$-generalized labeled multi-Bernoulli posterior density as well as the multi-sensor adaptive labeled multi-Bernoulli birth distribution. However, only a limited discussion has been provided regarding key Gibbs sampler architecture details including the Markov chain Monte Carlo sample generation technique and early termination criteria. This paper begins with a brief background on Markov chain Monte Carlo methods and a review of the Gibbs sampler implementations proposed for labeled random finite sets filters. Next, we propose a short chain, multi-simulation sample generation technique that is well suited for these applications and enables a parallel processing implementation. Additionally, we present two heuristic early termination criteria that achieve similar sampling performance with substantially fewer Markov chain observations. Finally, the benefits of the proposed Gibbs samplers are demonstrated via two Monte Carlo simulations.

In this paper, we present an efficient methodology to design precoders for distributed detection of unknown high dimensional signals. We consider a wireless sensor network, where several distributed sensors collaborate to perform binary hypothesis testing based on observations of an unknown high dimensional signal corrupted by noise. The sensors collect data over both temporal and spatial domains. Due to network resource constraints, each sensor performs a linear compression (through precoding) of the observed high dimensional signal at each time instant and forwards the compressed signal to the fusion center (FC). The FC then employs the generalized likelihood ratio test (GLRT) to make a decision on the presence or absence of the signal. We propose online linear precoding/compression strategies for such sensors that collect data over spatio-temporal domain, so that the detection performance at the FC is maximized under certain network resource constraints. Through the measure of non-centrality parameter and receiver operating characteristics (ROC), we show that our proposed precoder design achieves very good detection performance.

The multi-dimensional assignment problem, and by extension the problem of finding the T-best (i.e., the T most likely) multi-sensor assignments, represent the main challenges of centralized and especially distributed multi-sensor tracking. In this paper, we propose a distributed multi-target tracking filter based on the δ-Generalized Labeled Multi-Bernoulli (δ-GLMB) family of labeled random finite set densities. Consensus is reached for high-scoring multi-sensor assignments jointly across the network by employing the cross-entropy method in conjunction with average consensus. This ensures that multi-sensor information is jointly used to select high-scoring multi-assignments without exchanging the measurements across the network and without exploring all possible single-target multi-assignments. In contrast, tracking algorithms that rely on posterior fusion, i.e., merging local posteriors of neighboring nodes until convergence, are suboptimal due to the use of only local information to select the T-best local assignments in the construction of local posteriors. Numerical simulations showcase this performance improvement of the proposed method with respect to a posterior-fusion δ-GLMB filter.

This paper proposes an energy-efficient counting rule for distributed detection by ordering sensor transmissions in wireless sensor networks. In the counting rule-based detection in an N-sensor network, the local sensors transmit binary decisions to the fusion center, where the number of all N local-sensor detections are counted and compared to a threshold. In the ordering scheme, sensors transmit their unquantized statistics to the fusion center in a sequential manner; highly informative sensors enjoy higher priority for transmission. When sufficient evidence is collected at the fusion center for decision making, the transmissions from the sensors are stopped. The ordering scheme achieves the same error probability as the optimum unconstrained energy approach (which requires observations from all the N sensors) with far fewer sensor transmissions. The scheme proposed in this paper improves the energy efficiency of the counting rule detector by ordering the sensor transmissions: each sensor transmits at a time inversely proportional to a function of its observation. The resulting scheme combines the advantages offered by the counting rule (efficient utilization of the network's communication bandwidth, since the local decisions are transmitted in binary form to the fusion center) and ordering sensor transmissions (bandwidth efficiency, since the fusion center need not wait for all the N sensors to transmit their local decisions), thereby leading to significant energy savings. As a concrete example, the problem of target detection in large-scale wireless sensor networks is considered. Under certain conditions the ordering-based counting rule scheme achieves the same detection performance as that of the original counting rule detector with fewer than N/2 sensor transmissions; in some cases, the savings in transmission approaches (N-1).

Allowing humans to act as soft sensors is increasingly becoming an attractive solution to enhance decision making performance when the available physical (hard) sensors are limited. While the fusion problem with hard data has a rich history, fusion of hard and soft data requires further understanding due to human related factors associated with human sensor data. In this work, we investigate how the presence of human sensors can be modeled in the statistical signal processing framework and the factors that need to be taken into account when integrating soft human sensor data with hard data in a signal detection framework. We consider two cases. In the first case, both types of sensors are assumed to make threshold based individual decisions using identical observations. While physical sensors use a fixed threshold, the thresholds used by human sensors are assumed to be random variables. With a given distribution for the random thresholds used at the human sensors, by properly designing the thresholds at the physical sensors, an enhanced detection performance can be observed in the integrated system compared to performing fusion with only physical sensors. In the second case, we evaluate the fusion performance when human sensors possess some side information regarding the phenomenon in addition to the common observations available at the two types of sensors.

This paper presents a novel parallel platform, C-Storm (Copula-based Storm), for the computationally complex problem of fusion of heterogeneous data streams for inference. C-Storm is designed by marrying copula-based dependence modeling for highly accurate inference and a highly-regarded parallel computing platform Storm for fast stream data processing. C-Storm has the following desirable features: 1) C-Storm offers fast inference responses. 2) C-Storm provides high inference accuracies. 3) C-Storm is a general-purpose inference platform that can support data fusion applications. 4) C-Storm is easy to use and its users do not need to know deep knowledge of Storm or copula theory. We implemented C-Storm based on Apache Storm 1.0.2 and conducted extensive experiments using a typical data fusion application. Experimental results show that C-Storm offers a significant 4.7× speedup over a commonly used sequential baseline and higher degree of parallelism leads to better performance.

This paper considers the decentralized fusion problem involving local sensor detection as well as the fusion of decisions transmitted over non-ideal transmission channels in a wireless sensor network. Prime emphasis is given to the enhancement of several fusion rules using a recently developed stochastic resonance methodology applied at the local sensors. Further, it is shown that the optimal form of the stochastic resonance probability mass density for the decentralized sensor fusion problem retains the same form as that previously developed for the single sensor case.

In this paper, we propose a new maximumlikelihood (ML) target location estimator which uses quantized sensor data and wireless channel statistics in a wireless sensor network. The novelty of our approach comes from the fact that imperfect channel statistics between wireless sensors and the fusion center are incorporated in the localization algorithm. We call this approach “channel-aware target localization”. Furthermore, we derive the Cramer-Rao lower bound as a performance bound for our channel-aware ML estimator. Simulation results are presented to show that the performance of the channel-aware ML location estimator is quite close to its theoretical performance bound even with relatively small number of sensors and it has superior performance compared to that of the channel-unaware ML estimator.

This paper presents a new framework for distributed target detection in wireless sensor networks (WSNs). In our previous work, for multiple networked sensors collaboratively detecting the presence or absence of a target in the sensor field, every sensor uses an identical threshold for local decision-making. In this paper, we propose a framework where the sensors in the network collaboratively decide and select non-identical thresholds to improve network-wide detection performance in a dynamic manner. This threshold selection scheme is based on a new statistical metric called False Discovery Rate (FDR). Assuming a signal attenuation model, where the received signal power decays as the distance from the target increases, various performance indices like system level probability of detection and probability of false alarm are studied. Analytical and simulation results are provided for system level probability of false alarm and probability of detection. Performance comparison between the proposed approach and the classical identical local sensor threshold approach is provided to demonstrate the effectiveness of this scheme.

A distributed detection method is developed for the detection of a nuclear radioactive source using a small number of radiation counters. Local one bit decisions are made at each sensor over a period of time and a fusion center makes the global decision. A novel test for the fusion of correlated decisions is derived using the theory of copulas and optimal sensor thresholds are obtained using the Normal copula function. The performance of the derived fusion rule is compared with that of the Chair-Varshney rule. An increase in detection performance is observed. A method to estimate the correlation between the sensor observations using only the vector of sensor decisions is also proposed.

Hyperspectral imaging is becoming increasingly important in a variety of applications. These images contain a large number of contiguous bands to provide information at a fine spectral resolution and, therefore, cannot be displayed directly using an RGB color display. There has been some recent work on the problem of fusing hyperspectral images to three-band images for color display purposes. In this paper, we evaluate the performance of our recently proposed approach based on independent component analysis, correlation coefficient and mutual information (ICA- CCMI) to fuse the information from a large number of bands to three images suitable for color display. Depending on whether the reference images are available or not, several image quality metrics such as entropy and edge correlation have been proposed and employed to evaluate the fusion performance via three widely used hyperspectral image datasets.

Stochastic-resonance (SR), a nonlinear physical phenomenon in which the performance of some nonlinear systems can be enhanced by adding suitable noise, has been observed and applied in many areas. However, it has not been shown whether or not this phenomenon plays a role in distributed detection. It seems counterintuitive that adding additional noise to the received decisions at the fusion center can improve detection performance. However, in this paper, we demonstrate the existence of the SR phenomenon in decision fusion by examples. An explanation for its existence is provided

This paper considers the problem tracking a moving target in a multisensor environment using distributed particle filters (DPFs). Particle filters have a great potential for solving highly nonlinear and non-Gaussian estimation problems, in which the traditional Kalman filter (KF) and extended Kalman filter (EKF) generally fail. How ever, in a sensor network, the implementation of distributed particle filters requires huge communications between local sensor nodes and the fusion center. To make the DPF approach feasible for real time processing and to reduce communication requirements, we approximate a posteriori distribution obtained from the local particle filters by a Gaussian mixture model (GMM). We propose a modified EM algorithm to estimate the parameters of GMMs obtained locally. These parameters are transmitted to the fusion center where the best linear unbiased estimator (BLUE) is used for fusion. Simulation results are presented to illustrate the performance of the proposed algorithm

Busy tone multiple access protocols have been used in multihop networks to reduce the effect of the hidden terminal problem. Due to complexity, the performance of these protocols for large networks has not been analyzed. In this paper, using a Markov chain model and an approximation, we are able to analyze and evaluate the throughput performance of the non-persistent CSMA protocol, the conservative busy tone multiple access (C-BTMA) protocol and the ideal destination-based busy tone multiple access (ID-BTMA) protocol for large networks. The throughput comparison of the protocols is given. The results show that in a large multihop network, the BTMA protocols have a better performance than the non-persistent CSMA protocol and the ID-BTMA protocol has a better performance than the C-BTMA protocol at light channel loads.

Busy tone multiple access protocols have been used in multihop networks to reduce the effect of the hidden terminal problem. This paper demonstrates another approach to reduce the effect of the hidden terminal problem namely the use of multiple channel schemes. A protocol that uses both the busy tone and the multiple channel techniques achieves the best performance. Using a Markov chain model and an approximation, the throughput performance of the multiple channel non-persistent CSMA protocol and the multiple channel conservative BTMA protocol in a large network is evaluated and compared. The results show that the multichannel CSMA and BTMA schemes exhibit a better performance over their single channel counterparts in a multihop network.