Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

Decision Fusion for Large-Scale Sensor Networks with Nonideal Channels

Since there has been an increasing interest in the areas of Internet of Things (IoT) and artificial intelligence that often deals with a large number of sensors, this chapter investigates the decision fusion problem for large-scale sensor networks. Due to unavoidable transmission channel interference, we consider sensor networks with nonideal channels that are prone to errors. When the fusion rule is fixed, we present the necessary condition for the optimal sensor rules that minimize the Monte Carlo cost function. For the K-out-of-L fusion rule chosen very often in practice, we analytically derive the optimal sensor rules. For general fusion rules, a Monte Carlo Gauss-Seidel optimization algorithm is developed to search for the optimal sensor rules. The complexity of the new algorithm is of the order of OLN compared with OLNL of the previous algorithm that was based on Riemann sum approximation, where L is the number of sensors and N is the number of samples. Thus, the proposed method allows us to design the decision fusion rule for large-scale sensor networks. Moreover, the algorithm is generalized to simultaneously search for the optimal sensor rules and the optimal fusion rule. Finally, numerical examples show the effectiveness of the new algorithms for large-scale sensor networks with nonideal channels

Copula-based Multimodal Data Fusion for Inference with Dependent Observations

Fusing heterogeneous data from multiple modalities for inference problems has been an attractive and important topic in recent years. There are several challenges in multi-modal fusion, such as data heterogeneity and data correlation. In this dissertation, we investigate inference problems with heterogeneous modalities by taking into account nonlinear cross-modal dependence. We apply copula based methodology to characterize this dependence. In distributed detection, the goal often is to minimize the probability of detection error at the fusion center (FC) based on a fixed number of observations collected by the sensors. We design optimal detection algorithms at the FC using a regular vine copula based fusion rule. Regular vine copula is an extremely flexible and powerful graphical model used to characterize complex dependence among multiple modalities. The proposed approaches are theoretically justified and are computationally efficient for sensor networks with a large number of sensors. With heterogeneous streaming data, the fusion methods applied for processing data streams should be fast enough to keep up with the high arrival rates of incoming data, and meanwhile provide solutions for inference problems (detection, classification, or estimation) with high accuracy. We propose a novel parallel platform, C-Storm (Copula-based Storm), by marrying copula-based dependence modeling for highly accurate inference and a highly-regarded parallel computing platform Storm for fast stream data processing. The efficacy of C-Storm is demonstrated. In this thesis, we consider not only decision level fusion but also fusion with heterogeneous high-level features. We investigate a supervised classification problem by fusing dependent high-level features extracted from multiple deep neural network (DNN) classifiers. We employ regular vine copula to fuse these high-level features. The efficacy of the combination of model-based method and deep learning is demonstrated. Besides fixed-sample-size (FSS) based inference problems, we study a distributed sequential detection problem with random-sample-size. The aim of the distributed sequential detection problem in a non-Bayesian framework is to minimize the average detection time while satisfying the pre-specified constraints on probabilities of false alarm and miss detection. We design local memory-less truncated sequential tests and propose a copula based sequential test at the FC. We show that by suitably designing the local thresholds and the truncation window, the local probabilities of false alarm and miss detection of the proposed local decision rules satisfy the pre-specified error probabilities. Also, we show the asymptotic optimality and time efficiency of the proposed distributed sequential scheme. In large scale sensors networks, we consider a collaborative distributed estimation problem with statistically dependent sensor observations, where there is no FC. To achieve greater sensor transmission and estimation efficiencies, we propose a two-step cluster-based collaborative distributed estimation scheme. In the first step, sensors form dependence driven clusters such that sensors in the same cluster are dependent while sensors from different clusters are independent, and perform copula-based maximum a posteriori probability (MAP) estimation via intra-cluster collaboration. In the second step, the estimates generated in the first step are shared via inter-cluster collaboration to reach an average consensus. The efficacy of the proposed scheme is justified

Heterogeneous Sensor Signal Processing for Inference with Nonlinear Dependence

Inferring events of interest by fusing data from multiple heterogeneous sources has been an interesting and important topic in recent years. Several issues related to inference using heterogeneous data with complex and nonlinear dependence are investigated in this dissertation. We apply copula theory to characterize the dependence among heterogeneous data. In centralized detection, where sensor observations are available at the fusion center (FC), we study copula-based fusion. We design detection algorithms based on sample-wise copula selection and mixture of copulas model in different scenarios of the true dependence. The proposed approaches are theoretically justified and perform well when applied to fuse acoustic and seismic sensor data for personnel detection. Besides traditional sensors, the access to the massive amount of social media data provides a unique opportunity for extracting information about unfolding events. We further study how sensor networks and social media complement each other in facilitating the data-to-decision making process. We propose a copula-based joint characterization of multiple dependent time series from sensors and social media. As a proof-of-concept, this model is applied to the fusion of Google Trends (GT) data and stock/flu data for prediction, where the stock/flu data serves as a surrogate for sensor data. In energy constrained networks, local observations are compressed before they are transmitted to the FC. In these cases, conditional dependence and heterogeneity complicate the system design particularly. We consider the classification of discrete random signals in Wireless Sensor Networks (WSNs), where, for communication efficiency, only local decisions are transmitted. We derive the necessary conditions for the optimal decision rules at the sensors and the FC by introducing a hidden random variable. An iterative algorithm is designed to search for the optimal decision rules. Its convergence and asymptotical optimality are also proved. The performance of the proposed scheme is illustrated for the distributed Automatic Modulation Classification (AMC) problem. Censoring is another communication efficient strategy, in which sensors transmit only informative observations to the FC, and censor those deemed uninformative . We design the detectors that take into account the spatial dependence among observations. Fusion rules for censored data are proposed with continuous and discrete local messages, respectively. Their computationally efficient counterparts based on the key idea of injecting controlled noise at the FC before fusion are also investigated. In this thesis, with heterogeneous and dependent sensor observations, we consider not only inference in parallel frameworks but also the problem of collaborative inference where collaboration exists among local sensors. Each sensor forms coalition with other sensors and shares information within the coalition, to maximize its inference performance. The collaboration strategy is investigated under a communication constraint. To characterize the influence of inter-sensor dependence on inference performance and thus collaboration strategy, we quantify the gain and loss in forming a coalition by introducing the copula-based definitions of diversity gain and redundancy loss for both estimation and detection problems. A coalition formation game is proposed for the distributed inference problem, through which the information contained in the inter-sensor dependence is fully explored and utilized for improved inference performance

Distributed estimation over a low-cost sensor network: a review of state-of-the-art

Proliferation of low-cost, lightweight, and power efficient sensors and advances in networked systems enable the employment of multiple sensors. Distributed estimation provides a scalable and fault-robust fusion framework with a peer-to-peer communication architecture. For this reason, there seems to be a real need for a critical review of existing and, more importantly, recent advances in the domain of distributed estimation over a low-cost sensor network. This paper presents a comprehensive review of the state-of-the-art solutions in this research area, exploring their characteristics, advantages, and challenging issues. Additionally, several open problems and future avenues of research are highlighted

Bathtub-Shaped Failure Rate of Sensors for Distributed Detection and Fusion

We study distributed detection and fusion in sensor networks with bathtub-shaped failure (BSF) rate of the sensors which may or not send data to the Fusion Center (FC). The reliability of semiconductor devices is usually represented by the failure rate curve (called the “bathtub curve”), which can be divided into the three following regions: initial failure period, random failure period, and wear-out failure period. Considering the possibility of the failed sensors which still work but in a bad situation, it is unreasonable to trust the data from these sensors. Based on the above situation, we bring in new characteristics to failed sensors. Each sensor quantizes its local observation into one bit of information which is sent to the FC for overall fusion because of power, communication, and bandwidth constraints. Under this sensor failure model, the Extension Log-likelihood Ratio Test (ELRT) rule is derived. Finally, the ROC curve for this model is presented. The simulation results show that the ELRT rule improves the robust performance of the system, compared with the traditional fusion rule without considering sensor failures

Resource aware distributed detection and estimation of random events in wireless sensor networks

In this dissertation, we develop several resource aware approaches for detection and estimation in wireless sensor networks (WSNs). Tolerating an acceptable degradation from the best achievable performance, we seek more resource efficient solutions than the state-of-the-art methods. We first define a multi-objective optimization problem and find the trade-off solutions between two conflicting objectives for the distributed detection problem in WSNs: minimizing the probability of error and minimizing the total energy consumption. Simulation results show that Pareto-optimal solutions can provide significant energy savings at the cost a slight increase in the probability of error from its minimum achievable value. Having detected the presence of the source, accurate source localization is another important task to be performed by a WSN. The state-of-the-art one-shot location estimation scheme requires simultaneous transmission of all sensor data to the fusion center. We propose an iterative source localization algorithm where a small set of anchor sensors first detect the presence of the source and arrive at a coarse location estimate. Then a number of non-anchor sensors are selected in an iterative manner to refine the location estimate. The iterative localization scheme reduces the communication requirements as compared to the one-shot location estimation while introducing some estimation latency. For sensor selection at each iteration, two metrics are proposed which are derived based on the mutual information (MI) and the posterior Cramer-Rao lower bound (PCRLB) of the location estimate. In terms of computational complexity, the PCRLB-based sensor selection metric is more efficient as compared to the MI-based sensor selection metric, and under the assumption of perfect communication channels between sensors and the fusion center, both sensor selection schemes achieve the similar estimation performance that is the mean squared error of the source location gets very close to the PCRLB of one-shot location estimator within a few iterations. The proposed iterative method is further extended to the case which considers fading on the channels between sensors and the fusion center. Simulation results are presented for the cases when partial or complete channel knowledge are available at the fusion center. We finally consider a heterogenous sensing field and define a distributed parameter estimation problem where the quantization data rate of a sensor is determined as a function of its observation SNR. The inverse of the average Fisher information is then defined as a lower bound on the average PCRLB which is hard to compute. The inverse of the average Fisher information is minimized subject to the total bandwidth and bandwidth utilization constraints and we find the optimal transmission probability of each possible quantization rate. Under stringent bandwidth availability, the proposed scheme outperforms the scheme where the total bandwidth is equally distributed among sensors

Proceedings of the Fourth MIT/ONR Workshop on Distributed Information and Decision Systems Motivated by Command-Control-Communications (C3) Problems, June 15-June 26, 1981, San Diego, California

"OSP number 85552"--Cover.Library has v. 2 only.Includes bibliographies.Workshop suppported by the Office of Naval Research under contract ONR/N00014-77-C-0532edited by Michael Athans ... [et al.].v.1. Surveillance and target tracking--v.2. Systems architecture and evaluation--v.3. Communication, data bases & decision support--v.4. C3 theory

Cooperative Detection and Network Coding in Wireless Networks

In cooperative communication systems, multiple terminals in wireless networks share their antennas and resources for information exchange and processing. Recently, cooperative communications have been shown to achieve significant performance improvements in terms of transmission reliability, coverage area extension, and network throughput, with respect to existing classical communication systems. This dissertation is focused on two important applications of cooperative communications, namely: (i) cooperative distributed detection in wireless sensor networks, and (ii) many-to-many communications via cooperative space-time network coding. The first application of cooperative communications presented in this dissertation is concerned with the analysis and modeling of the deployment of cooperative relay nodes in wireless sensor networks. Particularly, in dense wireless sensor networks, sensor nodes continuously observe and collect measurements of a physical phenomenon. Such observations can be highly correlated, depending on the spatial separation between the sensor nodes as well as how the physical properties of the phenomenon are evolving over time. This unique characteristic of wireless sensor networks can be effectively exploited with cooperative communications and relays deployment such that the distributed detection performance is significantly improved as well as the energy efficiency. In particular, this dissertation studies the Amplify-and-Forward (AF) relays deployment as a function of the correlation of the observations and analyzes the achievable spatial diversity gains as compared with the classical wireless sensor networks. Moreover, it is demonstrated that the gains of cooperation can be further leveraged to alleviate bandwidth utilization inefficiencies in current sensor networks. Specifically, the deployment of cognitive AF cooperative relays to exploit empty/under-utilized time-slots and the resulting energy savings are studied, quantified and compared. The multiple terminal communication and information exchange form the second application of cooperative communications in this dissertation. Specifically, the novel concept of Space-Time-Network Coding (STNC) that is concerned with formulation of the many-to-many cooperative communications over Decode-and-Forward (DF) nodes is studied and analyzed. Moreover, the exact theoretical analysis as well as upper-bounds on the network symbol error rate performance are derived. In addition, the tradeoff between the number of communicating nodes and the timing synchronization errors is analyzed and provided as a network design guideline. With STNC, it is illustrated that cooperative diversity gains are fully exploited per node and significant performance improvements are achieved. It is concluded that the STNC scheme serves as a potential many-to-many cooperative communications scheme and that its scope goes much further beyond the generic source-relay-destination communications