Fusion of finite set distributions: Pointwise consistency and global cardinality

A recent trend in distributed multi-sensor fusion is to use random finite set filters at the sensor nodes and fuse the filtered distributions algorithmically using their exponential mixture densities (EMDs). Fusion algorithms which extend the celebrated covariance intersection and consensus based approaches are such examples. In this article, we analyse the variational principle underlying EMDs and show that the EMDs of finite set distributions do not necessarily lead to consistent fusion of cardinality distributions. Indeed, we demonstrate that these inconsistencies may occur with overwhelming probability in practice, through examples with Bernoulli, Poisson and independent identically distributed (IID) cluster processes. We prove that pointwise consistency of EMDs does not imply consistency in global cardinality and vice versa. Then, we redefine the variational problems underlying fusion and provide iterative solutions thereby establishing a framework that guarantees cardinality consistent fusion.Comment: accepted for publication in the IEEE Transactions on Aerospace and Electronics System

Sensor Placement for Damage Localization in Sensor Networks

The objective of this thesis is to formulate and solve the sensor placement problem for damage localization in a sensor network. A Bayesian estimation problem is formulated with the time-of-flight (ToF) measurements. In this model, ToF of lamb waves, which are generated and received by piezoelectric sensors, is the total time for each wave to be transmitted, reflected by the target, and received by the sensor. The ToF of the scattered lamb wave has characteristic information about the target location. By using the measurement model and prior information, the target location is estimated in a centralized sensor network with a Monte Carlo approach. Then we derive the Bayesian Fisher information matrix (B-FIM) and based on that posterior Cramer-Rao lower bound (PCRLB), which sets a limit on the mean squared error (MSE) of any Bayesian estimator. In addition, we develop an optimal sensor placement approach to achieve more accurate damage localization, which is based on minimizing the PCRLB. Simulation results show that the optimal sensor placement solutions lead to much lower estimation errors than some sub-optimal sensor placement solutions

Likelihood Consensus and Its Application to Distributed Particle Filtering

We consider distributed state estimation in a wireless sensor network without a fusion center. Each sensor performs a global estimation task---based on the past and current measurements of all sensors---using only local processing and local communications with its neighbors. In this estimation task, the joint (all-sensors) likelihood function (JLF) plays a central role as it epitomizes the measurements of all sensors. We propose a distributed method for computing, at each sensor, an approximation of the JLF by means of consensus algorithms. This "likelihood consensus" method is applicable if the local likelihood functions of the various sensors (viewed as conditional probability density functions of the local measurements) belong to the exponential family of distributions. We then use the likelihood consensus method to implement a distributed particle filter and a distributed Gaussian particle filter. Each sensor runs a local particle filter, or a local Gaussian particle filter, that computes a global state estimate. The weight update in each local (Gaussian) particle filter employs the JLF, which is obtained through the likelihood consensus scheme. For the distributed Gaussian particle filter, the number of particles can be significantly reduced by means of an additional consensus scheme. Simulation results are presented to assess the performance of the proposed distributed particle filters for a multiple target tracking problem

Generalized Linear Quaternion Complementary Filter for Attitude Estimation from Multi-Sensor Observations: An Optimization Approach

International audienceFocusing on generalized sensor combinations, this paper deals with attitude estimation problem using a linear complementary filter. The quaternion observation model is obtained via a gradient descent algorithm (GDA). An additive measurement model is then established according to derived results. The filter is named as the generalized complementary filter (GCF) where the observation model is simplified to its limit as a linear one that is quite different from previous-reported brute-force computation results. Moreover, we prove that representative derivative-based optimization algorithms are essentially equivalent to each other. Derivations are given to establish the state model based on the quaternion kinematic equation. The proposed algorithm is validated under several experimental conditions involving free-living environment, harsh external field disturbances and aerial flight test aided by robotic vision. Using the specially designed experimental devices, data acquisition and algorithm computations are performed to give comparisons on accuracy, robustness, time-consumption and etc. with representative methods. The results show that not only the proposed filter can give fast, accurate and stable estimates in terms of various sensor combinations, but it also produces robust attitude estimation in the presence of harsh situations e.g. irregular magnetic distortion. Note to Practitioners-Multi-sensor attitude estimation is a crucial technique in robotic devices. Many existing methods focus on the orientation fusion of specific sensor combinations. In this paper we make the problem more abstract. The results given in this paper are very general and can significantly decrease the space consumption and computation burden without losing the original estimation accuracy. Such performance will be of benefit to robotic platforms requiring flexible and easy-to-tune attitude estimation in the future

Enabling Resilience in Cyber-Physical-Human Water Infrastructures

Rapid urbanization and growth in urban populations have forced community-scale infrastructures (e.g., water, power and natural gas distribution systems, and transportation networks) to operate at their limits. Aging (and failing) infrastructures around the world are becoming increasingly vulnerable to operational degradation, extreme weather, natural disasters and cyber attacks/failures. These trends have wide-ranging socioeconomic consequences and raise public safety concerns. In this thesis, we introduce the notion of cyber-physical-human infrastructures (CPHIs) - smart community-scale infrastructures that bridge technologies with physical infrastructures and people. CPHIs are highly dynamic stochastic systems characterized by complex physical models that exhibit regionwide variability and uncertainty under disruptions. Failures in these distributed settings tend to be difficult to predict and estimate, and expensive to repair. Real-time fault identification is crucial to ensure continuity of lifeline services to customers at adequate levels of quality. Emerging smart community technologies have the potential to transform our failing infrastructures into robust and resilient future CPHIs.In this thesis, we explore one such CPHI - community water infrastructures. Current urban water infrastructures, that are decades (sometimes over a 100 years) old, encompass diverse geophysical regimes. Water stress concerns include the scarcity of supply and an increase in demand due to urbanization. Deterioration and damage to the infrastructure can disrupt water service; contamination events can result in economic and public health consequences. Unfortunately, little investment has gone into modernizing this key lifeline.To enhance the resilience of water systems, we propose an integrated middleware framework for quick and accurate identification of failures in complex water networks that exhibit uncertain behavior. Our proposed approach integrates IoT-based sensing, domain-specific models and simulations with machine learning methods to identify failures (pipe breaks, contamination events). The composition of techniques results in cost-accuracy-latency tradeoffs in fault identification, inherent in CPHIs due to the constraints imposed by cyber components, physical mechanics and human operators. Three key resilience problems are addressed in this thesis; isolation of multiple faults under a small number of failures, state estimation of the water systems under extreme events such as earthquakes, and contaminant source identification in water networks using human-in-the-loop based sensing. By working with real world water agencies (WSSC, DC and LADWP, LA), we first develop an understanding of operations of water CPHI systems. We design and implement a sensor-simulation-data integration framework AquaSCALE, and apply it to localize multiple concurrent pipe failures. We use a mixture of infrastructure measurements (i.e., historical and live water pressure/flow), environmental data (i.e., weather) and human inputs (i.e., twitter feeds), combined and enhanced with the domain model and supervised learning techniques to locate multiple failures at fine levels of granularity (individual pipeline level) with detection time reduced by orders of magnitude (from hours/days to minutes). We next consider the resilience of water infrastructures under extreme events (i.e., earthquakes) - the challenge here is the lack of apriori knowledge and the increased number and severity of damages to infrastructures. We present a graphical model based approach for efficient online state estimation, where the offline graph factorization partitions a given network into disjoint subgraphs, and the belief propagation based inference is executed on-the-fly in a distributed manner on those subgraphs. Our proposed approach can isolate 80% broken pipes and 99% loss-of-service to end-users during an earthquake.Finally, we address issues of water quality - today this is a human-in-the-loop process where operators need to gather water samples for lab tests. We incorporate the necessary abstractions with event processing methods into a workflow, which iteratively selects and refines the set of potential failure points via human-driven grab sampling. Our approach utilizes Hidden Markov Model based representations for event inference, along with reinforcement learning methods for further refining event locations and reducing the cost of human efforts.The proposed techniques are integrated into a middleware architecture, which enables components to communicate/collaborate with one another. We validate our approaches through a prototype implementation with multiple real-world water networks, supply-demand patterns from water utilities and policies set by the U.S. EPA. While our focus here is on water infrastructures in a community, the developed end-to-end solution is applicable to other infrastructures and community services which operate in disruptive and resource-constrained environments

Distributed parameter and state estimation for wireless sensor networks

The research in distributed algorithms is linked with the developments of statistical inference in wireless sensor networks (WSNs) applications. Typically, distributed approaches process the collected signals from networked sensor nodes. That is to say, the sensors receive local observations and transmit information between each other. Each sensor is capable of combining the collected information with its own observations to improve performance. In this thesis, we propose novel distributed methods for the inference applications using wireless sensor networks. In particular, the efficient algorithms which are not computationally intensive are investigated. Moreover, we present a number of novel algorithms for processing asynchronous network events and robust state estimation. In the first part of the thesis, a distributed adaptive algorithm based on the component-wise EM method for decentralized sensor networks is investigated. The distributed component-wise Expectation-Maximization (EM) algorithm has been designed for application in a Gaussian density estimation. The proposed algorithm operates a component-wise EM procedure for local parameter estimation and exploit an incremental strategy for network updating, which can provide an improved convergence rate. Numerical simulation results have illustrated the advantages of the proposed distributed component-wise EM algorithm for both well-separated and overlapped mixture densities. The distributed component-wise EM algorithm can outperform other EM-based distributed algorithms in estimating overlapping Gaussian mixtures. In the second part of the thesis, a diffusion based EM gradient algorithm for density estimation in asynchronous wireless sensor networks has been proposed. Specifically, based on the asynchronous adapt-then-combine diffusion strategy, a distributed EM gradient algorithm that can deal with asynchronous network events has been considered. The Bernoulli model has been exploited to approximate the asynchronous behaviour of the network. Compared with existing distributed EM based estimation methods using a consensus strategy, the proposed algorithm can provide more accurate estimates in the presence of asynchronous networks uncertainties, such as random link failures, random data arrival times, and turning on or off sensor nodes for energy conservation. Simulation experiments have been demonstrated that the proposed algorithm significantly outperforms the consensus based strategies in terms of Mean-Square- Deviation (MSD) performance in an asynchronous network setting. Finally, the challenge of distributed state estimation in power systems which requires low complexity and high stability in the presence of bad data for a large scale network is addressed. A gossip based quasi-Newton algorithm has been proposed for solving the power system state estimation problem. In particular, we have applied the quasi-Newton method for distributed state estimation under the gossip protocol. The proposed algorithm exploits the Broyden- Fletcher-Goldfarb-Shanno (BFGS) formula to approximate the Hessian matrix, thus avoiding the computation of inverse Hessian matrices for each control area. The simulation results for IEEE 14 bus system and a large scale 4200 bus system have shown that the distributed quasi-Newton scheme outperforms existing algorithms in terms of Mean-Square-Error (MSE) performance with bad data