Limited-Feedback-Based Channel-Aware Power Allocation for Linear Distributed Estimation

This paper investigates the problem of distributed best linear unbiased estimation (BLUE) of a random parameter at the fusion center (FC) of a wireless sensor network (WSN). In particular, the application of limited-feedback strategies for the optimal power allocation in distributed estimation is studied. In order to find the BLUE estimator of the unknown parameter, the FC combines spatially distributed, linearly processed, noisy observations of local sensors received through orthogonal channels corrupted by fading and additive Gaussian noise. Most optimal power-allocation schemes proposed in the literature require the feedback of the exact instantaneous channel state information from the FC to local sensors. This paper proposes a limited-feedback strategy in which the FC designs an optimal codebook containing the optimal power-allocation vectors, in an iterative offline process, based on the generalized Lloyd algorithm with modified distortion functions. Upon observing a realization of the channel vector, the FC finds the closest codeword to its corresponding optimal power-allocation vector and broadcasts the index of the codeword. Each sensor will then transmit its analog observations using its optimal quantized amplification gain. This approach eliminates the requirement for infinite-rate digital feedback links and is scalable, especially in large WSNs.Comment: 5 Pages, 3 Figures, 1 Algorithm, Forty Seventh Annual Asilomar Conference on Signals, Systems, and Computers (ASILOMAR 2013

Distributed Recursive Least-Squares: Stability and Performance Analysis

The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary processes. In this paper, a distributed recursive least-squares (D-RLS) algorithm is developed for cooperative estimation using ad hoc wireless sensor networks. Distributed iterations are obtained by minimizing a separable reformulation of the exponentially-weighted least-squares cost, using the alternating-minimization algorithm. Sensors carry out reduced-complexity tasks locally, and exchange messages with one-hop neighbors to consent on the network-wide estimates adaptively. A steady-state mean-square error (MSE) performance analysis of D-RLS is conducted, by studying a stochastically-driven `averaged' system that approximates the D-RLS dynamics asymptotically in time. For sensor observations that are linearly related to the time-invariant parameter vector sought, the simplifying independence setting assumptions facilitate deriving accurate closed-form expressions for the MSE steady-state values. The problems of mean- and MSE-sense stability of D-RLS are also investigated, and easily-checkable sufficient conditions are derived under which a steady-state is attained. Without resorting to diminishing step-sizes which compromise the tracking ability of D-RLS, stability ensures that per sensor estimates hover inside a ball of finite radius centered at the true parameter vector, with high-probability, even when inter-sensor communication links are noisy. Interestingly, computer simulations demonstrate that the theoretical findings are accurate also in the pragmatic settings whereby sensors acquire temporally-correlated data.Comment: 30 pages, 4 figures, submitted to IEEE Transactions on Signal Processin

Distributed state estimation for uncertain Markov-type sensor networks with mode-dependent distributed delays

This the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & Sons, Ltd.In this paper, the distributed state estimation problem is investigated for a class of sensor networks described by uncertain discrete-time dynamical systems with Markovian jumping parameters and distributed time-delays. The sensor network consists of sensor nodes characterized by a directed graph with a nonnegative adjacency matrix that specifies the interconnection topology (or the distribution in the space) of the network. Both the parameters of the target plant and the sensor measurements are subject to the switches from one mode to another at different times according to a Markov chain. The parameter uncertainties are norm-bounded that enter into both the plant system as well as the network outputs. Furthermore, the distributed time-delays are considered, which are also dependent on the Markovian jumping mode. Through the measurements from a small fraction of the sensors, this paper aims to design state estimators that allow the nodes of the sensor network to track the states of the plant in a distributed way. It is verified that such state estimators do exist if a set of matrix inequalities is solvable. A numerical example is provided to demonstrate the effectiveness of the designed distributed state estimators.This work was supported in part by the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 60804028 and 61028008, the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers in China under Grant 200802861044, the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, the International Science and Technology Cooperation Project of China under Grant No. 2009DFA32050, and the Alexander von Humboldt Foundation of Germany

Power Allocation for Distributed BLUE Estimation with Full and Limited Feedback of CSI

This paper investigates the problem of adaptive power allocation for distributed best linear unbiased estimation (BLUE) of a random parameter at the fusion center (FC) of a wireless sensor network (WSN). An optimal power-allocation scheme is proposed that minimizes the $L^2$-norm of the vector of local transmit powers, given a maximum variance for the BLUE estimator. This scheme results in the increased lifetime of the WSN compared to similar approaches that are based on the minimization of the sum of the local transmit powers. The limitation of the proposed optimal power-allocation scheme is that it requires the feedback of the instantaneous channel state information (CSI) from the FC to local sensors, which is not practical in most applications of large-scale WSNs. In this paper, a limited-feedback strategy is proposed that eliminates this requirement by designing an optimal codebook for the FC using the generalized Lloyd algorithm with modified distortion metrics. Each sensor amplifies its analog noisy observation using a quantized version of its optimal amplification gain, which is received by the FC and used to estimate the unknown parameter.Comment: 6 pages, 3 figures, to appear at the IEEE Military Communications Conference (MILCOM) 201

A new approach to distributed fusion filtering for networked systems with random parameter matrices and correlated noises

This paper is concerned with the distributed filtering problem for a class of discrete-time stochastic systems over a sensor network with a given topology. The system presents the following main features: (i) random parameter matrices in both the state and observation equations are considered; and (ii) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. The state estimation is performed in two stages. At the first stage, through an innovation approach, intermediate distributed least-squares linear filtering estimators are obtained at each sensor node by processing available output measurements not only from the sensor itself but also from its neighboring sensors according to the network topology. At the second stage, noting that at each sampling time not only the measurement but also an intermediate estimator is available at each sensor, attention is focused on the design of distributed filtering estimators as the least-squares matrix-weighted linear combination of the intermediate estimators within its neighborhood. The accuracy of both intermediate and distributed estimators, which is measured by the error covariance matrices, is examined by a numerical simulation example where a four-sensor network is considered. The example illustrates the applicability of the proposed results to a linear networked system with state-dependent multiplicative noise and different network-induced stochastic uncertainties in the measurements; more specifically, sensor gain degradation, missing measurements and multiplicative observation noises are considered as particular cases of the proposed observation model.This research is supported by Ministerio de Economía y Competitividad and Fondo Europeo de Desarrollo Regional FEDER (grant no. MTM2014- 52291-P, MTM2017-84199-P)

Distributed Target Tracking and Synchronization in Wireless Sensor Networks

Wireless sensor networks provide useful information for various applications but pose challenges in scalable information processing and network maintenance. This dissertation focuses on statistical methods for distributed information fusion and sensor synchronization for target tracking in wireless sensor networks. We perform target tracking using particle filtering. For scalability, we extend centralized particle filtering to distributed particle filtering via distributed fusion of local estimates provided by individual sensors. We derive a distributed fusion rule from Bayes\u27 theorem and implement it via average consensus. We approximate each local estimate as a Gaussian mixture and develop a sampling-based approach to the nonlinear fusion of Gaussian mixtures. By using the sampling-based approach in the fusion of Gaussian mixtures, we do not require each Gaussian mixture to have a uniform number of mixture components, and thus give each sensor the flexibility to adaptively learn a Gaussian mixture model with the optimal number of mixture components, based on its local information. Given such flexibility, we develop an adaptive method for Gaussian mixture fitting through a combination of hierarchical clustering and the expectation-maximization algorithm. Using numerical examples, we show that the proposed distributed particle filtering algorithm improves the accuracy and communication efficiency of distributed target tracking, and that the proposed adaptive Gaussian mixture learning method improves the accuracy and computational efficiency of distributed target tracking. We also consider the synchronization problem of a wireless sensor network. When sensors in a network are not synchronized, we model their relative clock offsets as unknown parameters in a state-space model that connects sensor observations to target state transition. We formulate the synchronization problem as a joint state and parameter estimation problem and solve it via the expectation-maximization algorithm to find the maximum likelihood solution for the unknown parameters, without knowledge of the target states. We also study the performance of the expectation-maximization algorithm under the Monte Carlo approximations used by particle filtering in target tracking. Numerical examples show that the proposed synchronization method converges to the ground truth, and that sensor synchronization significantly improves the accuracy of target tracking

A Sensor Self-aware Distributed Consensus Filter for Simultaneous Localization and Tracking

This is the author accepted manuscript. The final version is available from Springer via the DOI in this recordBackground/Introduction: Simultaneous localization and tracking (SLAT) has become a very hot topic in both academia and industry for its potential wide applications in robotic equipment, sensor networks and smart devices. In order to exploit the advantages supported by state filtering and parameter estimation, researchers have proposed adaptive structures for solving SLAT problems. Existing solutions for SLAT problems that rely on belief propagation often have limited accuracy or high complexity. To adapt the brain decision mechanism for solving SLAT problems, we introduce a specific framework that is suitable for wireless sensor networks. Methods: Motivated by the high efficiency and performance of brain decision making built upon partial information and information updating, we propose a cognitively distributed SLAT algorithm based on an adaptive distributed filter, which is composed of two stages for target tracking and sensor localization. The first stage is consensus filtering that updates the target state with respect to each sensor. The second stage employs a recursive parameter estimation that exploits an on-line optimization method for refining the sensor localization. As an integrated framework, each consensus filter is specific to a separate sensor subsystem and gets feedback information from its parameter estimation. Results: The performance comparison in terms of positioning accuracy with respect to RMSE is shown and the simulation results demonstrate that the proposed ICF-RML performs better than the BPF-RML. This is expected since the distributed estimation with sufficient communication mechanism often achieves higher accuracy than that of less sufficient cases. Furthermore, the performance of the ICF-RML is comparable with that of the BPF-RML even if the latter assumes known prior network topology. We also observe from the results of tracking errors that ICF-RML accomplishes a remarkable improvement in the precision of target tracking and achieves more stable convergence than BPF-RML, in the scenario that all sensors are used to calculate the effect from data association errors. Conclusion: We apply this approach to formulate the SLAT problem and propose an effective solution, summarized in the paper. For small-size sensor networks with Gaussian distribution, our algorithm can be implemented through a distributed version of weighted information filter and a consensus protocol. Comparing the existing method, our solution shows a higher accuracy in estimation but with less complexity.National Natural Science Foundation of ChinaShandong Provincial Natural Science FoundationShandong Outstanding Young Scientist FundRoyal SocietyFundamental Research Funds for the Central Universitie

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