Diffusion Adaptation over Networks under Imperfect Information Exchange and Non-stationary Data

Adaptive networks rely on in-network and collaborative processing among distributed agents to deliver enhanced performance in estimation and inference tasks. Information is exchanged among the nodes, usually over noisy links. The combination weights that are used by the nodes to fuse information from their neighbors play a critical role in influencing the adaptation and tracking abilities of the network. This paper first investigates the mean-square performance of general adaptive diffusion algorithms in the presence of various sources of imperfect information exchanges, quantization errors, and model non-stationarities. Among other results, the analysis reveals that link noise over the regression data modifies the dynamics of the network evolution in a distinct way, and leads to biased estimates in steady-state. The analysis also reveals how the network mean-square performance is dependent on the combination weights. We use these observations to show how the combination weights can be optimized and adapted. Simulation results illustrate the theoretical findings and match well with theory.Comment: 36 pages, 7 figures, to appear in IEEE Transactions on Signal Processing, June 201

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

Multitask Diffusion Adaptation over Networks

Adaptive networks are suitable for decentralized inference tasks, e.g., to monitor complex natural phenomena. Recent research works have intensively studied distributed optimization problems in the case where the nodes have to estimate a single optimum parameter vector collaboratively. However, there are many important applications that are multitask-oriented in the sense that there are multiple optimum parameter vectors to be inferred simultaneously, in a collaborative manner, over the area covered by the network. In this paper, we employ diffusion strategies to develop distributed algorithms that address multitask problems by minimizing an appropriate mean-square error criterion with $\ell_2$-regularization. The stability and convergence of the algorithm in the mean and in the mean-square sense is analyzed. Simulations are conducted to verify the theoretical findings, and to illustrate how the distributed strategy can be used in several useful applications related to spectral sensing, target localization, and hyperspectral data unmixing.Comment: 29 pages, 11 figures, submitted for publicatio

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

Data-Reserved Periodic Diffusion LMS With Low Communication Cost Over Networks

In this paper, we analyze diffusion strategies in which all nodes attempt to estimate a common vector parameter for achieving distributed estimation in adaptive networks. Under diffusion strategies, each node essentially needs to share processed data with predefined neighbors. Although the use of internode communication has contributed significantly to improving convergence performance based on diffusion, such communications consume a huge quantity of power in data transmission. In developing low-power consumption diffusion strategies, it is very important to reduce the communication cost without significant degradation of convergence performance. For that purpose, we propose a data-reserved periodic diffusion least-mean-squares (LMS) algorithm in which each node updates and transmits an estimate periodically while reserving its measurement data even during non-update time. By applying these reserved data in an adaptation step at update time, the proposed algorithm mitigates the decline in convergence speed incurred by most conventional periodic schemes. For a period p, the total cost of communication is reduced to a factor of 1/p relative to the conventional adapt-then-combine (ATC) diffusion LMS algorithm. The loss of combination steps in this process leads naturally to a slight increase in the steady-state error as the period p increases, as is theoretically confirmed through mathematical analysis. We also prove an interesting property of the proposed algorithm, namely, that it suffers less degradation of the steady-state error than the conventional diffusion in a noisy communication environment. Experimental results show that the proposed algorithm outperforms related conventional algorithms and, in particular, outperforms ATC diffusion LMS over a network with noisy links.11Ysciescopu

Diffusion Adaptation Strategies for Distributed Optimization and Learning over Networks

We propose an adaptive diffusion mechanism to optimize a global cost function in a distributed manner over a network of nodes. The cost function is assumed to consist of a collection of individual components. Diffusion adaptation allows the nodes to cooperate and diffuse information in real-time; it also helps alleviate the effects of stochastic gradient noise and measurement noise through a continuous learning process. We analyze the mean-square-error performance of the algorithm in some detail, including its transient and steady-state behavior. We also apply the diffusion algorithm to two problems: distributed estimation with sparse parameters and distributed localization. Compared to well-studied incremental methods, diffusion methods do not require the use of a cyclic path over the nodes and are robust to node and link failure. Diffusion methods also endow networks with adaptation abilities that enable the individual nodes to continue learning even when the cost function changes with time. Examples involving such dynamic cost functions with moving targets are common in the context of biological networks.Comment: 34 pages, 6 figures, to appear in IEEE Transactions on Signal Processing, 201