We consider the problem of distributed estimation, where a set of nodes is required to collectively estimate some parameter of interest from noisy measurements. The problem is useful in several contexts including wireless and sensor networks, where scalability, robustness, and low power consumption are desirable features. Diffusion cooperation schemes have been shown to provide good performance, robustness to node and link failure, and are amenable to distributed implementations. In this work we focus on diffusion-based adaptive solutions of the LMS type. We motivate and propose new versions of the diffusion LMS algorithm that outperform previous solutions. We provide performance and convergence analysis of the proposed algorithms, together with simulation results comparing with existing techniques. We also discuss optimization schemes to design the diffusion LMS weights.

Diffusion LMS Strategies for Distributed Estimation

We formulate and study distributed estimation algorithms based on diffusion protocols to implement cooperation among individual adaptive nodes. The individual nodes are equipped with local learning abilities. They derive local estimates for the parameter of interest and share information with their neighbors only, giving rise to peer-to-peer protocols. The resulting algorithm is distributed, cooperative and able to respond in real time to changes in the environment. It improves performance in terms of transient and steady-state mean-square error, as compared with traditional noncooperative schemes. Closed-form expressions that describe the network performance in terms of mean-square error quantities are derived, presenting a very good match with simulations.

Diffusion Least-Mean Squares Over Adaptive Networks: Formulation and Performance Analysis

A heart monitoring system for a person includes one or more wireless nodes; and a wearable appliance in communication with the one or more wireless nodes, the appliance monitoring vital signs.

Health monitoring appliance

We study the problem of distributed Kalman filtering and smoothing, where a set of nodes is required to estimate the state of a linear dynamic system from in a collaborative manner. Our focus is on diffusion strategies, where nodes communicate with their direct neighbors only, and the information is diffused across the network through a sequence of Kalman iterations and data-aggregation. We study the problems of Kalman filtering, fixed-lag smoothing and fixed-point smoothing, and propose diffusion algorithms to solve each one of these problems. We analyze the mean and mean-square performance of the proposed algorithms, provide expressions for their steady-state mean-square performance, and analyze the convergence of the diffusion Kalman filter recursions. Finally, we apply the proposed algorithms to the problem of estimating and tracking the position of a projectile. We compare our simulation results with the theoretical expressions, and note that the proposed approach outperforms existing techniques.

Diffusion Strategies for Distributed Kalman Filtering and Smoothing

We propose an adaptive diffusion mechanism to optimize global cost functions 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.

Diffusion Adaptation Strategies for Distributed Optimization and Learning Over Networks

We study the problem of distributed estimation over adaptive networks where a collection of nodes are required to estimate in a collaborative manner some parameter of interest from their measurements. The centralized solution to the problem uses a fusion center, thus, requiring a large amount of energy for communication. Incremental strategies that obtain the global solution have been proposed, but they require the definition of a cycle through the network. We propose a diffusion recursive least-squares algorithm where nodes need to communicate only with their closest neighbors. The algorithm has no topology constraints, and requires no transmission or inversion of matrices, therefore saving in communications and complexity. We show that the algorithm is stable and analyze its performance comparing it to the centralized global solution. We also show how to select the combination weights optimally.

Diffusion recursive least-squares for distributed estimation over adaptive networks

We study the problem of distributed detection, where a set of nodes is required to decide between two hypotheses based on available measurements. We seek fully distributed and adaptive implementations, where all nodes make individual real-time decisions by communicating with their immediate neighbors only, and no fusion center is necessary. The proposed distributed detection algorithms are based on diffusion strategies [C. G. Lopes and A. H. Sayed, “Diffusion Least-Mean Squares Over Adaptive Networks: Formulation and Performance Analysis,” IEEE Trans. Signal Process., vol. 56, no. 7, pp. 3122-3136, July 2008; F. S. Cattivelli and A. H. Sayed, “Diffusion LMS Strategies for Distributed Estimation,” IEEE Trans. Signal Process., vol. 58, no. 3, pp. 1035-1048, March 2010; F. S. Cattivelli, C. G. Lopes, and A. H. Sayed, “Diffusion Recursive Least-Squares for Distributed Estimation Over Adaptive Networks,” IEEE Trans. Signal Process., vol. 56, no. 5, pp. 1865-1877, May 2008] for distributed estimation. Diffusion detection schemes are attractive in the context of wireless and sensor networks due to their scalability, improved robustness to node and link failure as compared to centralized schemes, and their potential to save energy and communication resources. The proposed algorithms are inherently adaptive and can track changes in the active hypothesis. We analyze the performance of the proposed algorithms in terms of their probabilities of detection and false alarm, and provide simulation results comparing with other cooperation schemes, including centralized processing and the case where there is no cooperation. Finally, we apply the proposed algorithms to the problem of spectrum sensing in cognitive radios.

Distributed Detection Over Adaptive Networks Using Diffusion Adaptation

We study the problem of noninvasively estimating Blood Pressure (BP) without using a cuff, which is attractive for continuous monitoring of BP over Body Area Networks. It has been shown that the Pulse Arrival Time (PAT) measured as the delay between the ECG peak and a point in the finger PPG waveform can be used to estimate systolic and diastolic BP. Our aim is to evaluate the performance of such a method using the available MIMIC database, while at the same time improve the performance of existing techniques. We propose an algorithm to estimate BP from a combination of PAT and heart rate, showing improvement over PAT alone. We also show how the method achieves recalibration using an RLS adaptive algorithm. Finally, we address the use case of ECG and PPG sensors wirelessly communicating to an aggregator and study the effect of skew and jitter on BP estimation.

Federico S. Cattivelli

Papers

Diffusion LMS Strategies for Distributed Estimation

Diffusion Strategies for Distributed Kalman Filtering and Smoothing

Diffusion recursive least-squares for distributed estimation over adaptive networks

Distributed Detection Over Adaptive Networks Using Diffusion Adaptation

Noninvasive Cuffless Estimation of Blood Pressure from Pulse Arrival Time and Heart Rate with Adaptive Calibration