-
[show abstract]
[hide abstract]
ABSTRACT: We study, by large deviations analysis, the asymptotic performance of Gaussian running consensus distributed detection over random networks; in other words, we determine the exponential decay rate of the detection error probability. With running consensus, at each time step, each sensor averages its decision variable with the neighbors' decision variables and accounts on-the-fly for its new observation. We show that: 1) when the rate of network information flow (the speed of averaging) is above a threshold, then Gaussian running consensus is asymptotically equivalent to the optimal centralized detector, i.e., the exponential decay rate of the error probability for running consensus equals the Chernoff information; and 2) when the rate of information flow is below a threshold, running consensus achieves only a fraction of the Chernoff information rate. We quantify this achievable rate as a function of the network rate of information flow. Simulation examples demonstrate our theoretical findings on the behavior of running consensus detection over random networks.
IEEE Transactions on Signal Processing 10/2011; · 2.63 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: This paper considers gossip distributed estimation of a (static) distributed random field (a.k.a., large-scale unknown parameter vector) observed by sparsely interconnected sensors, each of which only observes a small fraction of the field. We consider linear distributed estimators whose structure combines the information flow among sensors (the consensus term resulting from the local gossiping exchange among sensors when they are able to communicate) and the information gathering measured by the sensors (the sensing or innovations term). This leads to mixed time scale algorithms-one time scale associated with the consensus and the other with the innovations. The paper establishes a distributed observability condition (global observability plus mean connectedness) under which the distributed estimates are consistent and asymptotically normal. We introduce the distributed notion equivalent to the (centralized) Fisher information rate, which is a bound on the mean square error reduction rate of any distributed estimator; we show that under the appropriate modeling and structural network communication conditions (gossip protocol) the distributed gossip estimator attains this distributed Fisher information rate, asymptotically achieving the performance of the optimal centralized estimator. Finally, we study the behavior of the distributed gossip estimator when the measurements fade (noise variance grows) with time; in particular, we consider the maximum rate at which the noise variance can grow and still the distributed estimator being consistent, by showing that, as long as the centralized estimator is consistent, the distributed estimator remains consistent.
IEEE Journal of Selected Topics in Signal Processing 09/2011; · 2.88 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: A time reversal (TR) based direction of arrival (DOA) estimation framework for multiple-input/multiple-output (MIMO) radars is presented. We develop minimum variance distortionless response (MVDR) and multiple signal classification (MUSIC) based DOA estimators for the TR/MIMO setup. The TR/MIMO estimation algorithms outperform their conventional counterparts in: (i) analytical Cramér Rao Bounds (CRB) comparisons, and; (ii) numerical Monte Carlo simulations for a range of signal to noise ratios that we tested.
Statistical Signal Processing Workshop (SSP), 2011 IEEE; 07/2011
-
[show abstract]
[hide abstract]
ABSTRACT: We show that distributed detection over random networks, or using a random protocol, e.g., of the gossip type, is asymptotically optimal, if the rate of information flow across the random network is large enough. Asymptotic optimality is in the sense of Chernoff information; in other words, we determine when the exponential rate of decay of the error probability for distributed detection is the best possible and equal to the rate of decay of the best centralized detector. The rate of information flow is defined by |log r|, where r is the second largest eigenvalue of the second moment of the random, consensus weight matrix. We quantify interesting tradeoffs in distributed detection, between the rate of information flow and the achievable detection performance.
Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on; 06/2011 · 4.63 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: Networks of biological agents (for example, ants, bees, fish, birds) and complex man-made cyberphysical infrastructures (for example, the power grid, transportation networks) exhibit one thing in common - the emergence of collective global phenomena from apparently random local interactions. This paper proposes a distributed graphical model of interacting agents (a stochastic network type model) and studies its appropriate asymptotics. We show that metastability may occur - i.e., under certain conditions, the agents act in synchrony and may exhibit collectively possibly different stable equilibria - these are the global emergent behaviors of the cloud of interacting agents. We characterize these global behaviors as synchronous fixed points determined from ordinary differential equations that arise as mean field limits of the adopted stochastic model.
Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on; 06/2011 · 4.63 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: The paper presents the gossip interactive Kalman filter (GIKF) for distributed Kalman filtering for networked systems and sensor networks, where intersensor communication and observations occur at the same time-scale. The communication among sensors is random; each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link. We show that under a weak distributed detectability condition: 1) the GIKF error process remains stochastically bounded, irrespective of the instability of the random process dynamics; and 2) the network achieves weak consensus, i.e., the conditional estimation error covariance at a (uniformly) randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semidefinite matrices (independent of the initial state). To prove these results, we interpret the filtering states (estimates and error covariances) at each node in the GIKF as stochastic particles with local interactions. We analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched (random) Riccati equation, the switching being dictated by a nonstationary Markov chain on the network graph.
IEEE Transactions on Signal Processing 05/2011; · 2.63 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We introduce a new model of social learning and distributed estimation in which the state to be estimated is governed by a potentially unstable linear model driven by noise. The state is observed by a network of agents, each with its own linear noisy observation models. We assume the state to be globally observable, but no agent is able to estimate the state with its own observations alone. We propose a single consensus-step estimator that consists of an innovation step and a consensus step, both performed at the same time-step. We show that if the instability of the dynamics is strictly less than the Network Tracking Capacity (NTC), a function of network connectivity and the observation matrices, the single consensus-step estimator results in a bounded estimation error. We further quantify the trade-off between: (i) (in)stability of the parameter dynamics, (ii) connectivity of the underlying network, and (iii) the observation structure, in the context of single timescale algorithms. This contrasts with prior work on distributed estimation that either assumes scalar dynamics (which removes local observability issues) or assumes that enough iterates can be carried out for the consensus to converge between each innovation (observation) update.
Decision and Control (CDC), 2010 49th IEEE Conference on; 01/2011
-
[show abstract]
[hide abstract]
ABSTRACT: Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This paper presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.
Proceedings of the IEEE 12/2010; · 6.81 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We apply large deviations theory to study asymptotic performance of running consensus distributed detection in sensor networks. Running consensus is a stochastic approximation type algorithm, recently proposed. At each time step k, the state at each sensor is updated by a local averaging of the sensor's own state and the states of its neighbors (consensus) and by accounting for the new observations (innovation).We assume Gaussian, spatially correlated observations. We allow the underlying network be time varying, provided that the graph that collects the union of links that are online at least once over a finite time window is connected. This paper shows through large deviations that, under stated assumptions on the network connectivity and sensors' observations, the running consensus detection asymptotically approaches in performance the optimal centralized detection. That is, the Bayes probability of detection error (with the running consensus detector) decays exponentially to zero as k → ∞ at the Chernoff information rate-the best achievable rate of the asymptotically optimal centralized detector.
Communication, Control, and Computing (Allerton), 2010 48th Annual Allerton Conference on; 11/2010
-
[show abstract]
[hide abstract]
ABSTRACT: EM multipath propagation is common in radar and wireless communications. Most radar systems are designed assuming line-of-sight (LOS), not multipath. In this paper, we extend our prior work on Multi-Input Multi-Output (MIMO) radar in the absence of interference [1], to consider MIMO radar detection in high clutter. We develop a subspace MIMO target model and a statistical model for MIMO radar clutter that accounts for the spatial and spectral properties of radar returns. We show that, using orthogonal waveform signaling, the time reversal MIMO radar yields higher detection performance than conventional statistical MIMO radar in high clutter.
Electromagnetics in Advanced Applications (ICEAA), 2010 International Conference on; 10/2010
-
[show abstract]
[hide abstract]
ABSTRACT: This paper proposes modeling the rapidly evolving energy systems as cyber-based physical systems. It introduces a novel cyber-based dynamical model whose mathematical description depends on the cyber technologies supporting the physical system. This paper discusses how such a model can be used to ensure full observability through a cooperative information exchange among its components; this is achieved without requiring local observability of the system components. This paper also shows how this cyber-physical model is used to develop interactive protocols between the controllers embedded within the system layers and the network operator. Our approach leads to a synergistic framework for model-based sensing and control of future energy systems. The newly introduced cyber-physical model has network structure-preserving properties that are key to effective distributed decision making. The aggregate load modeling that we develop using data mining techniques and novel sensing technologies facilitates operations of complex electric power systems.
IEEE Transactions on Systems Man and Cybernetics - Part A Systems and Humans 08/2010; · 2.12 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We design the weights in consensus algorithms for spatially correlated random topologies. These arise with 1) networks with spatially correlated random link failures and 2) networks with randomized averaging protocols. We show that the weight optimization problem is convex for both symmetric and asymmetric random graphs. With symmetric random networks, we choose the consensus mean-square error (MSE) convergence rate as the optimization criterion and explicitly express this rate as a function of the link formation probabilities, the link formation spatial correlations, and the consensus weights. We prove that the MSE convergence rate is a convex, nonsmooth function of the weights, enabling global optimization of the weights for arbitrary link formation probabilities and link correlation structures. We extend our results to the case of asymmetric random links. We adopt as optimization criterion the mean-square deviation (MSdev) of the nodes' states from the current average state. We prove that MSdev is a convex function of the weights. Simulations show that significant performance gain is achieved with our weight design method when compared with other methods available in the literature.
IEEE Transactions on Signal Processing 08/2010; · 2.63 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: The paper considers higher dimensional consensus (HDC). HDC is a general class of linear distributed algorithms for large-scale networks that generalizes average-consensus and includes other interesting distributed algorithms, like sensor localization, leader-follower algorithms in multiagent systems, or distributed Jacobi algorithm. In HDC, the network nodes are partitioned into ??anchors??, nodes whose states are fixed over the HDC iterations, and ??sensors??, nodes whose states are updated by the algorithm. The paper starts by briefly considering what we call the forward problem by presenting the conditions for HDC to converge, the limiting state to which it converges, and what is its convergence rate. The main focus of the paper is the inverse or design problem, i.e., learning the weights or parameters of the HDC so that the algorithm converges to a desired prespecified state. This generalizes the well-known problem of designing the weights in average-consensus. We pose learning as a constrained nonconvex optimization problem that we cast in the framework of multiobjective optimization (MOP) and to which we apply Pareto optimality. We derive the solution to the learning problem by proving relevant properties satisfied by the MOP solutions and by the Pareto front. Finally, the paper shows how the MOP approach leads to interesting tradeoffs (speed of convergence versus performance) arising in resource constrained networks. Simulation studies illustrate our approach for a leader-follower architecture in multiagent systems.
IEEE Transactions on Signal Processing 06/2010; · 2.63 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: This paper is concerned with a moving target detection using time reversal in dense multipath environments. We show that the Doppler shift in the time reversal re-transmission simplifies the detector design, yet still achieves the focusing effect. Thus, the Doppler diversity is utilized to achieve high target detectability by time reversal.
Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on; 04/2010 · 4.63 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: In this paper, we study the synthesis problem in linear high dimensional consensus (HDC) algorithms for large-scale networks. In HDC, we partition the network nodes into leaders and followers. Each follower updates its state as a linear combination of its neighboring states, whereas, the state of the leaders remains fixed. Hence, linear HDC can be thought of as a linear time-invariant (LTI) system. The synthesis problem for this LTI system is to design its parameters such that the system converges to a desired pre-specified state. We cast this synthesis problem as a multi-objective optimization problem (MOP) to which we apply Pareto-optimality. We show that the optimal solution of the synthesis problem is a Pareto-optimal (P.O.) solution of the MOP. We then provide a graphical method to extract the optimal MOP solution from the set of all P.O. solutions. Casting the synthesis problem as an MOP naturally lends itself to interesting performance vs speed trade-offs in HDC.
Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on; 04/2010 · 4.63 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: We present an algorithm for distributed sensor localization with noisy distance measurements (DILAND) that extends and makes the DLRE more robust. DLRE is a distributed sensor localization algorithm in R<sup>m</sup> (m ?? 1) introduced in our previous work (IEEE Trans. Signal Process., vol. 57, no. 5, pp. 2000-2016, May 2009). DILAND operates when: 1) the communication among the sensors is noisy; 2) the communication links in the network may fail with a nonzero probability; and 3) the measurements performed to compute distances among the sensors are corrupted with noise. The sensors (which do not know their locations) lie in the convex hull of at least m + 1 anchors (nodes that know their own locations). Under minimal assumptions on the connectivity and triangulation of each sensor in the network, we show that, under the broad random phenomena described above, DILAND converges almost surely (a.s.) to the exact sensor locations.
IEEE Transactions on Signal Processing 04/2010; · 2.63 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: The paper studies the problem of distributed average consensus in sensor networks with quantized data and random link failures. To achieve consensus, dither (small noise) is added to the sensor states before quantization. When the quantizer range is unbounded (countable number of quantizer levels), stochastic approximation shows that consensus is asymptotically achieved with probability one and in mean square to a finite random variable. We show that the mean-squared error (mse) can be made arbitrarily small by tuning the link weight sequence, at a cost of the convergence rate of the algorithm. To study dithered consensus with random links when the range of the quantizer is bounded, we establish uniform boundedness of the sample paths of the unbounded quantizer. This requires characterization of the statistical properties of the supremum taken over the sample paths of the state of the quantizer. This is accomplished by splitting the state vector of the quantizer in two components: one along the consensus subspace and the other along the subspace orthogonal to the consensus subspace. The proofs use maximal inequalities for submartingale and supermartingale sequences. From these, we derive probability bounds on the excursions of the two subsequences, from which probability bounds on the excursions of the quantizer state vector follow. The paper shows how to use these probability bounds to design the quantizer parameters and to explore tradeoffs among the number of quantizer levels, the size of the quantization steps, the desired probability of saturation, and the desired level of accuracy ?? away from consensus. Finally, the paper illustrates the quantizer design with a numerical study.
IEEE Transactions on Signal Processing 04/2010; · 2.63 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: Time reversal explores the rich scattering in a multipath environment to achieve high target detectability. Multiple-input multiple-output (MIMO) radar is an emerging active sensing technology that uses diverse waveforms transmitted from widely spaced antennas to achieve increased target sensitivity when compared to standard phased arrays. In this paper, we combine MIMO radar with time reversal to automatically match waveforms to a scattering channel and further improve the performance of radar detection. We establish a radar target model in multipath rich environments and develop likelihood ratio tests for the proposed time-reversal MIMO radar (TR-MIMO). Numerical simulations demonstrate improved target detectability compared with the commonly used statistical MIMO strategy.
IEEE Journal of Selected Topics in Signal Processing 03/2010; · 2.88 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: In this paper, we propose a linear complexity encoding method for arbitrary LDPC codes. We start from a simple graph-based encoding method ¿label-and-decide.¿ We prove that the ¿label-and-decide¿ method is applicable to Tanner graphs with a hierarchical structure-pseudo-trees-and that the resulting encoding complexity is linear with the code block length. Next, we define a second type of Tanner graphs-the encoding stopping set. The encoding stopping set is encoded in linear complexity by a revised label-and-decide algorithm-the ¿label-decide-recompute.¿ Finally, we prove that any Tanner graph can be partitioned into encoding stopping sets and pseudo-trees. By encoding each encoding stopping set or pseudo-tree sequentially, we develop a linear complexity encoding method for general low-density parity-check (LDPC) codes where the encoding complexity is proved to be less than 4 ·M ·(( k¿ - 1), where M is the number of independent rows in the parity-check matrix and k¿ represents the mean row weight of the parity-check matrix.
IEEE Transactions on Information Theory 02/2010; · 3.01 Impact Factor
-
[show abstract]
[hide abstract]
ABSTRACT: In this paper, we review our work on distributed sensor localization using barycentric coordinates. We present an algorithm for localization in m-dimensional Euclidean spaces. The algorithm is distributed and requires at least m + 1 anchors. Anchors are the nodes that know their exact locations. We require that the nonanchor nodes (all the network nodes that do not know their locations) lie in the convex hull of at least m + 1 anchors. Using barycentric coordinates, each non-anchor node updates its location estimate as a linear combination of its (carefully chosen) neighboring nodes. Under minimal network connectivity assumptions, we show that the distributed localization algorithm converges to the exact sensor locations. We further extend the localization algorithm to include imperfect barycentric computation, communication link failures, and communication noise. We show that, with the aid of stochastic approximation, the localization algorithm converges almost surely to the exact locations under the random phenomena described before.
Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2009 3rd IEEE International Workshop on; 01/2010
