Vincenzo Matta

Distributed Detection in the Presence of Byzantine Attacks

Distributed detection in the presence of cooperative (Byzantine) attack is considered. It is assumed that a fraction of the monitoring sensors are compromised by an adversary, and these compromised (Byzantine) sensors are reprogrammed to transmit fictitious observations aimed at confusing the decision maker at the fusion center. For detection under binary hypotheses with quantized sensor observations, the optimal attacking distributions for Byzantine sensors that minimize the detection error exponent are obtained using a ldquowater-fillingrdquo procedure. The smallest error exponent, as a function of the Byzantine sensor population, characterizes the power of attack. Also obtained is the minimum fraction of Byzantine sensors that destroys the consistency of detection at the fusion center. The case when multiple measurements are made at the remote nodes is also considered, and it is shown that the detection performance scales with the number of sensors differently from the number of observations at each sensor.

Asymptotic Optimality of Running Consensus in Testing Binary Hypotheses

Consensus in sensor networks is a procedure to corroborate the local measurements of the sensors with those of the surrounding nodes, and leads to a final agreement about a common value that, in detection applications, represents the decision statistic. As the amount of collected data increases, the convergence toward the final statistic is ruled by suitable scaling laws, and the question arises if the asymptotic (large sample) properties of a detection statistic are retained when this statistic is approximated via consensus algorithms. We investigate the asymptotic properties of running consensus detectors both under the Neyman-Pearson paradigm (fixed number of data) and in the sequential case. An appropriate asymptotic framework is developed, and exact theoretical results are provided, showing the asymptotic optimality of the running consensus detector. In addition, numerical experiments are performed to address nonasymptotic scenarios.

Enforcing Consensus While Monitoring the Environment in Wireless Sensor Networks

In many environmental monitoring applications of Wireless Sensor Networks (WSNs), safe information retrieval from any subset of sensors, at an arbitrary instant of time, should be guaranteed. Accordingly, we study the behavior of a WSN that continuously senses the surrounding environment, while consensus among its nodes is simultaneously enforced. For this running consensus scheme, analytical bounds in terms of consensus degree and comparison with an ideal centralized system are provided, and example of applications are presented.

Distributed Detection With Censoring Sensors Under Physical Layer Secrecy

We consider distributed binary detection problems in which the remote sensors of a network implement a censoring strategy to fulfill energy constraints, and the network works under the attack of an eavesdropper. The attacker wants to discover the state of the nature scrutinized by the system, but the network implements appropriate countermeasures to make this task hopeless. The goal is to achieve perfect secrecy at the physical layer, making the data available at the eavesdropper useless for its detection task. Adopting as performance metric certain Ali-Silvey distances, we characterize the detection performance of the system under physical layer secrecy. Two communication scenarios are addressed: parallel access channels and a multiple access channel. In both cases the optimal operative points from the network perspective are found. The most economic operative solution is shown to lie in the asymptote of low energy regime. How the perfect secrecy requirement impacts on the achievable performances, with respect to the absence of countermeasures, is also investigated.

Bayesian Tracking in Underwater Wireless Sensor Networks With Port-Starboard Ambiguity

Port-starboard ambiguity is an important issue in underwater tracking systems with anti-submarine warfare applications, especially for wireless sensor networks based upon autonomous underwater vehicles. In monostatic systems this ambiguity leads to a ghost track of the target symmetrically displaced with respect to the sensor. Removal of such artifacts is usually made by rough and heuristic approaches. In the context of Bayesian filtering approximated by means of particle filtering techniques, we show that optimal disambiguation can be pursued by deriving the full Bayesian posterior distribution of the target state. The analysis is corroborated by simulations that show the effectiveness of the particle-filtering tracking. A full validation of the approach relies upon real-world experiments conducted by the NATO Science and Technology Organization - Centre for Maritime Research and Experimentation during the sea trials Generic Littoral Interoperable Network Technology 2011 and Exercise Proud Manta 2012, results which are also reported.

Asymptotic Efficiency of the PHD in Multitarget/Multisensor Estimation

Tracking an unknown number of objects is challenging, and often requires looking beyond classical statistical tools. When many sensors are available the estimation accuracy can reasonably be expected to improve, but there is a concomitant rise in the complexity of the inference task. Nowadays, several practical algorithms are available for multitarget/multisensor estimation and tracking. In terms of current research activity one of the most popular is the probability hypothesis density, commonly referred to as the PHD, in which the goal is estimation of object locations (unlabeled estimation) without concern for object identity (which is which). While it is relatively well understood in terms of its implementation, little is known about its performance and ultimate limits. This paper is focused on the characterization of PHD estimation performance for the static multitarget case, in the limiting regime where the number of sensors goes to infinity. It is found that the PHD asymptotically behaves as a mixture of Gaussian components, whose number is the true number of targets, and whose peaks collapse in the neighborhood of the classical maximum likelihood estimates, with a spread ruled by the Fisher information. Similar findings are obtained with reference to a naïve, two-step algorithm which first detects the number of targets, and then estimates their positions.

Distributed Estimation in Large Wireless Sensor Networks via a Locally Optimum Approach

A wireless sensor network (WSN) engaged in a decentralized estimation problem is considered. The nonrandom unknown parameter lies in some small neighborhood of a nominal value and, exploiting this knowledge, a locally optimum estimator (LOE) is introduced. Under the LOE paradigm, the sensors of the network process their observations by means of a suitable nonlinearity (the score function), before delivering data to the fusion center that outputs the final estimate. Usually continuous-valued data cannot be reliably delivered from sensors to the fusion center, and some form of data compression is necessary. Accordingly, we design the scalar quantizers that must be used at the networks nodes in order to comply with the estimation problem at hand. Such a difficult multiterminal inference problem is shown to be asymptotically equivalent to the already solved problem of designing optimum quantizers for reconstruction (as opposed to inference) purposes.

Consensus-based Page's test in sensor networks

Pages test is a well-known statistical technique to approach quickest detection problems, namely the detection of an abrupt change in the statistical distribution of a certain monitored phenomenon. Running consensus is a recently proposed signal processing procedure aimed at reaching agreement among the nodes of a fully flat network, and its peculiar feature is the simultaneity of two stages: that of acquiring new measurements by the sensors, and that of data fusion involving inter-sensor communications. In this paper we study a quickest detector based on the running consensus scheme, and compare it to a bank of independent Pages tests. Exploiting insights from previous studies, we propose closed-form analytical approximations of the performances of these detection schemes and address a comparison in terms of relative efficiencies. The approximated performance figures are then checked by simulation to validate the analysis and to investigate non-asymptotic scenarios.

Sequential Sampling in Sensor Networks for Detection With Censoring Nodes

A wireless sensor network designed according to the sensor network with mobile agents (SENMA) architecture is engaged in a detection task, with a mobile agent (MA) that sequentially queries the networks nodes. The focus is on the effect of censoring: sensors respond to the query from the MA only if the local observations are deemed sufficiently informative; otherwise, they stay silent. Delivered data, if any, can be either unquantized or quantized to a single bit. The study is limited to shift-in-mean problems, involving two simple statistical hypotheses, where the noise distribution must be an even function but is otherwise arbitrary. Simple analytical relationships characterizing the tradeoff between the detection delay and the energy consumption of the network are derived, and examples of their applications are provided.

A Likelihood-Based Multiple Access for Estimation in Sensor Networks

In a wireless sensor network (WSN), the nodes collect independent observations about a nonrandom parameter thetas to be estimated, and deliver informations to a fusion center (FC) by transmitting suitable waveforms through a common multiple access channel (MAC). The FC implements some appropriate fusion rule and outputs the final estimate of thetas. In this paper, we introduce a new access/estimation scheme, here referred to as likelihood-based multiple access (LBMA), and prove it to be asymptotically efficient in the limit of increasingly large number of sensors , when the used bandwidth is allowed to scale as W ~capalpha,O.5 < alpha < 1 . The proposed approach is easy to implement, and simply relies upon the very basic property that the log likelihood is additive for independent observations, and upon the fact that the (noiseless) output of the MAC is just the sum of its inputs. Thus, the optimal fusion rule is automatically implemented by the MAC itself.