Estimating the unknown parameters of a statistical model based on the observations collected by a sensor network is an important problem with application in multiple fields. In this setting, distributed processing, by which computations are carried out within the network in order to avoid raw data transmission to a fusion centre, is a desirable feature resulting in improved robustness and energy savings. In the presence of incomplete data, the expectation-maximisation (EM) algorithm is a popular means to iteratively compute the maximum likelihood (ML) estimate. It has found application in diverse fields such as computational biology, anomaly detection, speech segmentation, reinforcement learning, and motion estimation, among others. In this chapter we will review the formulation of the centralised EM estimation algorithm as a starting point and then discuss distributed versions well suited for implementation in sensor networks. The first class of these distributed versions requires specialised routing through the network in terms of a linear or circular path visiting all nodes, whereas the second class does away with this requirement by using the concept of network consensus to diffuse information through the network. Our focus will be on a relevant sensor network application, in which the parameter of a linear model is to be estimated in the presence of an unknown number of randomly malfunctioning sensors.

%B Data Fusion in Wireless Sensor Networks: A statistical signal processing perspective %I The Institution of Engineering and Technology (IET) %C London, UK %P 201-230 %@ 978-1-78561-584-9 %G eng %& 9 %0 Journal Article %J Signal Processing %D 2018 %T Parameter estimation in wireless sensor networks with faulty transducers: A distributed EM approach %A Silvana Silva Pereira %A R. López-Valcarce %A Alba Pagès-Zamora %K winter %K wsn %XWe address the problem of distributed estimation of a vector-valued parameter performed by a wireless sensor network in the presence of noisy observations which may be unreliable due to faulty transducers. The proposed distributed estimator is based on the Expectation-Maximization (EM) algorithm and combines consensus and diffusion techniques: a term for information diffusion is gradually turned off, while a term for updated information averaging is turned on so that all nodes in the network approach the same value of the estimate. The proposed method requires only local exchanges of information among network nodes and, in contrast with previous approaches, it does not assume knowledge of the a priori probability of transducer failures or the noise variance. A convergence analysis is provided, showing that the convergent points of the centralized EM iteration are locally asymptotically convergent points of the proposed distributed scheme. Numerical examples show that the distributed algorithm asymptotically attains the performance of the centralized EM method.

%B Signal Processing %V 144 %P 226-237 %8 03/2018 %G eng %U https://authors.elsevier.com/a/1W90XbZX4rsob %R 10.1016/j.sigpro.2017.10.012 %0 Journal Article %J Digital Signal Processing %D 2017 %T CDMA-based Acoustic Local Positioning System for Portable Devices with Multipath Cancellation %A Fernando J. Alvarez %A Teodoro Aguilera %A R. López-Valcarce %K compass %K wsn %XThis paper presents an acoustic local positioning system (ALPS) suitable for indoor positioning

of portable devices such as smartphones or tablets, based on the transmission of high frequency

CDMA-coded signals from a fixed network of beacons. The main novelty of the proposed ALPS is

its capability to mitigate the effects of multipath propagation by performing an accurate estimation

of the Line-of-Sight Time-of-Flights (LOS-TOF) through the Matching Pursuit algorithm. Signal

detection, multipath cancellation and positioning estimation all take place within the portable device,

which provides a graphical representation of the updated position in less than a second. The

performance of the Matching Pursuit algorithm is analyzed in a real scenario and the results show

that the proposed method is capable to retrieve the multipath-free System Availability under strong

multipath conditions with SNR levels as low as 0 dB.

%B Digital Signal Processing
%V 62
%P 38-51
%8 03/2017
%G eng
%R 10.1016/j.dsp.2016.11.001
%0 Conference Paper
%B European Signal Processing Conference (EUSIPCO)
%D 2017
%T Defending Surveillance Sensor Networks Against Data-Injection Attacks via Trusted Nodes
%A R. López-Valcarce
%A Daniel Romero
%K winter
%K wsn
%X By injecting false data through compromised sensors, an adversary can drive the probability of detection in a sensor network-based spatial field surveillance system to arbitrarily low values. As a countermeasure, a small subset of sensors may be secured. Leveraging the theory of Matched Subspace Detection, we propose and evaluate several detectors that add robustness to attacks when such trusted nodes are available. Our results reveal the performance-security tradeoff of these schemes and can be used to determine the number of trusted nodes required for a given performance target.

%B European Signal Processing Conference (EUSIPCO)
%C Kos Island, Greece
%8 08/2017
%G eng
%0 Journal Article
%J IEEE Transactions on Signal Processing
%D 2017
%T Learning Power Spectrum Maps from Quantized Power Measurements
%A Daniel Romero
%A Seung-Jun Kim
%A Georgios Giannakis
%A R. López-Valcarce
%K cognitive radio
%K compass
%K compressed sensing
%K spectrum sensing
%K winter
%K wsn
%X Using power measurements collected by a network of low-cost sensors, power spectral density (PSD) maps are con-

structed to capture the distribution of RF power across space and frequency. Linearly compressed and quantized power measure-

ments enable wideband sensing at affordable implementation complexity using a small number of bits. Strengths of data- and model-

driven approaches are combined to develop estimators capable of incorporating multiple forms of spectral and propagation prior

information while fitting the rapid variations of shadow fading across space. To this end, novel nonparametric and semiparametric

formulations are investigated. It is shown that the desired PSD maps can be obtained using support vector machine-type solvers.

In addition to batch approaches, an online algorithm attuned to real-time operation is developed. Numerical tests assess the performance of the novel algorithms.

%B IEEE Transactions on Signal Processing
%V 65
%P 2547-2560
%8 05/2017
%G eng
%N 10
%R 10.1109/TSP.2017.2666775
%0 Conference Paper
%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
%D 2017
%T Robust clustering of data collected via crowdsourcing
%A Alba Pagès-Zamora
%A Georgios Giannakis
%A R. López-Valcarce
%A Pere Gimenez-Febrer
%K winter
%K wsn
%X Crowdsourcing approaches rely on the collection of multiple individuals to solve problems that require analysis of large data sets in a timely accurate manner. The inexperience of participants or annotators motivates well robust techniques. Focusing on clustering setups, the data provided by all annotators is suitably modeled here as a mixture of Gaussian components plus a uniformly distributed random variable to capture outliers. The proposed algorithm is based on the expectation-maximization algorithm and allows for soft assignments of data to clusters, to rate annotators according to their performance, and to estimate the number of Gaussian components in the non-Gaussian/Gaussian mixture model, in a jointly manner.

%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) %C New Orleans %P 4014 - 4018 %8 03/2017 %G eng %R 10.1109/ICASSP.2017.7952910 %0 Conference Paper %B IEEE Workshop on Statistical Signal Processing (SSP) %D 2016 %T Design of data-injection adversarial attacks against spatial field detectors %A R. López-Valcarce %A Daniel Romero %K adversarial signal processing %K compass %K wsn %XData-injection attacks on spatial field detection corrupt a subset of measurements to cause erroneous decisions. We consider a centralized decision scheme exploiting spatial field smoothness to overcome lack of knowledge on system parameters such as noise variance. We obtain closed-form expressions for system performance and investigate strategies for an intruder injecting false data in a fraction of the sensors in order to reduce the probability of detection. The problem of determining the most vulnerable subset of sensors is also analyzed.

%B IEEE Workshop on Statistical Signal Processing (SSP) %C Palma de Mallorca, Spain %8 06/2016 %G eng %0 Conference Paper %B IEEE Workshop on Statistical Signal Processing (SSP) %D 2016 %T Distributed multivariate regression with unknown noise covariance in the presence of outliers: a minimum description length approach %A R. López-Valcarce %A Daniel Romero %A Josep Sala %A Alba Pagès-Zamora %K compass %K wsn %XWe consider the problem of estimating the coefficients in a multivariable linear model by means of a wireless sensor network

which may be affected by anomalous measurements. The noise covariance matrices at the different sensors are assumed

unknown. Treating outlying samples, and their support, as additional nuisance parameters, the Maximum Likelihood

estimate is investigated, with the number of outliers being estimated according to the Minimum Description Length

principle. A distributed implementation based on iterative consensus techniques is then proposed, and it is shown effective

for managing outliers in the data.

%B IEEE Workshop on Statistical Signal Processing (SSP)
%C Palma de Mallorca, Spain
%G eng
%0 Conference Paper
%B European Signal Processing Conference (EUSIPCO)
%D 2016
%T Online EM-based distributed estimation in sensor networks with faulty nodes
%A Pere Gimenez-Febrer
%A Alba Pagès-Zamora
%A R. López-Valcarce
%K compass
%K wsn
%X This paper focuses on the problem of the distributed estimation of a parameter vector based on noisy observations regularly acquired by the nodes of a wireless sensor network and assuming that some of the nodes have faulty sensors. We propose two online schemes, both centralized and distributed, based on the Expectation-Maximization (EM) algorithm. These algorithms are able to identify and disregard the faulty nodes, and provide a refined estimate of the parameters each time instant after a new set of observations is acquired. Simulation results demonstrate that the centralized versions of the proposed online algorithms attain the same estimation error as the centralized batch EM, whereas the distributed versions come very close to matching the batch EM.

%B European Signal Processing Conference (EUSIPCO)
%C Budapest, Hungary
%8 09/2016
%G eng
%0 Conference Paper
%B European Signal Processing Conf. (EUSIPCO)
%D 2015
%T Attack detectors for data aggregation in clustered sensor networks
%A R. López-Valcarce
%A Daniel Romero
%K adversarial signal processing
%K compass
%K wsn
%X Among many security threats to sensor networks, compromised sensing is particularly challenging due to the fact that it cannot be addressed by standard authentication approaches. We consider a clustered scenario for data aggregation in which an attacker injects a disturbance in sensor readings. Casting the problem in an estimation framework, we systematically apply the Generalized Likelihood Ratio approach to derive attack detectors. The analysis under different attacks reveals that detectors based on similarity of means across

clusters are suboptimal, with Bartlett’s test for homoscedasticity constituting a good candidate when lacking a priori knowledge of the variance of the underlying distribution.

%B European Signal Processing Conf. (EUSIPCO)
%I EURASIP
%C Nice, France
%P 2098-2102
%8 accepted
%G eng
%0 Conference Paper
%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
%D 2015
%T Distributed AoA-based Source Positioning in NLOS with Sensor Networks
%A Pere Gimenez-Febrer
%A Alba Pagès-Zamora
%A Silvana Silva Pereira
%A R. López-Valcarce
%K compass
%K wsn
%X This paper focuses on the problem of positioning a source using angle-of-arrival measurements taken by a wireless sensor network in which some of the nodes experience non-line-of-sight (NLOS) propagation conditions. In order to mitigate the errors induced by the nodes in NLOS, we derive an algorithm that combines the expectation-maximization algorithm with a weighted least-squares estimation of the source position so that the nodes in NLOS are eventually identified and discarded. Moreover, a distributed version of this algorithm based on a diffusion strategy that iteratively refines the position estimate while driving the network to a consensus is presented.

%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
%I IEEE
%C Brisbane, Australia
%8 04/2015
%G eng
%0 Conference Paper
%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
%D 2015
%T Distributed TLS Estimation under Random Data Faults
%A Silvana Silva Pereira
%A Alba Pagès-Zamora
%A R. López-Valcarce
%K compass
%K wsn
%X This paper addresses the problem of distributed estimation of a parameter vector in the presence of noisy input and output data as well as data faults, performed by a wireless sensor network in which only local interactions among the nodes are allowed. In the presence of unreliable observations, standard estimators become biased and perform poorly in low signal-to-noise ratios. We propose two different distributed approaches based on the Expectation-Maximization algorithm: in the first one the regressors are estimated at each iteration,

whereas the second one does not require explicit regressor estimation. Numerical results show that the proposed methods approach the performance of a clairvoyant scheme with knowledge of the random data faults.

%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)
%I IEEE
%C Brisbane, Australia
%8 04/2015
%G eng
%0 Thesis
%D 2015
%T Estimation, Detection, and Learning for Dynamic Spectrum Access
%A Daniel Romero
%K cognitive radio
%K compass
%K dynacs
%K wsn
%I University of Vigo
%C Vigo, Spain
%V Ph.D.
%8 05/2015
%G eng
%9 Ph.D. Thesis
%0 Journal Article
%J Information Processing Letters
%D 2015
%T A Greedy Topology Design to Accelerate Consensus in Broadcast Wireless Sensor Networks
%A Massimo Vecchio
%A R. López-Valcarce
%K compass
%K wsn
%X We present techniques to improve convergence speed of distributed average consensus algorithms in wireless sensor networks by means of topology design. A broadcast network is assumed, so that only the transmit power of each node can be independently controlled, rather than each individual link. Starting with a maximally connected configuration in which all nodes transmit at full power, the proposed methods successively reduce the transmit power of a chosen node in order to remove one and only one link; nodes are greedily selected either in order to yield fastest convergence at each step, or if they have the largest degree in the network. These greedy schemes provide a good complexity-performance tradeoff with respect to full-blown global search methods. As a side benefit, improving the convergence speed also results in savings in energy consumption with respect to the maximally connected setting.

%B Information Processing Letters %V 115 %P 408-413 %8 03/2015 %G eng %N 3 %& 408 %R 10.1016/j.ipl.2014.11.009 %0 Journal Article %J Journal of Network and Computer Applications %D 2015 %T Improving Area Coverage of Wireless Sensor Networks Via Controllable Mobile Nodes: a Greedy Approach %A Massimo Vecchio %A R. López-Valcarce %K compass %K wsn %XReliable wide-area monitoring with Wireless Sensor Networks (WSNs) remains a problem of

interest: simply deploying more nodes to cover wider areas is generally not a viable solution, due to

deployment and maintenance costs and the increase in radio interference. One possible solution

gaining popularity is based on the use of a reduced number of mobile nodes with controllable

trajectories in the monitored field. In this framework, we present a distributed technique for iteratively

computing the trajectories of the mobile nodes in a greedy fashion. The static sensor nodes actively

assist the mobile nodes in this task by means of a bidding protocol, thus participating towards the goal

of maximizing the area coverage of the monitored field. The performance of the proposed technique is

evaluated on various simulation scenarios with different number of mobile and static nodes in terms of

achieved coverage and mean time to achieve X% coverage. Comparison with previous state-of-the-art

techniques reveals the effectiveness and stability of the proposed method.

%B Journal of Network and Computer Applications
%V 48
%P 1-13
%8 02/2015
%G eng
%R 10.1016/j.jnca.2014.10.007
%0 Conference Paper
%B IEEE 9th International Symposium on Intelligent Signal Processing (WISP)
%D 2015
%T Multipath cancellation in broadband acoustic local positioning systems
%A Fernando J. Alvarez
%A R. López-Valcarce
%K compass
%K wsn
%X This work proposes a novel method to estimate the Line-of-Sight Time-of-Flights (LOS-TOFs) in a broadband acoustic local positioning system (ALPS) with strong multipath interference. The proposed method is based on the Matching Pursuit channel estimation algorithm that provides a low complexity approximation to the Maximum Likelihood solution for sparse channels. A multichannel version of this algorithm has been implemented to estimate a minimum of three coefficients in the channel responses of a particular ALPS, composed of four beacons that perform the simultaneous emission of BPSK modulated 255-bit Kasami codes. A statistical analysis of performance has been carried out by using a set of test signals synthetically generated to simulate different positions and reflection coefficients of the environment. The results of this analysis show the enhanced capability of the proposed method to estimate the LOS-TOFs under strong multipath interference, with respect to that of a classical system based on correlation + thresholding.

%B IEEE 9th International Symposium on Intelligent Signal Processing (WISP) %I IEEE %C Siena, Italy %8 05/2015 %G eng %R 10.1109/WISP.2015.7139174 %0 Conference Paper %B IEEE Sensor Array Multichannel Signal Process. Workshop (SAM) %D 2014 %T Cooperative compressive power spectrum estimation %A Dyonisius D Ariananda %A Daniel Romero %A Geert Leus %K cognitive radio %K wsn %B IEEE Sensor Array Multichannel Signal Process. Workshop (SAM) %G eng %0 Conference Paper %B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) %D 2014 %T Distributed Total Least Squares Estimation over Networks %A R. López-Valcarce %A Silvana Silva Pereira %A Alba Pagès-Zamora %K dynacs %K wsn %XWe consider Total Least Squares (TLS) estimation in a network in which each node has access to a subset of equations of an overdetermined linear system. Previous distributed approaches require that the number of equations at each node be larger than the dimension L of the unknown parameter. We present novel distributed TLS estimators which can handle as few as a single equation per node. In the first scheme, the network computes an extended correlation matrix via standard iterative average consensus techniques, and the TLS estimate is extracted afterwards by means of an eigenvalue decomposition (EVD). The second scheme is EVD-free, but requires that a linear system of size L be solved at each iteration by each node. Replacing this step by a single Gauss-Seidel subiteration is shown to be an effective means to reduce computational cost without sacrificing performance.

%B IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) %C Florence, Italy %G eng %R 10.1109/ICASSP.2014.6855074 %0 Conference Paper %B IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM) %D 2014 %T How to Implement Doubly-Stochastic Matrices for Consensus-Based Distributed Algorithms %A S. Valcárcel-Macua %A C. Moreno-León %A J. S. Romero %A Silvana Silva Pereira %A Javier Zazo %A Alba Pagès-Zamora %A R. López-Valcarce %A S. Zazo %K compass %K dynacs %K wsn %XDoubly-stochastic matrices are usually required by

consensus-based distributed algorithms. We propose a simple

and efficient protocol and present some guidelines for implementing

doubly-stochastic combination matrices even in noisy,

asynchronous and changing topology scenarios. The proposed

ideas are validated with the deployment of a wireless sensor

network, in which nodes run a distributed algorithm for robust

estimation in the presence of nodes with faulty sensors.

%B IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)
%C A Coruña, Spain
%G eng
%R 10.1109/SAM.2014.6882409
%0 Journal Article
%J Engineering Applications of Artificial Intelligence
%D 2013
%T On the design of a novel two-objective harmony search approach for distance- and connectivity-based localization in wireless sensor networks
%A Diana Manjarres
%A Javier Del Ser
%A Sergio Gil-Lopez
%A Massimo Vecchio
%A Itziar Landa-Torres
%A Sancho Salcedo-Sanz
%A R. López-Valcarce
%K dynacs
%K wsn
%B Engineering Applications of Artificial Intelligence
%V 26
%P 669-676
%8 02/2013
%G eng
%N 2
%& 669
%R 10.1016/j.engappai.2012.06.002
%0 Conference Paper
%B Int. Conf. Acoust., Speech, Signal Process. (ICASSP)
%D 2013
%T A Diffusion-based distributed EM algorithm for density estimation in wireless sensor networks
%A Silvana Silva Pereira
%A Alba Pagès-Zamora
%A R. López-Valcarce
%K dynacs
%K wsn
%X Distributed implementations of the Expectation-Maximization

(EM) algorithm reported in the literature have been proposed for

applications to solve specific problems. In general, a primary

requirement to derive a distributed solution is that the

structure of the centralized version enables the computation

involving global information in a distributed fashion. This

paper treats the problem of distributed estimation of Gaussian

densities by means of the EM algorithm in wireless sensor

networks using diffusion strategies, where the information

is gradually diffused across the network for the computation

of the global functions. The low-complexity implementation

presented here is based on a two time scale operation

for information averaging and diffusion. The convergence to

a fixed point of the centralized solution has been studied and

the appealing results motivates our choice for this model. Numerical

examples provided show that the performance of the

distributed EM is, in practice, equal to that of the centralized

scheme.

%B Int. Conf. Acoust., Speech, Signal Process. (ICASSP)
%G eng
%R 10.1109/ICASSP.2013.6638501
%0 Journal Article
%J IEEE Signal Processing Letters
%D 2013
%T A Diffusion-Based EM Algorithm for Distributed Estimation in Unreliable Sensor Networks
%A Silvana Silva Pereira
%A R. López-Valcarce
%A Alba Pagès-Zamora
%K dynacs
%K wsn
%X We address the problem of distributed estimation of a parameter from a set of noisy observations collected by a sensor network, assuming that some sensors may be subject to data failures and report only noise. In such scenario, simple schemes such as the Best Linear Unbiased Estimator result in an error floor in moderate and high signal-to-noise ratio (SNR), whereas previously proposed methods based on hard decisions on data failure events degrade as the SNR decreases. Aiming at optimal performance within the whole range of SNRs, we adopt a Maximum Likelihood framework based on the Expectation-Maximization (EM) algorithm. The statistical model and the iterative nature of the EM method allow for a diffusion-based distributed implementation, whereby the information propagation is embedded in the iterative update of the parameters. Numerical examples show that the proposed algorithm practically attains the Cramer–Rao Lower Bound at all SNR values and compares favorably with other approaches.

%B IEEE Signal Processing Letters %V 20 %P 595-598 %8 06/2013 %G eng %N 6 %& 595 %R 10.1109/LSP.2013.2260329 %0 Journal Article %J Soft Computing %D 2013 %T A novel heuristic approach for distance- and connectivity-based multihop node localization in wireless sensor networks %A Diana Manjarres %A Javier Del Ser %A Sergio Gil-Lopez %A Massimo Vecchio %A Itziar Landa-Torres %A R. López-Valcarce %K dynacs %K wsn %B Soft Computing %V 17 %P 17-28 %8 01/2013 %G eng %N 1 %& 17 %R 10.1007/s00500-012-0897-2 %0 Journal Article %J Applied Soft Computing %D 2011 %T A two-objective evolutionary approach based on topological constraints for node localization in wireless sensor networks %A Massimo Vecchio %A R. López-Valcarce %A Francesco Marcelloni %K dynacs %K Multiobjective evolutionary algorithms %K Node localization %K Range measurements %K Stochastic optimization %K wsn %XTo know the location of nodes plays an important role in many current and envisioned wireless sensor network applications. In this framework, we consider the problem of estimating the locations of all the nodes of a network, based on noisy distance measurements for those pairs of nodes in range of each other, and on a small fraction of anchor nodes whose actual positions are known a priori. The methods proposed so far in the literature for tackling this non-convex problem do not generally provide accurate estimates. The difficulty of the localization task is exacerbated by the fact that the network is not generally uniquely localizable when its connectivity is not sufficiently high. In order to alleviate this drawback, we propose a two-objective evolutionary algorithm which takes concurrently into account during the evolutionary process both the localization accuracy and certain topological constraints induced by connectivity considerations. The proposed method is tested with different network configurations and sensor setups, and compared in terms of normalized localization error with another metaheuristic approach, namely SAL, based on simulated annealing. The results show that, in all the experiments, our approach achieves considerable accuracies and significantly outperforms SAL, thus manifesting its effectiveness and stability.

%B Applied Soft Computing %V 12 %P 1891-1901 %8 07/2012 %G eng %N 7 %R 10.1016/j.asoc.2011.03.012