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In this paper, we consider the problem of designing and implementing a distributed strategy to estimate the channel parameters for a generic Wireless Sensor-Actor Network. To this aim, we present a distributed least-square algorithm that complies with the constraint of transmitting only integer data through the wireless communication, which often is required in Wireless Sensor-Actor Network embedded architectures. In this respect, we propose a quantized consensus strategy that mitigates the effects of the rounding operations applied to the wireless exchanged floating data. Formally based on a symmetric random gossip strategy, an open-source application designed to implement the distributed algorithm is also presented. Finally, the effectiveness of the proposed algorithm is illustrated through the application to radio-frequency localization experiments in a real world testbed, comparing its performances with those of a centralized strategy.

The paper considers the classification problem using Support Vector Machines, and investigates how to maximally reduce the size of the training set without losing information. Under linearly separable dataset assumptions, we derive the exact conditions stating which observations can be discarded without diminishing the overall information content. For this purpose, we introduce the concept of Potential Support Vectors, i.e., those data that can become Support Vectors when future data become available. Complementary, we also characterize the set of Discardable Vectors, i.e., those data that, given the current dataset, can never become Support Vectors. These vectors are thus useless for future training purposes, and can eventually be removed without loss of information. We then provide an efficient algorithm based on linear programming which returns the potential and discardable vectors by constructing a simplex tableau. Finally we compare it with alternative algorithms available in the literature on some synthetic data as well as on datasets from standard repositories.

We address the problem of distributed unconstrained convex optimization under separability assumptions, i.e., the framework where a network of agents, each endowed with local private multidimensional convex cost and subject to communication constraints, wants to collaborate to compute the minimizer of the sum of the local costs. We propose a design methodology that combines average consensus algorithms and separation of time-scales ideas. This strategy is proven, under suitable hypotheses, to be globally convergent to the true minimizer. Intuitively, the procedure lets the agents distributedly compute and sequentially update an approximated Newton-Raphson direction by means of suitable average consensus ratios. We show with numerical simulations that the speed of convergence of this strategy is comparable with alternative optimization strategies such as the Alternating Direction Method of Multipliers. Finally, we propose some alternative strategies which trade-off communication and computational requirements with convergence speed.

In this work the design and implementation of an application to track multiple agents in a indoor Wireless Sensor Actor Network (WSAN) is proposed. We developed a tracking algorithm that falls into the category of the radio frequency localization/tracking methods, that exploit the strength of the wireless communications among fixed and mobile agents to establish the position of the mobile ones. The algorithm resorts to an Extended Kalman Filter to process the agents measurements and reach a desired level of tracking performance. The tracking application, namely Teseo, is composed by a low-level NesC management software for the agents side and a Java graphical interface provided to users connected to mobile agents. A detailed description of the operations performed by Teseo is given, accompanied both by simulations to validate the tracking algorithm and experiments on a real testbed to test Teseo.

This paper considers a variation of the 17$^{\text{th}}$ century problem commonly known as the Newton-Pepys problem, or the John Smith's problem. We provide its solution, interpreting the result in terms of maximum likelihood estimation and Ockham's razor. In addition, we illustrate the practical relevance of these findings for solving size-estimation problems, and in particular for determining the number of agents in a wireless sensor network.

The request for very accurate 3D reconstruction in several applications is leading to the development of very large motion capture systems. A good synchronization of all the cameras in the system is of fundamental importance to guarantee the effectiveness of the 3D reconstruction.
In this work, first, an approximation of the reconstruction error variance taking into account of synchronization errors is derived. Then, a Kalman filter approach is considered to estimate the cameras synchronization errors. The estimated delays can be used to compensate the synchronization error effect on the reconstruction of target positions. The results obtained in some simulations suggest that the proposed strategy allows to obtain a significant reduction of the 3D reconstruction error.

We consider the distributed unconstrained minimization of separable convex costfunctions, where the global cost is given by the sum of several local and private costs, eachassociated to a specific agent of a given communication network. We specifically address anasynchronous distributed optimization technique called Newton-Raphson consensus. Besidehaving low computational complexity, low communication requirements and being interpretableas a distributed Newton-Raphson algorithm, the technique has also the beneficial properties ofrequiring very little coordination and naturally support time-varying topologies. In this workwe analytically prove that under some assumptions it shows local convergence properties, andcorroborate this result by means of numerical simulations.

In this paper we focus on collaborative wireless sensor networks, where agents are randomly distributed over a region of interest and collaborate to achieve a common estimation goal. In particular, we introduce two consensus-based distributed linear estimators. The first one is designed for a Bayesian scenario, where an unknown common finite-dimensional parameter vector has to be reconstructed,  while the second one  regards the nonparametric reconstruction of an unknown function sampled at different locations by the sensors. Both of the algorithms are characterized in terms of the trade-off between estimation performance, communication, computation and memory complexity. In the finite-dimensional setting, we derive mild sufficient conditions which ensure that distributed estimator performs better than the local optimal ones in terms of estimation error variance. In the nonparametric setting, we introduce an on-line algorithm that allows the agents both to compute the function estimate with small computational, communication and data storage efforts, and to quantify its distance from the centralized estimate given by a Regularization Network, one of the most powerful regularized kernel methods. These results are obtained by deriving bounds on the estimation error that provide insights on how the uncertainty inherent in a sensor network, such as imperfect knowledge on the number of agents and the measurement models used by the sensors, can degrade the performance of the estimation process. Numerical experiments are included to support the theoretical findings.

In this paper we study the problem of real-time optimal distributed partitioning for perimeter patrolling in the context of multi-camera networks for surveillance. The objective is to partition a given segment into non-overlapping sub-segments, each assigned to a different camera to patrol. Each camera has both physical mobility range and limited speed, and it must patrol its assigned sub-segment by sweeping it back and forth at maximum speed. Here we first review the solution for the centralized optimal partitioning. Then we propose two different distributed control strategies to determine the extremes of the optimal patrolling areas of each camera. Both these strategies require only local communication with the neighboring cameras but adopt different communication schemes, respectively, symmetric gossip and asynchronous asymmetric broadcast. The first scheme is shown to be provably convergent to the optimal solution. Some theoretical insights are provided also for the second scheme whose effectiveness is validated through numerical simulations.

In this work the design and implementation of an application to track multiple agents in a indoor Wireless Sensor Actor Network (WSAN) is proposed. The adopted embedded hardware for the network nodes is theTmote Sky, an ultra low power IEEE 802.15.4 compliant wireless device, which has become a reference in the academia for the early development of algorithms and applications for Wireless Sensor Actor Networks (WSANs). These devices are based on the TinyOS operative system and are programmed in NesC a C-derived language specifically developed for embedded systems. NesC has become indispensable for low-level management ofindividual agents while Java was chosen to provide the user with a simple and intuitive graphical interface with whom showing and coordinating the tracking.

In this work an algorithm to track multiple agents in an indoor Wireless Sensor Actor Network (WSAN) is proposed. The algorithm falls into the category of the radio frequency localization methods, since it exploits the strength of the wireless communications among nodes to establish the position of a set of mobile nodes within a network of fixed nodes placed in known locations. In this sense, a radio channel model is introduced that allows to estimate the distances among nodes to attain localization and tracking (range-based approach). Moreover, to compensate for the scant robustness of power measurements, the loss effects induced by wireless communication,the intrinsic uncertainty of unstructured environments, the algorithm resorts to an Extended Kalman Filter to process the node measurements and reach a desired level of localization performance. Finally, the design phase is validated through the implementation and the experiments on a real testbed.

In this work we consider a multidimensional distributed optimization technique that is suitable for multiagents systems subject to limited communication connectivity. In particular, we consider a convex unconstrained additive problem, i.e. a case where the global convex unconstrained multidimensional cost function is given by the sum of local cost functions available only to the specific owning agents. We show how, by exploiting the separation of time-scales principle,the multidimensional consensus-based strategy approximates a Newton-Raphson descent algorithm. We propose two alternative optimization strategies corresponding to approximations of the main procedure. These approximations introduce tradeoffs between the required communication bandwidth and the convergence speed/accuracy of the results. We provide analytical proofs of convergence and numerical simulations supporting the intuitions developed through the paper.

Geometric triangulation is at the basis of the estimation of the 3D position of a target from a set of camera measurements. The problem of optimal estimation (minimizing the L2 norm) of the target position from multi-view perspective projective measurements is typically a hard problem to solve. In literature there are different types of algorithms for this purpose, based for example on the exhaustive check of all the local minima of a proper eigenvalue problem [2], or branch- and-bound techniques [3]. However, such methods typically become unfeasible for real time applications when the number of cameras and targets become large, calling for the definition of approximate procedures to solve the reconstruction problem.
In the first part of this paper, linear (fast) algorithms, computing an approximate solution to such problems, are described and compared in simulation. Then, in the second part, a Gaussian approximation to the measurement error is used to express the reconstruction error’s standard deviation as a function of the position of the reconstructed point. An upper bound, valid over all the target domain, to this expression is obtained for a case of interest. Such upper bound allows to compute a number of cameras sufficient to obtain a user defined level of position estimation accuracy.

We consider the convergence rates of two peculiar2 convex optimization strategies in the context of multi agent3 systems, namely the Newton-Raphson consensus optimization4 and a distributed Gradient-Descent opportunely derived from5 the first. To allow analytical derivations, the convergence6 analyses are performed under the simplificative assumption of7 quadratic local cost functions. In this framework we derive8 sufficient conditions which guarantee the convergence of the9 algorithms. From these conditions we then obtain closed form10 expressions that can be used to tune the parameters for11 maximizing the rate of convergence. Despite these formulae12 have been derived under quadratic local cost functions13 assumptions, they can be used as rules-of-thumb for tuning14 the parameters of the algorithms in general situations.

In this work we study the problem of unconstrained distributed optimization in the context of multi-agents systems subject to limited communication connectivity. In particular we focus on the minimization of a sum of convex cost functions, where each component of the global function is available only to a specific agent and can thus be seen as a private local cost. The agents need to cooperate to compute the minimizer of the sum of all costs. We propose a consensus-like strategy to estimate a Newton-Raphson descending update for the local estimates of the global minimizer at each agent. In particular, the algorithm is based on the separation of time-scales principle and it is proved to converge to the global minimizer if a specific parameter that tunes the rate of convergence is chosen sufficiently small. We also provide numerical simulations and compare them with alternative distributed optimization strategies like the Alternating Direction Method of Multipliers and the Distributed Subgradient Method.

In this paper we study the problem of estimating the channel parameters for a generic wireless sensor network (WSN) in a completely distributed manner, using consensus algorithms. Specifically, we first propose a distributed strategy to minimize the effects of unknown constant offsets in the reading ofthe Radio Strength Signal Indicator (RSSI) due to uncalibrated sensors. Then we show how the computation of the optimal wireless channels parameters, which are the solution of a global least-square optimization problem, can be obtained with a consensus-based algorithm. The proposed algorithms are general algorithms for sensor calibration and distributed least-square parameter identification,and do not require any knowledge on the global topology of the network nor the total number of nodes. Finally, we apply these algorithms to experimental data collected from an indoor wireless sensor network.

The distributed estimation of the number of active sensors in a network can be important for estimation and organization purposes. We propose a design methodology based on the following paradigm: some locally randomly generated values are exchanged among the various sensors and thus modified by known consensus-based strategies. Statistical analysis of the a-consensus values allows estimation of the number of participant sensors. The main features of this approach are: algorithms are completely distributed, since they do not require leader election steps; sensors are not requested to transmit authenticative information (for example identificative numbers or similar data), and thus the strategy can be implemented whenever privacy problems arise. After a rigorous formulation of the paradigma we analyze some practical examples, fully characterize them from a statistical point of view, and finally we provide some general theoretical results and asymptotic analyses.

In this paper we analyze the problem of estimating a function from different noisy data sets collected by spatially distributed sensors and subject to unknown temporal shifts. We propose a novel approach based on non-parametric Gaussian regression and reproducing kernel Hilbert space theory that exploit compact and accurate representations of function estimates. As a first result, suitable minimization of inner products in reproducing kernel Hilbert spaces is used to obtain a novel time delay estimation technique when attention is restricted only to two signals. Then, we derive both a centralized and a distributed estimator to simultaneously identify the unknown function and delays for a generic number of networked sensors subject to a restricted communication graph. Numerical simulations are used to test the effectiveness of the proposed approaches.

In this paper we study the problem of estimatingthe channel parameters for a generic wireless sensor network(WSN) in a completely distributed manner, using consensusalgorithms. Specifically, we first propose a distributed strategyto minimize the effects of unknown constant offsets in thereading of the Radio Strength Signal Indicator (RSSI) due touncalibrated sensors. Then we show how the computation of theoptimal wireless channels parameters, which are the solutionof a global least-square optimization problem, can be obtainedwith a consensus-based algorithm. The proposed algorithmsare general algorithms for sensor calibration and distributedleast-square parameter identification, and do not require anyknowledge on the global topology of the network nor thetotal number of nodes. Finally, we apply these algorithms toexperimental data collected from an indoor WSN.