performance limits in sensor localization in this paper we study the cramer rao lower bound crlb in single hop sensor localization using measurements derived from received signal strength rss time of arrival toa and bearing respectively from a novel perspective differently from the existing work we use a statistical sensor anchor geometry modeling method with the result that the trace of the associated crlb matrix as a scalar metric for performance limits of sensor localization becomes a random variable given a probability measure for the sensor anchor geometry the statistical properties of the metric are analyzed to demonstrate properties of sensor localization using the central limit theorems for u statistics we show that as the number of anchors increases the metric is asymptotically normal in the rss bearing case and converges to a random variable which is an affine transformation of a chi square random variable of degree 2 in the toa case we provide formulas quantitatively describing the relationship among the mean and standard deviation of the metric the number of the anchors the parameters of communication channels the noise statistics in measurements and the spatial distribution of the anchors these formulas though asymptotic in the number of the anchors in many cases turn out to be remarkably accurate in predicting performance limits even if the number is small simulations are carried out to confirm our results

bias reduction for an explicit solution of source localization using tdoa this paper proposes two methods to reduce the bias of the well known algebraic explicit solution chan and ho a simple and efficient estimator for hyperbolic location ieee trans signal process vol 42 pp 1905 1915 aug 1994 for source localization using tdoa bias of a source location estimate is significant when the measurement noise is large and the geolocation geometry is poor bias also dominates performance when multiple times of independent measurements are available such as in uwb localization or in target tracking the paper starts by deriving the bias of the source location estimate from chan and ho the bias is found to be considerably larger than that of the maximum likelihood estimator two methods called biassub and biasred are developed to reduce the bias the biassub method subtracts the expected bias from the solution of chan and ho s work where the expected bias is approximated by the theoretical bias using the estimated source location and noisy data measurements the biasred method augments the equation error formulation and imposes a constraint to improve the source location estimate the biassub method requires the exact knowledge of the noise covariance matrix and biasred only needs the structure of it analysis shows that both methods reduce the bias considerably and achieve the crlb performance for distant source when the noise is gaussian and small the biassub method can nearly eliminate the bias and the biasred method is able to lower the bias to the same level as the maximum likelihood estimator the biasred method is extended for tdoa and fdoa positioning simulations corroborate the performance of the proposed methods

dqm decentralized quadratically approximated alternating direction method of multipliers this paper considers decentralized consensus optimization problems where nodes of a network have access to different summands of a global objective function nodes cooperate to minimize the global objective by exchanging information with neighbors only a decentralized version of the alternating directions method of multipliers dadmm is a common method for solving this category of problems dadmm exhibits linear convergence rate to the optimal objective for strongly convex functions but its implementation requires solving a convex optimization problem at each iteration this can be computationally costly and may result in large overall convergence times the decentralized quadratically approximated admm algorithm dqm which minimizes a quadratic approximation of the objective function that dadmm minimizes at each iteration is proposed here the consequent reduction in computational time is shown to have minimal effect on convergence properties convergence still proceeds at a linear rate with a guaranteed factor that is asymptotically equivalent to the dadmm linear convergence rate factor numerical results demonstrate advantages of dqm relative to dadmm and other alternatives in a logistic regression problem

semidefinite programming relaxations for semialgebraic problems a hierarchy of convex relaxations for semialgebraic problems is introduced for questions reducible to a finite number of polynomial equalities and inequalities it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility the main tools employed are a semidefinite programming formulation of the sum of squares decomposition for multivariate polynomials and some results from real algebraic geometry the techniques provide a constructive approach for finding bounded degree solutions to the positivstellensatz and are illustrated with examples from diverse application fields

distributed parameter estimation in sensor networks nonlinear observation models and imperfect communication the paper studies distributed static parameter vector estimation in sensor networks with nonlinear observation models and noisy intersensor communication it introduces separably estimable observation models that generalize the observability condition in linear centralized estimation to nonlinear distributed estimation it studies two distributed estimation algorithms in separably estimable models the nu with its linear counterpart lu and the nlu their update rule combines a consensus step where each sensor updates the state by weight averaging it with its neighbors states and an innovation step where each sensor processes its local current observation this makes the three algorithms of the consensus innovations type very different from traditional consensus this paper proves consistency all sensors reach consensus almost surely and converge to the true parameter value efficiency and asymptotic unbiasedness for lu and nu it proves asymptotic normality and provides convergence rate guarantees the three algorithms are characterized by appropriately chosen decaying weight sequences algorithms lu and nu are analyzed in the framework of stochastic approximation theory algorithm nlu exhibits mixed time scale behavior and biased perturbations and its analysis requires a different approach that is developed in this paper

forced synchronization of a delayed feedback oscillator abstract dynamics of a delayed feedback oscillator with cubic nonlinearity driven by an external harmonic signal is considered regimes of forced synchronization and their stability conditions are studied analytically and numerically for the cases of single frequency and multiple frequency self modulation operation of the free running oscillator special attention is paid to synchronization of the oscillator with bistability of steady states which arises near the boundary of generation zone results of numerical simulation of bifurcation transitions to synchronization regime for different driving frequencies are presented main differences from the classical picture of synchronization for a system with one degree of freedom are discussed

asymptotic stability of ltv systems with applications to distributed dynamic fusion we investigate the behavior of linear time varying ltv systems with randomly appearing sub stochastic system matrices motivated by dynamic fusion over mobile networks we develop conditions on the system matrices that lead to asymptotic stability of the underlying ltv system by partitioning the sequence of system matrices into slices we obtain the stability conditions in terms of slice lengths and introduce the notion of unbounded connectivity i e the time intervals over which the multi agent network is connected do not have to be bounded as long as they do not grow faster than a certain exponential rate we further apply the above analysis to derive the asymptotic behavior of a dynamic leader follower algorithm

approximation of the stability number of a graph via copositive programming lovasz and schrijver siam j optim 1 1991 pp 166 190 showed how to formulate increasingly tight approximations of the stable set polytope of a graph by solving semidefinite programs sdps of increasing size lift and project method in this paper we present a similar idea we show how the stability number can be computed as the solution of a conic linear program lp over the cone of copositive matrices subsequently we show how to approximate the copositive cone ever more closely via a hierarchy of linear or semidefinite programs of increasing size liftings the latter idea is based on recent work by parrilo structured semidefinite programs and semi algebraic geometry methods in robustness and optimization ph d thesis california institute of technology pasadena ca 2000 in this way we can compute the stability number alpha g of any graph g v e after at most alpha g 2 successive liftings for the lp based approximations one can compare this to the n alpha g 1 bound for the lp based lift and project scheme of lovasz and schrijver our approach therefore requires fewer liftings for families of graphs where alpha g o sqrt n we show that the first sdp based approximation for alpha g in our series of increasingly tight approximations coincides with the vartheta function of schrijver ieee trans inform theory 25 1979 pp 425 429 we further show that the second approximation is tight for complements of triangle free graphs and for odd cycles

decentralized quasi newton methods we introduce the decentralized broyden fletcher goldfarb shanno d bfgs method as a variation of the bfgs quasi newton method for solving decentralized optimization problems decentralized quasi newton methods are of interest in problems that are not well conditioned making first order decentralized methods ineffective and in which second order information is not readily available making second order decentralized methods impossible d bfgs is a fully distributed algorithm in which nodes approximate curvature information of themselves and their neighbors through the satisfaction of a secant condition we additionally provide a formulation of the algorithm in asynchronous settings convergence of d bfgs is established formally in both the synchronous and asynchronous settings and strong performance advantages relative to existing methods are shown numerically

diland an algorithm for distributed sensor localization with noisy distance measurements 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 rm 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

distributed consensus algorithms in sensor networks with imperfect communication link failures and channel noise the paper studies average consensus with random topologies intermittent links and noisy channels consensus with noise in the network links leads to the bias variance dilemma running consensus for long reduces the bias of the final average estimate but increases its variance we present two different compromises to this tradeoff the a nd algorithm modifies conventional consensus by forcing the weights to satisfy a persistence condition slowly decaying to zero and the a nc algorithm where the weights are constant but consensus is run for a fixed number of iterations iota then it is restarted and rerun for a total of p runs and at the end averages the final states of the p runs monte carlo averaging we use controlled markov processes and stochastic approximation arguments to prove almost sure convergence of a nd to a finite consensus limit and compute explicitly the mean square error mse variance of the consensus limit we show that a nd represents the best of both worlds zero bias and low variance at the cost of a slow convergence rate rescaling the weights balances the variance versus the rate of bias reduction convergence rate in contrast a nc because of its constant weights converges fast but presents a different bias variance tradeoff for the same number of iterations iota p shorter runs smaller iota lead to high bias but smaller variance larger number p of runs to average over for a static nonrandom network with gaussian noise we compute the optimal gain for a nc to reach in the shortest number of iterations iota p with high probability 1 delta epsiv delta consensus epsiv residual bias our results hold under fairly general assumptions on the random link failures and communication noise

complete positivity and distance avoiding sets we introduce the cone of completely positive functions a subset of the cone of positive type functions and use it to fully characterize maximum density distance avoiding sets as the optimal solutions of a convex optimization problem as a consequence of this characterization it is possible to reprove and improve many results concerning distance avoiding sets on the sphere and in euclidean space

winding number locking on a two dimensional torus synchronization of quasiperiodic motions we propose a new autonomous dynamical system of dimension n 4 that demonstrates the regime of stable two frequency motions and period doubling bifurcations of a two dimensional torus it is shown that the period doubling bifurcation of the two dimensional torus is not followed by the resonance phenomenon and the two dimensional ergodic torus undergoes a period doubling bifurcation the interaction of two generators is also analyzed the phenomenon of external and mutual synchronization of two frequency oscillations is observed for which winding number locking on a two dimensional torus takes place

distributed sensor localization in random environments using minimal number of anchor nodes the paper introduces diloc a distributed iterative algorithm to locate m sensors with unknown locations in rm m ges 1 with respect to a minimal number of m 1 anchors with known locations the sensors and anchors nodes in the network exchange data with their neighbors only no centralized data processing or communication occurs nor is there a centralized fusion center to compute the sensors locations diloc uses the barycentric coordinates of a node with respect to its neighbors these coordinates are computed using the cayley menger determinants i e the determinants of matrices of internode distances we show convergence of diloc by associating with it an absorbing markov chain whose absorbing states are the states of the anchors we introduce a stochastic approximation version extending diloc to random environments i e when the communications among nodes is noisy the communication links among neighbors may fail at random times and the internodes distances are subject to errors we show a s convergence of the modified diloc and characterize the error between the true values of the sensors locations and their final estimates given by diloc numerical studies illustrate diloc under a variety of deterministic and random operating conditions

global optimization with polynomials and the problem of moments we consider the problem of finding the unconstrained global minimum of a real valued polynomial p x mathbb r n to mathbb r as well as the global minimum of p x in a compact set k defined by polynomial inequalities it is shown that this problem reduces to solving an often finite sequence of convex linear matrix inequality lmi problems a notion of karush kuhn tucker polynomials is introduced in a global optimality condition some illustrative examples are provided

cayley menger coordinates abstract a major obstacle in applying distance geometry techniques is the analytical complexity of the cayley menger determinants that are used to characterize euclidian spaces in terms of distances between points in this paper we show that with the aid of a theorem of jacobi the complex cayley menger determinants can be replaced by simpler determinants and we derive the concept of cayley menger coordinates a coordinate system in terms of which each point of en is characterized by n 1 distances to n 1 points of a reference we also show that this coordinate system provides a natural norm for the incomplete embedding problem this paper provides the tools to treat the problem of filling out an incomplete distance matrix so that our previous procedure can then be used to embed the corresponding structure in a three dimensional space

a semidefinite programming hierarchy for packing problems in discrete geometry packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible for finite graphs one popular way to compute upper bounds for the maximal size of an independent set is to use lasserre s semidefinite programming hierarchy we generalize this approach to infinite graphs for this we introduce topological packing graphs as an abstraction for infinite graphs coming from packing problems in discrete geometry we show that our hierarchy converges to the independence number

higher dimensional consensus learning in large scale networks 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

a copositive formulation for the stability number of infinite graphs in the last decade copositive formulations have been proposed for a variety of combinatorial optimization problems for example the stability number independence number in this paper we generalize this approach to infinite graphs and show that the stability number of an infinite graph is the optimal solution of some infinite dimensional copositive program for this we develop a duality theory between the primal convex cone of copositive kernels and the dual convex cone of completely positive measures we determine the extreme rays of the latter cone and we illustrate this theory with the help of the kissing number problem

peculiarities of synchronization of a resonant limit cycle on a two dimensional torus the peculiarities of external synchronization of a resonant limit cycle on a torus are studied in an autonomous oscillator of quasiperiodic oscillations with two basic frequencies we show numerically and experimentally that in the resonance conditions the synchronization effect takes place only at one of the two basic frequencies of the system while the oscillations at the second basic frequency remain unsynchronized our results convincingly indicate a principal difference between synchronization of the resonant limit cycle on the torus and of a typical limit cycle this is in contrast to the well established theory of synchronization of a limit cycle this finding opens new strategies for controlling systems with multiple time scales

simple and fast convex relaxation method for cooperative localization in sensor networks using range measurements we address the sensor network localization problem given noisy range measurements between pairs of nodes we approach the nonconvex maximum likelihood formulation via a known simple convex relaxation we exploit its favorable optimization properties to the full to obtain an approach that is completely distributed has a simple implementation at each node and capitalizes on an optimal gradient method to attain fast convergence we offer a parallel but also an asynchronous flavor both with theoretical convergence guarantees and iteration complexity analysis experimental results establish leading performance our algorithms top the accuracy of a comparable state of the art method by one order of magnitude using one order of magnitude fewer communications