an accurate algebraic solution for moving source location using tdoa and fdoa measurements this paper proposes an algebraic solution for the position and velocity of a moving source using the time differences of arrival tdoas and frequency differences of arrival fdoas of a signal received at a number of receivers the method employs several weighted least squares minimizations only and does not require initial solution guesses to obtain a location estimate it does not have the initialization and local convergence problem as in the conventional linear iterative method the estimated accuracy of the source position and velocity is shown to achieve the crame spl acute r rao lower bound for gaussian tdoa and fdoa noise at moderate noise level before the thresholding effect occurs simulations are included to examine the algorithm s performance and compare it with the taylor series iterative method

further relaxations of the semidefinite programming approach to sensor network localization recently a semidefinite programming sdp relaxation approach has been proposed to solve the sensor network localization problem although it achieves high accuracy in estimating the sensor locations the speed of the sdp approach is not satisfactory for practical applications in this paper we propose methods to further relax the sdp relaxation more precisely to relax the single semidefinite matrix cone into a set of small size semidefinite submatrix cones which we call a sub sdp ssdp approach we present two such relaxations although they are weaker than the original sdp relaxation they retain the key theoretical property and numerical experiments show that they are both efficient and accurate the speed of the ssdp is even faster than that of other approaches based on weaker relaxations the ssdp approach may also pave a way to efficiently solving general sdp problems without sacrificing the solution quality

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

freezing and collapse of flexible polymers on regular lattices in three dimensions we analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple cubic and face centered cubic lattices by means of sophisticated chain growth methods in contrast to the bond fluctuation polymer model in certain parameter ranges where these two conformational transitions were found to merge in the thermodynamic limit we conclude from our results that the two transitions remain well separated in the limit of infinite chain lengths the reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the lattice models considered here

cooperative joint synchronization and localization in wireless sensor networks in this paper cooperative sensor localization using asynchronous time of arrival measurements is investigated it is well known that localization performance in wireless networks using time based ranging or pseudo ranging methods is greatly affected by the accuracy of the timing synchronization between the nodes involved in the estimation commonly the original estimation problem is broken down into two subproblems the synchronization problem and the localization problem in what is known as a two step approach however in this paper the joint synchronization and localization problem is considered and examined for use in cooperative networks it is discussed that the cooperation between the source nodes eliminates the need for high anchor node densities and improves localization performance significantly furthermore the cramer rao lower bounds crlb and the maximum likelihood ml estimator are derived it is shown that the ml estimator is highly nonlinear and nonconvex and must therefore be solved by using computationally complex algorithms in order to reduce the complexity of the estimation a novel semidefinite programming sdp relaxation method is developed by relaxing the original nonconvex ml problem in such a way as to reformulate the estimation problem as a convex problem the performance of the proposed sdp method is shown through computer simulations to nearly equal that of the ml estimator the approach is also applied to the noncooperative case where it is found to be superior in performance than the previously proposed suboptimal estimators finally complexity analyses are included for the estimators under consideration

solution and analysis of tdoa localization of a near or distant source in closed form point positioning and direction of arrival doa localization require separate estimators depending on whether the source is near or distant from the sensors the use of modified polar representation mpr for the source location enables the integration of the two estimators together and eliminates the knowledge needed if the source is in the near field or far field the previous work on mpr only provides an iterative implementation of the maximum likelihood estimator mle initialized by a coarse semidefinite relaxation sdr solution this paper proposes a formulation for time difference of arrival tdoa localization of a 2 d or 3 d source in mpr that would lead to a closed form solution through the minimization of a quadratic function with a quadratic constraint two techniques the successive unconstrained minimization sum and the generalized trust region subproblem gtrs are applied to solve the optimization detailed analysis in the first order for mean square and in the second order for estimation bias is performed for both methods the theoretical results illustrate that the closed form solution from each of the methods provides the cramer rao lower bound performance for gaussian noise the gtrs solution has better accuracy than the sum solution when the source signal is arriving at an azimuth or elevation angle close to zero 90 circ or 180 circ or when the measurement noise level is large they yield comparable performance with the mle albeit having less complexity and avoiding possible divergence behavior they outperform the closed form solutions from the literature in angle estimation and have smaller bias

symmetrically separated sequences in the unit sphere of a banach space abstract we prove the symmetric version of kottman s theorem that is to say we demonstrate that the unit sphere of an infinite dimensional banach space contains an infinite subset a with the property that x y 1 for distinct elements x y a thereby answering a question of j m f castillo in the case where x contains an infinite dimensional separable dual space or an unconditional basic sequence the set a may be chosen in a way that x y 1 e for some e 0 and distinct x y a under additional structural properties of x such as non trivial cotype we obtain quantitative estimates for the said e certain renorming results are also presented

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

study of the θ point by enumeration of self avoiding walks on the triangular lattice the author reports series expansion analyses of self avoiding walks with nearest neighbour bond interactions the estimates 2 nu t 1 07 or 0 05 and phi 0 64 or 0 05 for the correlation and crossover exponents at the theta point were obtained by examining the number of walks and the end to end distance data up to 16 steps on the triangular lattice

star finite coverings of banach spaces abstract we study star finite coverings of infinite dimensional normed spaces a family of sets is called star finite if each of its members intersects only finitely many other members of the family it follows from our results that an lur or a uniformly frechet smooth infinite dimensional banach space does not admit star finite coverings by closed balls on the other hand we present a quite involved construction of a star finite covering of c 0 by frechet smooth centrally symmetric bounded convex bodies a similar but simpler construction shows that every normed space of countable dimension and hence incomplete has a star finite covering by closed balls

multiple source localization in wireless sensor networks based on time of arrival measurement we investigate the localization of multiple signal sources based on sensors performing time of arrival toa measurement in wireless sensor networks moving beyond the widely studied single source localization problem concurrently active multiple sources substantially complicate the problem since anchored sensor nodes are unaware of associations between measured signals and source nodes at the same time as the total number of possible source measurement associations grows exponentially with the number of sensor nodes it is inefficient to attempt conventional single source localization algorithm for each possible association in a brute force manner in this work we address this difficult problem from a joint optimization perspective specifically we consider simultaneous estimation of source measurement associations and the source locations in addition to finding the initial signal transmission time this joint optimization problem includes both discrete and continuous variables we propose an efficient three step algorithm that progressively simplifies the original problem through convex relaxation and sensible approximations our proposed algorithm demonstrates results comparable to a genie aided method that utilizes known source measurement associations

canonical primal dual algorithm for solving fourth order polynomial minimization problems this paper focuses on implementation of a general canonical primal dual algorithm for solving a class of fourth order polynomial minimization problems a critical issue in the canonical duality theory has been addressed i e in the case that the canonical dual problem has no interior critical point in its feasible space s a a quadratic perturbation method is introduced to recover the global solution through a primal dual iterative approach and a gradient based method is further used to refine the solution a series of test problems including the benchmark polynomials and several instances of the sensor network localization problems have been used to testify the effectiveness of the proposed algorithm

efficient multiple range random walk algorithm to calculate the density of states we present a new monte carlo algorithm that produces results of high accuracy with reduced simulational effort independent random walks are performed concurrently or serially in different restricted ranges of energy and the resultant density of states is modified continuously to produce locally flat histograms this method permits us to directly access the free energy and entropy is independent of temperature and is efficient for the study of both 1st order and 2nd order phase transitions it should also be useful for the study of complex systems with a rough energy landscape

global continuation for distance geometry problems distance geometry problems arise in the determination of protein structure we consider the case where only a subset of the distances between atoms is given and formulate this distance geometry problem as a global minimization problem with special structure we show that global smoothing techniques and a continuation approach for global optimization can be used to determine global solutions of this problem reliably and efficiently the global continuation approach determines a global solution with less computational effort than is required by a standard multistart algorithm moreover the continuation approach usually finds the global solution from any given starting point while the multistart algorithm tends to fail

robust convex approximation methods for tdoa based localization under nlos conditions in this paper we develop a novel robust optimization approach to source localization using time difference of arrival tdoa measurements that are collected under non line of sight nlos conditions a key feature of our approach is that it does not require knowledge of the distribution or statistics of the nlos errors which are often difficult to obtain in practice instead it only assumes that the nlos errors have bounded supports based on this assumption we formulate the tdoa based source localization problem as a robust least squares rls problem in which a location estimate that is robust against the nlos errors is sought since the rls problem is non convex we propose two efficiently implementable convex relaxation based approximation methods to tackle it we then conduct a thorough theoretical analysis of the approximation quality and computational complexity of these two methods in particular we establish conditions under which they will yield a unique localization of the source simulation results on both synthetic and real data show that the performance of our approach under various nlos settings is very stable and is significantly better than that of several existing non robust approaches

graph rigidity via euclidean distance matrices abstract let g v e be an incomplete graph with node set v edge set e and nonnegative weights ij s on the edges let each edge v i v j be viewed as a rigid bar of length ij which can rotate freely around its end nodes a realization of a graph g is an assignment of coordinates in some euclidean space to each node of g in this paper we consider the problem of determining whether or not a given realization of a graph g is rigid we show that each realization of g can be epresented as a point in a compact convex set r m and that a generic realization of g is rigid if and only if its corresponding point is a vertex of i e an extreme point with full dimensional normal cone

explicit sensor network localization using semidefinite representations and facial reductions the sensor network localization snl problem in embedding dimension r consists of locating the positions of wireless sensors given only the distances between sensors that are within radio range and the positions of a subset of the sensors called anchors current solution techniques relax this problem to a weighted nearest positive semidefinite programming sdp completion problem by using the linear mapping between euclidean distance matrices edm and semidefinite matrices the resulting sdp is solved using primal dual interior point solvers yielding an expensive and inexact solution this relaxation is highly degenerate in the sense that the feasible set is restricted to a low dimensional face of the sdp cone implying that the slater constraint qualification fails cliques in the graph of the snl problem give rise to this degeneracy in the sdp relaxation in this paper we take advantage of the absence of the slater constraint qualification and derive a technique for the snl problem with exact data that explicitly solves the corresponding rank restricted sdp problem no sdp solvers are used for randomly generated instances we are able to efficiently solve many huge instances of this np hard problem to high accuracy by finding a representation of the minimal face of the sdp cone that contains the sdp matrix representation of the edm the main work of our algorithm consists in repeatedly finding the intersection of subspaces that represent the faces of the sdp cone that correspond to cliques of the snl problem

transverse size critical exponent of directed percolation from yang lee zeros of survival probability by using transfer matrix method we compute survival probabilities for the directed percolation problem on strips of a square lattice and get very precise estimates of their yang lee zeros lying closest to the real axis in the complex plane of occupation probability this allows us to get accurate values for transverse size critical exponent and percolation threshold

enumeration of self avoiding walks on the square lattice we describe a new algorithm for the enumeration of self avoiding walks on the square lattice using up to 128 processors on a hp alpha server cluster we have enumerated the number of self avoiding walks on the square lattice to length 71 series for the metric properties of mean square end to end distance mean square radius of gyration and mean square distance of monomers from the end points have been derived to length 59 an analysis of the resulting series yields accurate estimates of the critical exponents and confirming predictions of their exact values likewise we obtain accurate amplitude estimates yielding precise values for certain universal amplitude combinations finally we report on an analysis giving compelling evidence that the leading non analytic correction to scaling exponent 1 3 2

partition function zeros of a square lattice homopolymer with nearest and next nearest neighbor interactions we study distributions of the partition function zeros in the complex temperature plane for a square lattice homopolymer with nearest neighbor nn and next nearest neighbor nnn interactions the dependence of distributions on the ratio of nn and nnn interaction strengths r is examined the finite size scaling of the zeros is performed to obtain the crossover exponent which is shown to be independent of r within error bars suggesting that all of these models belong to the same universality class the transition temperatures are also computed by the zeros to obtain the phase diagram and the results confirm that the model with stronger nnn interaction exhibits stronger effects of cooperativity

a new approach to the minimum cut problem this paper present a new approach to finding minimum cuts in undirected graphs the fundamental principle is simple the edges in a graph s minimum cut form an extremely small fraction of the graph s edges using this idea we give a randomized strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability the algorithm runs in o n 2 log 3 n time a significant improvement over the previous o mn time bounds based on maximum flows it is simple and intuitive and uses no complex data structures our algorithm can be parallelized to run in rnc with n 2 processors this gives the first proof that the minimum cut problem can be solved in rnc the algorithm does more than find a single minimum cut it finds all of them with minor modifications our algorithm solves two other problems of interest our algorithm finds all cuts with value within a multiplicative factor of of the minimum cut s in expected o n 2 time or in rnc with n 2 processors the problem of finding a minimum multiway cut of graph into r pieces is solved in expected o n 2 r 1 time or in rnc with n 2 r 1 processors the trace of the algorithm s execution on these two problems forms a new compact data structure for representing all small cuts and all multiway cuts in a graph this data structure can be efficiently transformed into the more standard cactus representing for minimum cuts

collapse of two dimensional linear polymers we study the collapse transition of a two dimensional very long polymer the model we consider is a lattice model where the chain is represented by a self avoiding walk with nearest neighbor attraction by using the transfer matrix technique we calculate exactly the thermal and geometrical properties of the polymer on strips of finite width we then use finite size scaling to determine the values of the tricritical point exponentsv1 0 55 0 01vu 1 15 0 15 1 v1 1 80 0 05 we compare these results to the other values already proposed in the literature

a trust region sqp filter method for nonlinear second order cone programming in this paper we consider the nonlinear second order cone programming problem by combining an sqp method and filter technique we present a trust region sqp filter method for solving this problem the proposed algorithm avoids using the classical merit function with penalty term furthermore under standard assumptions we prove that the iterative sequence generated by the presented algorithm converges globally preliminary numerical results indicate that the algorithm is promising

exact partition function zeros of a polymer on a simple cubic lattice we study conformational transitions of a polymer on a simple cubic lattice by calculating the zeros of the exact partition function up to chain length 24 in the complex temperature plane two loci of the partition function zeros are found for longer chains suggesting the existence of both the coil globule collapse transition and the melting freezing transition the locus corresponding to coil globule transition clearly approaches the real axis as the chain length increases and the transition temperature could be estimated by finite size scaling the form of the logarithmic correction to the scaling of the partition function zeros could also be obtained the other locus does not show clear scaling behavior but a supplementary analysis of the specific heat reveals a first order like pseudotransition

the dual model for an ising model with nearest and next nearest neighbors we construct and analyze a dual model to the next nearest neighbor ising nnni model on the rectangular lattice the hamiltonian of the dual model turns out to contain two and four spin interactions the free fermion approximation suggests that an increase in the critical temperature of the dual model caused by the four spin interactions is limited to a finite range

an epsilon relaxation method for separable convex cost network flow problems we propose a new method for the solution of the single commodity separable convex cost network flow problem the method generalizes the epsilon relaxation method developed for linear cost problems and reduces to that method when applied to linear cost problems we show that the method terminates with a near optimal solution and we provide an associated complexity analysis we also present computational results showing that the method is much faster than earlier relaxation methods particularly for ill conditioned problems

optimal source localization and tracking from passive array measurements if the signal of a moving source is observed at several spatially separated locations during a common time interval the received signals exhibit differential delays and doppler shifts which provide information about source location and velocity this paper deals with the optimal in the minimum mean square error sense source localization and tracking by utilizing differential delay and doppler observations at a linear array of receivers we shall be concerned with source ranges large compared with array baseline and with the distance traversed by the source during the observation interval it is shown that the optimal estimation procedure can be carried out in two sequential steps without any loss in performance in the first step source location is estimated from the differential delay group of measurements in the second step source velocity is estimated from the differential doppler group of measurements and the outcome of the first step furthermore by employing an intermediate track dependent parameter set the two step algorithm yields a closed form solution of the estimation problem

conformational space renormalisation group theory of tricritical theta point exponents for a polymer chain the marked difference between the n to 0 limit of o n phi 4 phi 6 field theory tricritical exponents and accepted values for a polymer in d 2 are shown to persist when renormalisation is performed away from the tricritical point the difference is removed by introducing a physically dictated renormalisation prescription for the field theoretic formulation of the polymer problem or the equivalent chain conformational space method

design of radar receive filters optimized according to l_ p norm based criteria this correspondence deals with the design of radar receive filters for pulse compression which optimize either the lp norm of the vector containing the filter sidelobe energies or the inverse signal to noise power ratio isnr under an upper bound constraint on the previously mentioned lp norm in both the cases we prove that the filter design can be formulated as a convex optimization second order cone programming socp problem which can be efficiently solved with a polynomial time computational complexity resorting to interior point methods at the analysis stage we assess the performance of the receive filters in correspondence of different values of the parameter p highlighting the performance compromises between the integrated sidelobe level isl the peak sidelobe level psl and the isnr finally we study the effects of the filter length on the performance as well as the doppler tolerance of the devised filters the results show that the proposed technique leads to satisfactory performance levels and good doppler tolerances

extension of hoffman s error bound to polynomial systems given any linear system defined by linear inequalities equalities in re n hoffman s error bound says that the distance from any point x in re n to the solution set of the linear system is bounded by a constant independent of x times a certain residual function evaluated at x this paper considers arbitrary possibly nonconvex polynomial systems defined by polynomial inequalities equalities it is shown that the solution sets of such systems are in general holder continuous as the right hand side changes in contrast to the lipschitzian continuity for the linear case also for any convex quadratic inequality system possessing an interior solution the authors show that its solution set behaves in a lipschitzian manner as the right hand side varies this result sharpens the earlier error bound results by mangasarian and robinson for general convex differentiable inequality systems which in addition to the interiority assumption require either an asymptotic constraint qualification con

interacting growth walk a model for generating compact self avoiding walks we propose an algorithm based on local growth rules for kinetically generating self avoiding walk configurations at any given temperature this algorithm called the interacting growth walk igw model does not suffer from attrition on a square lattice at zero temperature in contrast to the existing algorithms more importantly the igw model facilitates growing compact configurations at lower temperatures a feature that makes it attractive for studying a variety of processes such as the folding of proteins we demonstrate that our model correctly describes the collapse transition of a homopolymer in two dimensions

second order cone programming second order cone programming socp problems are convex optimization problems in which a linear function is minimized over the intersection of an affine linear manifold with the cartesian product of second order lorentz cones linear programs convex quadratic programs and quadratically constrained convex quadratic programs can all be formulated as socp problems as can many other problems that do not fall into these three categories these latter problems model applications from a broad range of fields from engineering control and finance to robust optimization and combinatorial optimization on the other hand semidefinite programming sdp that is the optimization problem over the intersection of an affine set and the cone of positive semidefinite matrices includes socp as a special case therefore socp falls between linear lp and quadratic qp programming and sdp like lp qp and sdp problems socp problems can be solved in polynomial time by interior point methods the computational effort per iteration required by these methods to solve socp problems is greater than that required to solve lp and qp problems but less than that required to solve sdp s of similar size and structure because the set of feasible solutions for an socp problem is not polyhedral as it is for lp and qp problems it is not readily apparent how to develop a simplex or simplex like method for socp while socp problems can be solved as sdp problems doing so is not advisable both on numerical grounds and computational complexity concerns for instance many of the problems presented in the survey paper of vandenberghe and boyd vb96 as examples of sdps can in fact be formulated as socps and should be solved as such in 2 3 below we give socp formulations for four of these examples the convex quadratically constrained quadratic programming qcqp problem problems involving fractional quadratic functions rutcor rutgers university e mail alizadeh rutcor rutgers edu research supported in part by the u s national science foundation grant ccr 9901991 ieor columbia university e mail gold ieor columbia edu research supported in part by the department of energy grant de fg02 92er25126 national science foundation grants dms 94 14438 cda 97 26385 and dms 01 04282

partition function zeros of the square lattice ising model with nearest and next nearest neighbor interactions the distributions of the partition function zeros in the complex a e 2 ensuremath beta j 1 plane of the square lattice ising model with nearest neighbor j 1 and next nearest neighbor j 2 interactions are investigated as a function of r j 2 j 1 starting from the well known two circle distribution of the zeros a ifmmode pm else textpm fi 1 sqrt 2 e i ensuremath theta for r 0 finally the partition function zeros lie on the unit circle a e i ensuremath theta for r ensuremath infty between these two ends the changes in the zero distributions are described using the partition function zeros the critical point a c r and the thermal scaling exponent y t r are estimated for the ising ferromagnet equivalently antiferromagnet and superantiferromagnet for the special case of r frac 1 2 the possible implications of the zero distributions are also discussed

a finite lattice study of the critical behaviour of the two dimensional biaxial next nearest neighbour ising model the critical behaviour of an ising model with competing first and third nearest neighbour interactions biaxial next nearest neighbour ising or bnnni model on the square lattice is investigated by finite lattice methods in the ferromagnetic region the phase boundary is located with an accuracy at least equal to that of alternative methods in the antiphase region distinctive structure in finite lattice estimators is found over an extended temperature range however the nature of the transition remains unclear

collapse transition of self avoiding walks on a square lattice in the bulk and near a linear wall the universality classes of the θ and θ points using the scanning method we study by extensive simulations the theta transition of self avoiding walks with nearest neighbor attractions in the bulk and near a linear wall on a square lattice consistent results for the two models are obtained for the radius of gyration but not for the end to end distance our results for the exponents nu and gamma agree with those derived by duplantier and saleur phys rev lett 59 539 1987 for the theta prime model however our results for the crossover exponent phi which constitute upper bounds for the correct value are significantly larger than the value of phi theta prime at the ordinary point our result for gamma sub 1 is larger even though not much than the value suggested by vanderzande stella and seno phys rev lett 67 2757 1991 for the theta prime model

polynomial time approximation algorithms for the ising model the paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic ising system to any specified degree of accuracy the running time of the algorithm in

on the solution of the gps localization and circle fitting problems we consider the problem of locating a user s position from a set of noisy pseudoranges to a group of satellites we consider both the nonlinear least squares formulation of the problem which is nonconvex and nonsmooth and the nonlinear squared least squares variant in which the objective function is smooth but still nonconvex we show that the squared least squares problem can be reformulated as a generalized trust region subproblem and as such can be solved efficiently conditions for attainment of the optimal solutions of both problems are derived the nonlinear least squares problem is shown to have tight connections to the well known geometric circle fitting and orthogonal regression problems finally a fixed point method for the nonlinear least squares formulation is derived and analyzed

collapse of two dimensional linear polymers a transfer matrix calculation of the exponent νt using a transfer matrix technique and finite size scaling the authors calculate the exponent nu t of two dimensional polymers at the theta point they find nu t 0 55 or 0 01 by two slightly different calculations on the square lattice this value is compared with those which had been previously proposed in the literature

asymptotic behavior of the central path for a special class of degenerate sdp problems this paper studies the asymptotic behavior of the central path x s y as 0 for a class of degenerate semidefinite programming sdp problems namely those that do not have strictly complementary primal dual optimal solutions and whose degenerate diagonal blocks of the central path are assumed to satisfy we establish the convergence of the central path towards a primal dual optimal solution which is characterized as being the unique optimal solution of a certain log barrier problem a characterization of the class of sdp problems which satisfy our assumptions are also provided it is shown that the re parametrization t 0 x t4 s t4 y t4 of the central path is analytic at t 0 the limiting behavior of the derivative of the central path is also investigated and it is shown that the order of convergence of the central path towards its limit point is finally we apply our results to the convex quadratically constrained convex programming cqccp problem and characterize the class of cqccp problems which can be formulated as sdps satisfying the assumptions of this paper in particular we show that cqccp problems with either a strictly convex objective function or at least one strictly convex constraint function lie in this class

iterative constrained weighted least squares source localization using tdoa and fdoa measurements this paper investigates the constrained weighted least squares cwls source localization problem by using time difference of arrival and frequency difference of arrival measurements the problem can be formulated as a quadratic programming with two indefinite quadratic equality constraints which is nonconvex and np hard moreover the weighting matrix is coupled with the unknown source position and velocity we propose an iterative cwls method that can efficiently solve this problem it iteratively performs a linearization procedure on the quadratic equality constraints to obtain an approximate programming with linear constraints which can be analytically solved and the weighting matrix is updated in each iteration theoretical analysis reveals that the proposed method if converges can lead to the global optimal solution of the formulated problem that reaches the crlb accuracy under mild assumptions on the measurement noises the monte carlo simulation results indicate that the percentage of convergence within mathbf 20 iterations is more than mathbf 96 and the localization accuracy is significantly improved over the previous methods with less computation time requirement moreover it is found from simulations that the iterative cwls method retains acceptable performance even under the ill conditioned situation when the sensor geometry is not desirable

successive and asymptotically efficient localization of sensor nodes in closed form accurate localization of nodes in a sensor network is a crucial step before the sensor network can be utilized for various applications this paper proposes a successive estimation method to self localize the sensor nodes using time of arrival toa measurements through the aid of a few anchor nodes whose positions are known a priori the successive nature of the proposed algorithm makes it attractive for distributed computation in a resource constrained environment the proposed technique uses subsets of toas to obtain coarse sensor node estimates depending on available computation and transmission resources the node positions are refined to improve their accuracies the solution of the proposed node localization algorithm is algebraic and closed form which simplifies computation and avoids possible local convergence or divergence problems as in the traditional iterative approaches a main benefit of the proposed algorithm is that although it is closed form and performs successive estimation of the node locations it is able to reach the cramer rao lower bound crlb accuracy under white gaussian measurement noise with sufficient snr this is confirmed by the theoretical analysis and corroborated by simulations

efficient convex relaxation methods for robust target localization by a sensor network using time differences of arrivals we consider the problem of target localization by a network of passive sensors when an unknown target emits an acoustic or a radio signal its position can be localized with multiple sensors using the time difference of arrival tdoa information in this paper we consider the maximum likelihood formulation of this target localization problem and provide efficient convex relaxations for this nonconvex optimization problem we also propose a formulation for robust target localization in the presence of sensor location errors two cramer rao bounds are derived corresponding to situations with and without sensor node location errors simulation results confirm the efficiency and superior performance of the convex relaxation approach as compared to the existing least squares based approach when large sensor node location errors are present

distributed wireless sensor network localization via sequential greedy optimization algorithm node localization is essential to most applications of wireless sensor networks wsns in this paper we consider both range based node localization and range free node localization with uncertainties in range measurements radio range and anchor positions first a greedy optimization algorithm named sequential greedy optimization sgo algorithm is presented which is more suitable for distributed optimization in networks than the classical nonlinear gauss seidel algorithm then a unified optimization framework is proposed for both range based localization and range free localization and two convex localization formulations are obtained based on semidefinite programming sdp relaxation techniques by applying the sgo algorithm to the edge based sdp relaxation formulation we propose a second order cone programming socp based distributed node localization algorithm two distributed refinement algorithms are also proposed by using the sgo algorithm to nonconvex localization formulations the proposed localization algorithms all can be implemented partially asynchronously in networks finally extensive simulations are conducted to demonstrate the efficiency and accuracy of the proposed distributed localization algorithms

distributed maximum likelihood sensor network localization we propose a class of convex relaxations to solve the sensor network localization problem based on a maximum likelihood ml formulation this class as well as the tightness of the relaxations depends on the noise probability density function pdf of the collected measurements we derive a computational efficient edge based version of this ml convex relaxation class and we design a distributed algorithm that enables the sensor nodes to solve these edge based convex programs locally by communicating only with their close neighbors this algorithm relies on the alternating direction method of multipliers admm it converges to the centralized solution it can run asynchronously and it is computation error resilient finally we compare our proposed distributed scheme with other available methods both analytically and numerically and we argue the added value of admm especially for large scale networks

second order cone programming relaxation of sensor network localization the sensor network localization problem has been much studied recently biswas and ye proposed a semidefinite programming sdp relaxation of this problem which has various nice properties and for which a number of solution methods have been proposed here we study a second order cone programming socp relaxation of this problem motivated by its simpler structure and its potential to be solved faster than sdp we show that the socp relaxation though weaker than the sdp relaxation has nice properties that make it useful as a problem preprocessor in particular sensors that are uniquely positioned among interior solutions of the socp relaxation are accurate up to the square root of the distance error thus these sensors which are easily identified are accurately positioned in our numerical simulation the interior solution found can accurately position up to 80 90p of the sensors we also propose a smoothing coordinate gradient descent method for finding an interior solution that is faster than an interior point method

a simple and efficient estimator for hyperbolic location an effective technique in locating a source based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors is proposed the approach is noniterative and gives an explicit solution it is an approximate realization of the maximum likelihood estimator and is shown to attain the cramer rao lower bound near the small error region comparisons of performance with existing techniques of beamformer spherical interpolation divide and conquer and iterative taylor series methods are made the proposed technique performs significantly better than spherical interpolation and has a higher noise threshold than divide and conquer before performance breaks away from the cramer rao lower bound it provides an explicit solution form that is not available in the beamforming and taylor series methods computational complexity is comparable to spherical interpolation but substantially less than the taylor series method

a binomial approximation method for the ising model a large portion of the computation required for the partition function of the ising model can be captured with a simple formula in this work we support this claim by defining an approximation to the partition function and other thermodynamic quantities of the ising model that requires no algorithm at all this approximation which uses the high temperature expansion is solely based on the binomial distribution and performs very well at low temperatures at high temperatures we provide an alternative approximation which also serves as a lower bound on the partition function and is trivial to compute we provide theoretical evidence and the results of numerical experiments to support the strength of these approximations