multipath time delay detection and estimation a transmitted and known signal is observed at the receiver through more than one path in additive noise the problem is to estimate the number of paths and for each of them the associated attenuation and delay we propose a deconvolution approach with an additive regularization term built around an l sub 1 norm the underlying optimization problem is transformed into a quadratic program and is thus easily and quickly solved by standard programs the procedure is able to handle more severe conditions than previous methods

direct sums of self small mixed groups abstract the class g of self small mixed abelian groups of finite rank has recently been the focus of a number of investigations it is known that up to quasi isomorphism g is dual to the category of locally free torsion free abelian groups of finite rank we utilize the reduced mixed groups in g as building blocks of a more extensive class g the smallest class containing the reduced groups in g that is closed under taking infinite direct sums and direct summands our central result is the determination of a complete set of isomorphism invariants for the groups in g we supplement this broad classification theorem with an investigation of the fine structure of completely decomposable groups in g

blind received signal strength difference based source localization with system parameter errors the problem of passive source localization has been extensively studied due to its many applications in signal processing and wireless communications signal strength based localization methods have the advantages of low cost and simple implementation in this paper blind source localization with unknown transmit power and unknown path loss exponent is considered based on the received signal strength difference rssd a nonlinear rssd based model is formulated for systems perturbed by noise solutions obtained using conventional least squares methods suffer from significant performance degradation as they only consider errors in the data vector thus an extended total least squares etls method is developed for blind localization which considers perturbations in the system parameters as well as the constraints imposed by the relationship between the observation matrix and data vector the nonlinear and nonconvex rssd based localization problem is then transformed to an etls problem with fewer constraints this is transformed to a convex semidefinite programming sdp problem using relaxation the corresponding etls sdp method is extended to the case with an unknown path loss exponent to jointly estimate the unknown source location and path loss exponent without resorting to transmit power estimation which is sensitive to errors the mean squared error of the proposed etls method is obtained and the corresponding cramer rao lower bound crlb is derived as a performance benchmark performance results are presented that show that the rssd based etls sdp method attains the crlb for a sufficiently large signal to noise ratio snr

a semi implicit numerical scheme for reacting flow an additive semi implicit projection scheme for the simulation of unsteady combustion in two dimensions is constructed the scheme relies on a zero mach number formulation of the compressible conservation equations with detailed chemistry the governing equations are discretized in space using second order differences and integrated in time using a semi implicit approach time integration of the evolution equations for species mass fraction thermodynamic pressure and density is performed using a semi implicit nonsplit scheme that combines a second order predictor corrector treatment of convection and diffusion terms and a stiff integrator for the reaction source terms meanwhile the momentum equations are integrated using a second order projection scheme the projection scheme is based on a predictor corrector approach that couples the evolution of the velocity and density fields in order to stabilize computations of reacting flows with large density variations a pressure poisson equation is inverted following both the predictor and corrector steps using a fast solver the advantages of the stiff integration of reaction source terms are analyzed by comparing the performance of the scheme to that of a predictor corrector scheme in which reaction and diffusion are integrated in a similar nonstiff fashion the comparison in based on both one dimensional 1d unsteady tests of a premixed methane air flame and unsteady two dimensional tests of the same flame interacting with a counterrotating vortex pair in both cases the grimech1 2 reaction mechanism with 32 species and 177 elementary reactions is used computed results show that the stiff reaction scheme enables selection of larger time steps and thus leads to substantial improvement in the performance of the computations for the present reaction mechanism and flame conditions speedup factors of about 10 are achieved in the 1d tests and about five in two dimensions possible extensions of the present scheme to further improve efficiency are also discussed

accurate localization of a rigid body using multiple sensors and landmarks this paper develops estimators for locating a rigid body using the time measurements and the doppler as well if it is moving between the sensors in the rigid body and a few landmarks outside the challenge of rigid body localization is that in addition to the position we are also interested in obtaining the rotation parameters of the rigid body that must belong to the special orthogonal group the proposed estimators are non iterative and have two steps preliminary and refinement the preliminary step provides a coarse estimate and the refinement step improves the first step estimate to yield an accurate solution when the rigid body is stationary we are able to locate the body with accuracy higher than the solutions of comparable complexity found in the literature when the rigid body is moving we develop an estimator that contains the additional unknowns of angular and translational velocities simulations show that the proposed estimators in both stationary and moving cases can approach the cramer rao lower bound performance under gaussian noise over the small error region

regular article a fast spectral algorithm for nonlinear wave equations with linear dispersion spectral algorithms offer very high spatial resolution for a wide range of nonlinear wave equations on periodic domains including well known cases such as the korteweg de vries and nonlinear schrodinger equations for the best computational efficiency one needs also to use high order methods in time while somehow bypassing the usual severe stability restrictions we use linearly implicit multistep methods with the innovation of choosing different methods for different ranges in fourier space high accuracy at low wavenumbers and a stability at high wavenumbers this new approach compares favorably to alternatives such as split step and integrating factor or linearly exact methods

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

balanced projectives and axiom 3 abstract a global definition of k nice subgroup is formulated which generalizes both the notion of a nice subgroup in the context of torsion groups and the notion of a k nice submodule used in a recent study of p local balanced projective groups it is shown analogous to hill s treatment of totally projective p groups that the global balanced projective groups of warfield are precisely those mixed abelian groups that satisfy the third axiom of countability for k nice subgroups a variety of equivalent characterizations of balanced projectives are derived by methods independent of the uniqueness and existence theorems previously established for these groups

a cognitive algorithm for received signal strength based localization in this paper we propose a method to localize a wireless and stationary blind node based on received signal strength measurements the positioning scheme relies on the statistical path loss model the operating environment is either non homogeneous i e the attenuation factors of the various links are different or homogeneous i e all links share one and the same attenuation factor we introduce a cognitive procedure to circumvent the a priori uncertainty on the actual scenario being in force the first stage is a properly designed hypothesis test fed by measurements between anchors moving along known trajectories to decide whether or not the environment is homogeneous based upon the output of the test a model dependent maximum likelihood localization algorithm is adopted using the measurements made by the blind node and the parameters estimated by the anchors at previous stage the performance assessment shows that the proposed approach could be a viable means to handle localization in uncertain scenarios

some global dynamical properties of the kuramoto sivashinsky equations nonlinear stability and attractors abstract the kuramoto sivashinsky equations model pattern formations on unstable flame fronts and thin hydrodynamic films they are characterized by the coexistence of coherent spatial structures with temporal chaos we investigate some global dynamical properties including nonlinear stability we demonstrate their low modal behavior in terms of determining modes and that the fractal dimension of all attractors is bounded by a universal constant times l 13 8 where l is a dimensionless pattern cell size in the one dimensional case such equations are indeed a paradigm of low dimensional behavior for infinite dimensional systems

fourth order time stepping for stiff pdes a modification of the exponential time differencing fourth order runge kutta method for solving stiff nonlinear pdes is presented that solves the problem of numerical instability in the scheme as proposed by cox and matthews and generalizes the method to nondiagonal operators a comparison is made of the performance of this modified exponential time differencing etd scheme against the competing methods of implicit explicit differencing integrating factors time splitting and fornberg and driscoll s sliders for the kdv kuramoto sivashinsky burgers and allen cahn equations in one space dimension implementation of the method is illustrated by short matlab programs for two of the equations it is found that for these applications with fixed time steps the modified etd scheme is the best

achieving asymptotic efficient performance for squared range and squared range difference localizations the estimation of a source location using directly the range or range difference measurements is difficult and requires numerical solution which is caused by the highly non linear relationship between the measurements and the unknown we can obtain a computationally efficient and non iterative algebraic solution by squaring the measurements first before solving for the unknown however a recent study has shown that such a solution is suboptimum in reaching the crlb performance and the localization accuracy could be significantly worse in some localization geometries this paper demonstrates that when range weighting factors are introduced to the squared measurements the resulting solution will be able to reach the crlb accuracy both the squared range and squared range difference cases are considered and the mean square error mse and the bias of the resulting solutions are derived the asymptotic efficiency of the proposed cost functions are proven theoretically and validated by simulations the effects of range weighting factors on the localization performance under different sensor number noise correlation and localization geometry are examined introducing range weightings to the squared range measurements increases the bias but it is negligible in the mse having range weightings in the squared range difference measurements improves both the mse and bias

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

solitons in triangular and honeycomb dynamical lattices with the cubic nonlinearity we study the existence and stability of localized states in the discrete nonlinear schrodinger equation on two dimensional nonsquare lattices the model includes both the nearest neighbor and long range interactions for the fundamental strongly localized soliton the results depend on the coordination number i e on the particular type of lattice the long range interactions additionally destabilize the discrete soliton or make it more stable if the sign of the interaction is respectively the same as or opposite to the sign of the short range interaction we also explore more complicated solutions such as twisted localized modes and solutions carrying multiple topological charge vortices that are specific to the triangular and honeycomb lattices in the cases when such vortices are unstable direct simulations demonstrate that they typically turn into zero vorticity fundamental solitons

effective masses for laplacians on periodic graphs abstract we consider laplacians on both periodic discrete and periodic metric equilateral graphs their spectrum consists of an absolutely continuous part which is a union of non degenerate spectral bands and flat bands i e eigenvalues of infinite multiplicity we estimate effective masses associated with the ends of each spectral band in terms of geometric parameters of the graphs moreover in the case of the bottom of the spectrum we determine two sided estimates on the effective mass in terms of geometric parameters of the graphs the proof is based on floquet theory factorization of fiber operators perturbation theory and the relation between effective masses for laplacians on discrete and metric graphs obtained in our paper

on the quasi splitting of exact sequences perhaps the most significant difference between the theories of torsion and torsion free abelian groups is the large number of splitting results in the former and the lack of such in the latter for instance szele s theorem f vol 1 proposition 27 11 has no obvious equivalent in the theory of torsion free abelian groups although it is one of the widely used results in the discussion of torsion and mixed groups let b g qji z p 7 be a subgroup of an abelian group g then b is a direct summand of g if and only if b np g 0 the author was able to extend szele s theorem to valuated p groups in a2 satz 6 81 using methods similar to those which proved useful in the discussion of baer s lemma in al a3 a4 it is the goal of this paper to prove a result which can be considered the equivalent of szele s theorem in the quasi category of torsion free abelian groups before we can describe the result it is necessary to introduce some notation we consider an abelian group a the class of a projective groups of finite a rank is obtained by closing a with respect to direct summands and finite direct sums if g is an abelian group then the a radical of g which is denoted by r g is r g n ker 41 e hom g a finally consider modules b and c over a ring r a homomorphism 1 b c quasi splits if there are a non zero integer n and a map 3 hom c b with cr n id where id denotes the identity map on b if the additive group of b is torsion free then a quasi splitting homomorphism is one to one jl 52 re we say that an abelian group a has the radical splitting property if every exact sequence 0 pa g of torsion free abelian groups in which p is a quasi summand of an a projective group of finite a rank and u p n r g 0 quasi splits szele s original result guarantees the splitting of the sequence in the case in which a z z p 7 for some n w moreover if a z z p z then r g p g theorem 3 1 of this paper establishes that every strongly indecomposable group of finite rank has the

a quasi steady state solver for the stiff ordinary differential equations of reaction kinetics abstract a quasi steady state method is presented that integrates stiff differential equations arising from reaction kinetics this predictor corrector method is a stable for linear equations and second order accurate the method is used for all species regardless of the time scales of the individual equations and it works well for problems typical of hydrocarbon combustion start up costs are low making the method ideal for use in process split reacting flow simulations which require the solution of an initial value problem in every computational cell for every global time step the algorithm is described and error analysis and linear stability analysis are included the algorithm is also applied to several test problems and the results are compared to those of the stiff integrator chemeq the method which we call qss is more stable more accurate and less costly than chemeq

the finite quasi baer property this paper discusses extensions of the baer splitting property to the class of self small abelian groups of finite torsion free rank this class is extensive containing the classes of torsion free abelian groups of finite rank and mixed quotient divisible groups the latter in particular includes the class g several applications of the main results are given

a ppp array aided precise point positioning with global navigation satellite systems in this paper the global navigation satellite system gnss precise point positioning ppp concept is generalized to array aided ppp a ppp a ppp is a measurement concept that uses gnss data from multiple antennas in an array of known geometry to realize improved gnss parameter estimation position attitude time and atmospheric delays the concept is formulated such that it applies to each current and future multifrequency gnss stand alone or in combination a ppp is made possible through solving a novel orthonormality constrained multivariate mixed integer least squares problem it is shown that the integer matrix constraint is necessary to obtain a precise instantaneous attitude and position solution whereas the inclusion of the orthonormality constraint in the integer ambiguity objective function is essential to achieve high instantaneous probabilities of correct integer estimation different a ppp applications are discussed with their performances illustrated by means of empirical gps results

chaos and coherent structures in partial differential equations abstract this paper addresses the possible connections between chaos the unpredictable behavior of solutions of finite dimensional systems of ordinary differential and difference equations and turbulence the unpredictable behavior of solutions of partial differential equations it is dedicated to martin kruskal on the occasion of his 60th birthday

exponential integrators for large systems of differential equations we study the numerical integration of large stiff systems of differential equations by methods that use matrix vector products with the exponential or a related function of the jacobian for large problems these can be approximated by krylov subspace methods which typically converge faster than those for the solution of the linear systems arising in standard stiff integrators the exponential methods also offer favorable properties in the integration of differential equations whose jacobian has large imaginary eigenvalues we derive methods up to order 4 which are exact for linear constant coefficient equations the implementation of the methods is discussed numerical experiments with reaction diffusion problems and a time dependent schrodinger equation are included

a composite runge kutta method for the spectral solution of semilinear pdes a new composite runge kutta rk method is proposed for semilinear partial differential equations such as korteweg de vries nonlinear schrodinger kadomtsev petviashvili kp kuramoto sivashinsky ks cahn hilliard and others having high order derivatives in the linear term the method uses fourier collocation and the classical fourth order rk method except for the stiff linear modes which are treated with a linearly implicit rk method the composite rk method is simple to implement indifferent to the distinction between dispersive and dissipative problems and as efficient on test problems for ks and kp as any other generally applicable method

rss based sensor localization in the presence of unknown channel parameters this correspondence studies the received signal strength based localization problem when the transmit power or path loss exponent is unknown the corresponding maximum likelihood estimator mle poses a difficult nonconvex optimization problem to avoid the difficulty in solving the mle we use suitable approximations and formulate the localization problem as a general trust region subproblem which can be solved exactly under mild conditions simulation results show a promising performance for the proposed methods which also have reasonable complexities compared to existing approaches

phase difference ambiguity resolution for a single frequency signal in the near field using a receiver triplet the problem of ambiguity in the phase difference of a signal received by widely spaced receivers is considered it is shown that a collinear receiver triplet with a specific configuration combined with a proposed algorithm can be utilized for phase difference disambiguation the identifiability condition is that the difference of the two smaller inter receiver spacings is not greater than a half wavelength of the impinging signal and is greater than zero the effect of the emitter location relative to the receiver array and the effect of noise are studied analytic formulae for the mean square error mse under gaussian white noise are obtained and are used to directly determine performance versus signal to noise ratio snr given the emitter location and the receiver configuration performance is found to exhibit an snr threshold effect that depends on the emitter location and the sensor configuration the analytic performance predictions are found to be close to the performance obtained in simulation

high order splitting methods for the incompressible navier stokes equations abstract a new pressure formulation for splitting methods is developed that results in high order time accurate schemes for the solution of the incompressible navier stokes equations in particular improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods a new family of stiffly stable schemes is employed in mixed explicit implicit time intgration rules these schemes exhibit much broader stability regions as compared to adams family schemes typically used in splitting methods their stability properties remain almost constant as the accuracy of the integration increases so that robust third or higher order time accurate schemes can readily be constructed that remain stable at relatively large cfl number the new schemes are implemented within the framework of spectral element discretizations in space so that flexibility and accuracy is guaranteed in the numerical experimentation a model stokes problem is studied in detail and several examples of navier stokes solutions of flows in complex geometries are reported comparison is made with the previously used first order in time spectral element splitting and non splitting e g uzawa schemes high order splitting spectral element methods combine accuracy in space and time and flexibility in geometry and thus can be very efficient in direct simulations of turbulent flows in complex geometries

robust differential received signal strength based localization source localization based on signal strength measurements has become very popular due to its practical simplicity however the severe nonlinearity and non convexity make the related optimization problem mathematically difficult to solve especially when the transmit power or the path loss exponent ple is unknown moreover even if the ple is known but not perfectly estimated or the anchor location information is not accurate the constructed data model will become uncertain making the problem again hard to solve this paper particularly focuses on differential received signal strength drss based localization with model uncertainties in case of unknown transmit power and ple a new whitened model for drss based localization with unknown transmit powers is first presented and investigated when assuming the ple is known we introduce two estimators based on an exact data model an advanced best linear unbiased estimator a blue and a lagrangian estimator le and then we present a robust semidefinite programming sdp based estimator rsdpe which can cope with model uncertainties imperfect ple and inaccurate anchor location information the three proposed estimators have their own advantages from different perspectives the a blue has the lowest complexity the le holds the best accuracy for a small measurement noise and the rsdpe yields the best performance under a large measurement noise and possesses a very good robustness against model uncertainties finally we propose a robust sdp based block coordinate descent estimator rsdp bcde to deal with a completely unknown ple and its performance converges to that of the rsdpe using a perfectly known ple

least squares algorithms for time of arrival based mobile location localization of mobile phones is of considerable interest in wireless communications in this correspondence two algorithms are developed for accurate mobile location using the time of arrival measurements of the signal from the mobile station received at three or more base stations the first algorithm is an unconstrained least squares ls estimator that has implementation simplicity the second algorithm solves a nonconvex constrained weighted least squares cwls problem for improving estimation accuracy it is shown that the cwls estimator yields better performance than the ls method and achieves both the crame spl acute r rao lower bound and the optimal circular error probability at sufficiently high signal to noise ratio conditions

the exponential accuracy of fourier and chebyshev differencing methods it is shown that when differencing analytic functions using the pseudospectral fourier or chebyshev methods the error committed decays to zero at an exponential rate

exact and approximate solutions of source localization problems we consider least squares ls approaches for locating a radiating source from range measurements which we call r ls or from range difference measurements rd ls collected using an array of passive sensors we also consider ls approaches based on squared range observations sr ls and based on squared range difference measurements srd ls despite the fact that the resulting optimization problems are nonconvex we provide exact solution procedures for efficiently computing the sr ls and srd ls estimates numerical simulations suggest that the exact sr ls and srd ls estimates outperform existing approximations of the sr ls and srd ls solutions as well as approximations of the r ls and rd ls solutions which are based on a semidefinite relaxation

exponential time differencing for stiff systems we develop a class of numerical methods for stiff systems based on the method of exponential time differencing we describe schemes with second and higher order accuracy introduce new runge kutta versions of these schemes and extend the method to show how it may be applied to systems whose linear part is nondiagonal we test the method against other common schemes including integrating factor and linearly implicit methods and show how it is more accurate in a number of applications we apply the method to both dissipative and dispersive partial differential equations after illustrating its behavior using forced ordinary differential equations with stiff linear parts

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

integer parameter estimation in linear models with applications to gps we consider parameter estimation in linear models when some of the parameters are known to be integers such problems arise for example in positioning using carrier phase measurements in the global positioning system gps where the unknown integers enter the equations as the number of carrier signal cycles between the receiver and the satellites when the carrier signal is initially phase locked given a linear model we address two problems 1 the problem of estimating the parameters and 2 the problem of verifying the parameter estimates we show that with additive gaussian measurement noise the maximum likelihood estimates of the parameters are given by solving an integer least squares problem theoretically this problem is very difficult computationally np hard verifying the parameter estimates computing the probability of estimating the integer parameters correctly requires computing the integral of a gaussian probability density function over the voronoi cell of a lattice this problem is also very difficult computationally however by using a polynomial time algorithm due to lenstra lenstra and lovasz 1982 the lll algorithm the integer least squares problem associated with estimating the parameters can be solved efficiently in practice sharp upper and lower bounds can be found on the probability of correct integer parameter estimation we conclude the paper with simulation results that are based on a synthetic gps setup

wave packet dynamics in slowly modulated photonic graphene abstract mathematical analysis on electromagnetic waves in photonic graphene a photonic topological material which has a honeycomb structure is one of the most important current research topics by modulating the honeycomb structure numerous topological phenomena have been observed recently the electromagnetic waves in such media are generally described by the 2 dimensional wave equation it has been shown that the corresponding elliptic operator with a honeycomb material weight has dirac points in its dispersion surfaces in this paper we study the time evolution of the wave packets spectrally concentrated at such dirac points in a modulated honeycomb material weight we prove that such wave packet dynamics is governed by the dirac equation with a varying mass in a large but finite time our analysis provides mathematical insights to those topological phenomena in photonic graphene

analysis of a nonlinear least squares procedure used in global positioning systems iterated least squares ils is a widely used parameter estimation algorithm for nonlinear least squares problems the ils estimation error covariance is usually written gtr 1g 1 where g is the jacobian matrix at the solution and r is the noise covariance using a first order expansion of the gain matrix in ils we provide a rigorous justification for the covariance formula the analysis includes uncertainty in the initial estimate and is capable of modeling the transient performance of the algorithm given convergence the usual ils covariance is obtained asymptotically the analysis makes use of matrix differential calculus to obtain the first differential of the ils gain matrix and includes as a special case the r i case where the gain matrix is the pseudoinverse of the jacobian matrix the results are harnessed to obtain a sensitivity analysis of the ils algorithm to additional random parametric variations the analysis is then applied to a global positioning system problem to characterize the effect of ephemeris errors on the ils position estimates results from a comparative monte carlo simulation demonstrate the approach s effectiveness

a framework for low complexity least squares localization with high accuracy in this paper a new framework is proposed for least squares localization based on estimated ranges covering time difference of arrival tdoa time of arrival toa and received signal strength rss cases the multidimensional nonlinear localization problem is first transformed to a lower dimension and then solved iteratively within the proposed transformed least squares tls framework we introduce a method in which the localization problem is transformed to one dimension 1 d in this way compared to the classical nonlinear least squares nls type of methods the amount of computations in each iteration is greatly reduced a reduction of 67 for a 3 d positioning system is shown hence the introduced 1 d iterative 1di method is fairly light on the computational load the way to choose the 1 d parameter is proposed and theoretical expressions for the convergence rate and the root mean squared error rmse of the 1di estimator are derived validation is performed mainly based on actual ultra wideband uwb radio measurements collected in typical office environments with signal bandwidths varying from 0 5 to 7 5 ghz supplementary simulations are also included for validation results show that in terms of rmse the 1di method performs better than the linear least squares lls method where the solution is obtained noniteratively and performs similarly as nls especially in tdoa cases

nonlinear waves in shallow honeycomb lattices the linear spectrum and corresponding bloch modes of shallow honeycomb lattices near dirac points are investigated via perturbation theory the dispersion relation is found to have threefold degeneracy at leading order with eigenvalue splitting at the following two orders i e the threefold eigenvalue splits into single and double values multiscale perturbation methods are employed to describe the nonlinear dynamics of the associated wave envelopes the dynamics of the envelope depends on different asymptotic balances whereupon a three level nonlinear dirac type equation or a two level nonlinear dirac equation is derived the analysis agrees well with direct numerical simulations

dynamic properties of the local linearization method for initial value problems some dynamic properties of the local linearization ll scheme for the numerical integration of initial value problems in ordinary differential equations odes are investigated specifically the general conditions under which this scheme preserves the stationary points and periodic orbits of the odes and the local stability at these steady states are studied these dynamic properties are also examined by means of numerical experiments and the results are compared with those achieved by other numerical schemes in addition a brief review of the computational implementations of the ll scheme is also presented

analysis of some krylov subspace approximations to the matrix exponential operator in this note a theoretical analysis of some krylov subspace approximations to the matrix exponential operation exp a v is presented and a priori and a posteriors error estimates are established several such approximations are considered the main idea of these techniquesis to approximately project the exponential operator onto a small krylov subspace and to carry out the resulting small exponential matrix computation accurately this general approach which has been used with success in several applications provides a systematic way of defining high order explicit type schemes for solving systems of ordinary differential equations or time dependent partial differential equations

the kuramoto sivashinsky equation a bridge between pde s and dynamical systems abstract through extensive numerical simulation we have characterized the transition to chaos of the solutions to the kuramoto sivashinsky equation the attracting solution manifolds undergo a complex bifurcation sequence including multimodal fixed points invariant tori traveling wave trains and homoclinic orbits we relate this behavior to earlier work where the kuramoto sivashinsky equation was shown to behave as a finite dimensional dynamical system of ordinary differential equations

on the existence of real spectra in mathcal pt symmetric honeycomb optical lattices this paper investigates the addition of complex potentials to schr dinger equations with honeycomb lattice potentials while self adjointness is lost symmetry with respect to the combined action of parity and time reversal is maintained necessary and sufficient conditions are found which establish whether the spectra of the perturbed schr dinger equation remains real or enters the complex plane after small perturbations numerical simulations show the impact of larger perturbations in particular nonlocal near degeneracies between dispersion bands are discussed

high resolution multiple wideband and nonstationary source localization with unknown number of sources in this paper a new algorithm for high resolution multiple wideband and nonstationary source localization using a sensor array is proposed the received signals of the sensor array are first converted into the time frequency domain via short time fourier transform stft and we find that a set of short time power spectrum matrices at different time instants have the joint diagonalization structure in each frequency bin based on such joint diagonalization structure a novel cost function is designed and a new spatial spectrum for direction of arrival doa estimation at hand is derived compared to the maximum likelihood ml method with high computational complexity the proposed algorithm obtains the doa estimates via one dimensional 1 d search instead of multidimensional search therefore its computational complexity is much lower than the ml method unlike the subspace based high resolution doa estimation techniques it is not necessary to determine the number of sources in advance for the proposed algorithm moreover the proposed method is robust to the effects of reverberation caused by multipath reflections hence it is suitable for multiple acoustic source localization in a reverberant room the results of numerical simulations and experiments in a real room with a moderate reverberation are provided to demonstrate the good performance of the proposed approach

joint ranging and synchronization for an anchorless network of mobile nodes synchronization and localization are critical challenges for the coherent functioning of a wireless network which are conventionally solved independently recently various estimators have been proposed for pairwise synchronization between immobile nodes based on time stamp exchanges via two way communication in this paper we consider a network of mobile nodes for which a novel joint time range model is presented treating both unsynchronized clocks and the pairwise distances as a polynomial functions of true time for a pair of nodes a least squares solution is proposed for estimating the pairwise range parameters between the nodes in addition to estimating the clock offsets and clock skews extending these pairwise solutions to network wide ranging and clock synchronization we present a central data fusion based global least squares algorithm a unique solution is nonexistent without a constraint on the cost function e g a clock reference node ergo a constrained framework is proposed and a new constrained cramer rao bound ccrb is derived for the joint time range model in addition to alleviate the need for a single clock reference various clock constraints are presented and their benefits are investigated using the proposed solutions simulations are conducted and the algorithms are shown to approach the theoretical limits

a novel weighted multidimensional scaling analysis for time of arrival based mobile location recently multidimensional scaling mds algorithms have been verified to be robust for the mobile localization however they do not achieve the cramer rao lower bound crlb even though the measurement noise is small in this paper a novel weighted mds method is proposed for time of arrival based mobile location it can achieve the crlb at moderate noise level before the threshold effect occurs in addition unlike the classical mds methods depending on the eigendecomposition of the scalar product matrix the proposed method is based on the matrix itself directly which in turn decreases the computational complexity

a lagrangian dual approach to the single source localization problem the single source localization problem sslp which is nonconvex by its nature appears in several important multidisciplinary fields such as signal processing and the global positioning system in this paper we cast sslp as a euclidean distance embedding problem and study a lagrangian dual approach it is proved that the lagrangian dual problem must have an optimal solution under the generalized slater condition we provide a sufficient condition for the zero duality gap and establish the equivalence between the lagrangian dual approach and the existing generalized trust region subproblem gtrs approach studied by beck et al exact and approximate solutions of source localization problems ieee trans signal process vol 56 pp 1770 1778 2008 we also reveal new implications of the assumptions made by the gtrs approach moreover the lagrangian dual approach has a straightforward extension to the multiple source localization problem numerical simulations demonstrate that the lagrangian dual approach can produce localization of similar quality as the gtrs and can significantly outperform the well known semidefinite programming solver for the multiple source localization problem on the tested cases

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

algorithms and bounds for distributed tdoa based positioning using ofdm signals one main drawback of using time difference of arrival tdoa methods for source localization and navigation is that they require centralization of multiple copies of a signal this paper considers blindly estimating the location of a cyclic prefix cp in an orthogonal frequency division multiplexing ofdm signal enabling distributed tdoa computation up to an integer ambiguity this ambiguity can be resolved using integer least squares methods if enough tdoas are available requiring only minimal cooperation between receivers the contributions of this paper are development of an algorithm for simultaneously resolving the integer ambiguities and obtaining a position estimate and derivation of the cramer rao lower bound crlb on locating the cp and hence on the underlying source localization and navigation problems

reformulation of pisarenko harmonic decomposition method for single tone frequency estimation based on the linear prediction lp property of sinusoidal signals a closed form unbiased frequency estimator for a real sinusoid in white noise is proposed the frequency estimator which is derived by minimizing a constrained least squares cost function can be considered as a reformulation of the well known pisarenko harmonic decomposer phd online computation of the frequency estimate can be achieved in a very simple manner and its variance is derived computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the phd maximum likelihood and lp based methods as well as crame spl acute r rao lower bound

accuracy comparison of ls and squared range ls for source localization in this correspondence we compute a closed form expression for the asymptotic large sample accuracy of the recently proposed squared range least squares sr ls method for source localization a beck p stoica and j li exact and approximate solutions of source localization problems ieee trans signal process vol 56 no 5 pp 1770 1778 may 2008 we compare its accuracy to that of the classical least squares ls method and show that ls and sr ls perform differently in general we identify geometries where the performances of the methods are identical but also geometries when the difference in performance is unbounded

fourier methods with extended stability intervals for the korteweg de vries equation a full leap frog fourier method for integrating the korteweg de vries kdv equation u t uu x varepsilon u xxx 0 results in an o n 3 stability constraint on the time step where n is the number of fourier modes used this stability limit is much more restrictive than the accuracy limit for many applications in this paper we propose a method for which the stability limit is extended by treating the linear dispersive u xxx term implicitly thus timesteps can be taken up to an accuracy limit larger than the explicit stability limit the implicit method is implemented without solving linear systems by integrating in time in the fourier space and discretizing the nonlinear uu x term by leap frog a second method we propose uses basis functions which solve the linear part of the kdv equation and leap frog for time integration a linearized stability analysis of the proposed schemes proves that a version of the first scheme possesses a certain kind of unconditional stability and that

symplectic integration of hamiltonian wave equations the numerical integration of a wide class of hamiltonian partial differential equations by standard symplectic schemes is discussed with a consistent hamiltonian approach we discretize the hamiltonian and the poisson structure separately then form the the resulting ode s the stability accuracy and dispersion of different explicit splitting methods are analyzed and we give the circumstances under which the best results can be obtained in particular when the hamiltonian can be split into linear and nonlinear terms many different treatments and examples are compared

characterizations of warfield groups abstract warfield groups are defined to be direct summands of simply presented abelian groups by introducing a global definition of quasi sequentially nice subgroups we prove some characterizations of warfield groups involving these groups knice subgroups and valuated coproducts furthermore we exhibit a new proof of a characterization of warfield groups in terms of nice subgroups and valuated coproducts

a pseudospectral procedure for the solution of nonlinear wave equations with examples from free surface flows an algorithm for the solution of general isotropic nonlinear wave equations is presented the algorithm is based on a symmetric factorization of the linear part of the wave operator followed by its exact integration through an integrating factor in spectral space the remaining nonlinear and forcing terms can be handled with any standard pseudospectral procedure solving the linear part of the wave operator exactly effectively eliminates the stiffness of the original problem characterized by a wide range of temporal scales the algorithm is tested and applied to several problems of three dimensional long surface waves solitary wave propagation interaction diffraction and the generation of waves by flow over slowly varying bottom topography other potential applications include waves in rotating and stratified flows and wave interaction with more pronounced topographic features

mimo radar waveform design via alternating projection waveform design is essential to unleash the performance advantages promised by multiple input multiple output mimo radar and this topic has attracted a lot of attention in the recent years revisiting an earlier examined mimo radar waveform design problem that optimizes both minimum mean square error estimation mmse and mutual information mi in this correspondence we formulate a new waveform design problem and provide some further results which complement the previous study more specifically we present an iterative optimization algorithm based on the alternating projection method to determine waveform solutions that can simultaneously satisfy a structure constraint and optimize the design criteria numerical examples are provided which illustrate the effectiveness of the proposed approach in particular we find that the waveform solutions obtained through our proposed algorithm can achieve very close and virtually indistinguishable performance from that predicted in the previous study

nonlinear wave packets in deformed honeycomb lattices the spectrum of a schrodinger operator with a perfect honeycomb lattice potential has special points called dirac points where the lowest two branches of the spectrum touch deformations can result in the merging and disappearance of the dirac points and the originally intersecting dispersion relation branches separate corresponding to these deformations nonlinear envelope equations are derived and their dynamics are studied in the region where dirac points exist a maximally balanced equation is derived which has limits to a nonlinear schrodinger kadomtsev petviashvili nlskp type equation and its dispersionless reduction when the dirac points disappear and a gap opens a different maximally balanced equation is derived which has the nlskp equation and a one dimensional nonlocal evolution equation as limits when the gap is sufficiently wide a nonlinear dirac equation with nonzero mass and a nonlinear schrodinger focusing defocusing system are found the latter two equations admit nonlinear lo

iterative minimization schemes for solving the single source localization problem we consider the problem of locating a single radiating source from several noisy measurements using a maximum likelihood ml criteria the resulting optimization problem is nonconvex and nonsmooth and thus finding its global solution is in principle a hard task exploiting the special structure of the objective function we introduce and analyze two iterative schemes for solving this problem the first algorithm is a very simple explicit fixed point based formula and the second is based on solving at each iteration a nonlinear least squares problem which can be solved globally and efficiently after transforming it into an equivalent quadratic minimization problem with a single quadratic constraint we show that the nonsmoothness of the problem can be avoided by choosing a specific good starting point for both algorithms and we prove the convergence of the two schemes to stationary points we present empirical results that support the underlying theoretical analysis and suggest that despite of its nonconvexity the ml problem can effectively be solved globally using the devised schemes

a new class of time discretization schemes for the solution of nonlinear pdes we consider issues of stability of time discretization schemes withexacttreatment of thelinear part elp schemes for solving nonlinear pdes a distinctive feature of elp schemes is the exact evaluation of the contribution of the linear term that is if the nonlinear term of the equation is zero then the scheme reduces to the evaluation of the exponential function of the operator representing the linear term computing and applying the exponential or other functions of operators with variable coefficients in the usual manner requires evaluating dense matrices and is highly inefficient it turns out that computing the exponential of strictly elliptic operators in the wavelet system of coordinates yields sparse matrices for a finite but arbitrary accuracy this observation makes our approach practical in a number of applications in particular we consider applications of elp schemes to advection diffusion equations we study the stability of these schemes and show that both explicit and implicit elp schemes have distinctly different stability properties if compared with known implicit explicit schemes for example we describe explicit schemes with stability regions similar to those of typical implicit schemes used for solving advection diffusion equations

large and small error performance limits for multipath time delay estimation the cramer rao lower bound crlb and a lower bound on the probability of large errors for multipath time delay estimation for a single resolvable multipath are developed these theoretical results are compared to the performance of the maximum likelihood estimator mle and an autocorrelator via computer simulation for small errors and large snr the mle reaches the crlb the variance of the time delay estimate for the autocorrelator is much larger than the crlb if the reflection coefficient for the delayed path is near unity for small errors and small snr the mle reduces to an autocorrelator hence their performance is identical for large errors and bandwidth time products greater than 500 the error probability for the autocorrelator is within 1 db in input snr of the lower bound on large error probability thus the autocorrelator is nearly an optimal instrumentation from the point of view of large errors at least for large bandwidth time products and the flat low pass spectrum considered here

on the maximum likelihood approach for source and network localization we consider the source and network localization problems seeking to strengthen the relationship between the weighted least square wls and the maximum likelihood ml solutions of these problems to this end we design an optimization algorithm for source and network localization under the principle that a the wls and the ml objectives should be the same and b the solution of the ml wls objective does not depend on any information besides the set of given distance measurements observations the proposed range global distance continuation r gdc algorithm solves the localization problems via iterative minimizations of smoothed variations of the wls objective each obtained by convolution with a gaussian kernel of progressively smaller variances since the last not smoothed wls objective derives directly from the ml formulation of the localization problem and the r gdc requires no initial estimate to minimize it final result is maximum likelihood approach to source and network localization problems the performance of the r gdc method is compared to that of state of the art techniques such as semidefinite programming sdp nonlinear newton least squares nls and the stress of a majorizing complex objective function smacof algorithms as well as to the cramer rao lower bound crlb the comparison reveals that the solutions obtained with the r gdc algorithm is insensitive to initial estimates and provides a localization error that closely approaches that of the corresponding fundamental bounds the r gdc is also found to achieve a complexity order comparable to that of the smacof which is known for its efficiency

high order multi implicit spectral deferred correction methods for problems of reactive flow models for reacting flow are typically based on advection diffusion reaction a d r partial differential equations many practical cases correspond to situations where the relevant time scales associated with each of the three sub processes can be widely different leading to disparate time step requirements for robust and accurate time integration in particular interesting regimes in combustion correspond to systems in which diffusion and reaction are much faster processes than advection the numerical strategy introduced in this paper is a general procedure to account for this time scale disparity the proposed methods are high order multi implicit generalizations of spectral deferred correction methods misdc methods constructed for the temporal integration of a d r equations spectral deferred correction methods compute a high order approximation to the solution of a differential equation by using a simple low order numerical method to solve a series of correction equations each of which increases the order of accuracy of the approximation the key feature of misdc methods is their flexibility in handling several sub processes implicitly but independently while avoiding the splitting errors present in traditional operator splitting methods and also allowing for different time steps for each process the stability accuracy and efficiency of misdc methods are first analyzed using a linear model problem and the results are compared to semi implicit spectral deferred correction methods furthermore numerical tests on simplified reacting flows demonstrate the expected convergence rates for misdc methods of orders three four and five the gain in efficiency by independently controlling the sub process time steps is illustrated for nonlinear problems where reaction and diffusion are much stiffer than advection although the paper focuses on this specific time scales ordering the generalization to any ordering combination is straightforward

linear least squares approach for accurate received signal strength based source localization a conventional approach for passive source localization is to utilize signal strength measurements of the emitted source received at an array of spatially separated sensors the received signal strength rss information can be converted to distance estimates for constructing a set of circular equations from which the target position is determined nevertheless a major challenge in this approach lies in the shadow fading effect which corresponds to multiplicative measurement errors by utilizing the mean and variance of the squared distance estimates we devise two linear least squares lls estimators for rss based positioning in this paper the first one is a best linear unbiased estimator while the second is its improved version by exploiting the known relation between the parameter estimates the variances of the position estimates are derived and confirmed by computer simulations in particular it is proved that the performance of the improved lls estimator achieves cramer rao lower bound at sufficiently small noise conditions