hybrid nearly singular integration for three dimensional isogeometric boundary element analysis of coatings and other thin structures abstract the isogeometric boundary element method igabem has great potential for the simulation of elasticity problems because of its exact geometric representation and good approximation properties these advantages can be extended to thin structures including coatings but the development of an accurate and efficient method to deal with the large number of nearly singular integrals existing in the igabem presents a great challenge for very thin sections in this paper we propose a new sinh scheme for weakly strongly and hyper near singular integrals arising in 3d igabem for thermoelastic problems based on the sinh transformation method and adaptive integral method the presented scheme is efficient since it combines the advantages of both methods 1 when the thickness of coatings thin structures is moderately small an accurate and efficient integral result will be obtained by the adaptive integral method 2 when is very small the nearly singular integrals are computed by the sinh scheme efficiently with the introduction of nurbs in igabem truncation errors arising in the taylor expansion cannot be ignored based on the values of these errors the computed knot spans are further divided into several sub knot spans and different methods will be used to evaluate the integral over each sub knot span in the new scheme in addition based on the analytical extension of the nurbs surface an adaptation of the sinh transformation method is proposed which can evaluate the near singular integrals accurately for cases in which the projection point lies outside of the considered knot span several numerical examples are presented to validate the accuracy and efficiency of the 3d igabem based on the sinh scheme in the analysis of thermoelastic problems

distributed finite element kalman filter for field estimation the paper deals with decentralized state estimation for spatially distributed systems described by linear partial differential equations from discrete in space and time noisy measurements provided by sensors deployed over the spatial domain of interest a fully scalable approach is pursued by decomposing the domain into possibly overlapping subdomains assigned to different processing nodes interconnected to form a network each node runs a local finite dimensional discrete time kalman filter which exploits the finite element approach for spatial discretization a backward euler method for time discretization and the parallel schwarz method to iteratively enforce continuity of the field predictions over the boundaries of adjacent subdomains numerical stability of the adopted approximation scheme and stability of the proposed distributed finite element kalman filter are mathematically proved the effectiveness of the proposed approach is then demonstrated via simulation experiments concerning the estimation of a bi dimensional temperature field

distributed linear estimation over sensor networks we consider a network of sensors in which each node may collect noisy linear measurements of some unknown parameter in this context we study a distributed consensus diffusion scheme that relies only on bidirectional communication among neighbour nodes nodes that can communicate and exchange data and allows every node to compute an estimate of the unknown parameter that asymptotically converges to the true parameter at each time iteration a measurement update and a spatial diffusion phase are performed across the network and a local least squares estimate is computed at each node the proposed scheme allows one to consider networks with dynamically changing communication topology and it is robust to unreliable communication links and failures in measuring nodes we show that under suitable hypotheses all the local estimates converge to the true parameter value

a sinh transformation for evaluating two dimensional nearly singular boundary element integrals a new transformation technique is introduced for evaluating the two dimensional nearly singular integrals which arise in the solution of laplace s equation in three dimensions using the boundary element method when the source point is very close to the element of integration the integrals are evaluated using in a product fashion a transformation which has recently been used to evaluate one dimensional near singular integrals this sinh transformation method automatically takes into account the position of the projection of the source point onto the element and also the distance b between the source point and the element the method is straightforward to implement and when it is compared with a number of existing techniques for evaluating two dimensional near singular integrals it is found that the sinh method is superior to the existing methods considered both for potential integrals across the full range of b values considered 0 0 01 for smaller values of b the use of the lmethod is recommended for flux integrals copyright 2006 john wiley sons ltd

acoustic scattering from an arbitrarily rough surface a method is described for dealing with acoustic scattering from a time independent pressure release surface as in work by previous authors the problem is formulated as an integral equation on the surface this formulation takes account of arbitrarily large surface roughness and multiple scattering phenomena at the surface the problem may be considered naturally in two stages the first part of the problem is to invert the integral equation to find the pressure gradient on the surface the eigenfunction expansion method used by holford j acoust soc am 70 1116 1128 1981 for periodic surfaces is extended to deal with more general aperiodic surfaces it is then shown that this approach is almost exactly equivalent to a direct collocation method the second part of the problem is to evaluate the scattered pressure away from the surface the method used here is to calculate the reflection coefficients from the fourier transform of the pressure gradient on the surface the reflection coefficients giv

distributed robust filtering with h consensus of estimates the paper addresses a problem of design of distributed robust filters using the recent vector dissipativity theory the main result is a sufficient condition which guarantees a suboptimal h level of disagreement of estimates in a network of filters it involves solving a convex optimization feasibility problem subject to lmi constraints the special case of balanced interconnection graphs is also considered a gradient descent type algorithm is presented which allows the nodes to compute their estimator parameters in a decentralized manner the proposed approach is applied to the problem of observer based robust synchronization of a nonlinear network to an isolated node

diffusion strategies for distributed kalman filtering and smoothing we study the problem of distributed kalman filtering and smoothing where a set of nodes is required to estimate the state of a linear dynamic system from in a collaborative manner our focus is on diffusion strategies where nodes communicate with their direct neighbors only and the information is diffused across the network through a sequence of kalman iterations and data aggregation we study the problems of kalman filtering fixed lag smoothing and fixed point smoothing and propose diffusion algorithms to solve each one of these problems we analyze the mean and mean square performance of the proposed algorithms provide expressions for their steady state mean square performance and analyze the convergence of the diffusion kalman filter recursions finally we apply the proposed algorithms to the problem of estimating and tracking the position of a projectile we compare our simulation results with the theoretical expressions and note that the proposed approach outperforms existing techniques

boundary integral equations for thin bodies summary a boundary integral equation formulation for thin bodies which uses cbie conventional bie only is well known to be degenerate a mixed formulation for a thin rigid scatterer which combines cbie and hbie hypersingular bie is motivated by examining the discretized form of the integral equations and this formulation is shown to be nondegenerate for thin non rigid inclusion problems a near singular integration procedure useful for singular integrals as well is presented finally numerical examples for acoustic wave scattering from rigid and soft scatterers are presented

consensus based linear and nonlinear filtering this note addresses distributed state estimation dse over sensor networks two existing consensus approaches for dse i e consensus on information ci and consensus on measurements cm are combined to provide a novel class of hybrid consensus filters named hybrid cmci which enjoy the complementary benefits of cm and ci novel theoretical results limitedly to linear systems on the guaranteed stability of the hybrid cmci filters under collective observability and network connectivity are proved finally the effectiveness of the proposed class of consensus filters is evaluated on a target tracking case study with both linear and nonlinear sensors

square root kalman filtering of descriptor systems abstract a novel square root information filter algorithm is proposed to solve the kalman filtering problem for discrete time descriptor systems unlike standard square root information filters the present approach does not impose restrictions on the state transition matrix or on the noise covariance matrix the resulting implementation exhibits a moderate computational burden and good numerical properties and has general applicability to the state estimation of discrete time linear dynamic descriptor systems

the linear quadratic optimal regulator for descriptor systems discrete time case abstract in this paper the linear quadratic optimal regulator problem for the discrete time descriptor system ex k 1 ax k bu k where e is in general a singular matrix is investigated the continuous time version of this problem was treated elsewhere the discrete time theory is largely parallel to the continuous time theory but there are several important differences one is that in the discrete time case a fairly general problem can be solved with singular cost matrices the key to the solution as for the continuous time problem is a coordinate system which can be computed by performing a singular value decomposition of e this is called an svd coordinate system the optimization problem is solved by applying hamiltonian minimization to compute the optimal trajectory of the vector consisting of the concatenated descriptor codescriptor and control vectors in the general singular cost case this trajectory is computed by recursively solving a discrete time riccati equation from the optimal trajectory the optimal descriptor variable feedback gain relating the control to the descriptor variable can be computed several riccati difference equations are derived all of which have the same solution this solution can be used to compute the optimal trajectory and cost for non singular problems even in the finite horizon case the optimal feedback gain can be computed non recursively by solving an eigenvalue eigenvector problem formulated from the system parameters in the svd coordinate system the optimal gain for the infinite horizon steady state problem on the other hand can be computed from the solution of an eigenvector problem involving the untransformed system parameters

non singular boundary integral representation of stresses this paper presents the derivation of the non singular integral representation of stresses in two and three dimensional elastostatics in contrast to the strongly singular and weakly singular integral representations the numerical computation of the nearly singular integrals is eliminated because all the integrands are made finite in this new formulation even if the internal point approaches the boundary thus the method gives accurate numerical results even in that portion of a solid which is very close to a discretized boundary three test problems are analysed in which we present a comparison of the accuracies achieved by the numerical computations based on the use of strongly singular weakly singular and non singular integral representations of stresses

the method of steepest descent for estimating quadrature errors this work presents an application of the method of steepest descent to estimate quadrature errors the method is used to provide a unified approach to estimating the truncation errors which occur when gauss legendre quadrature is used to evaluate the nearly singular integrals that arise as part of the two dimensional boundary element method the integrals considered here are of the form 1 1 h x d x x a 2 b 2 where h x is a well behaved function 0 and 1 a 1 since 0 b 1 the integral is nearly singular with a sharply peaked integrand the method of steepest descent is used to estimate the generally large truncation errors that occur when gauss legendre quadrature is used to evaluate these integrals as well as to estimate the much lower errors that occur when gauss legendre quadrature is performed on such integrals after a sinh transformation has been applied the new error estimates are highly accurate in the case of the transformed integral and are shown to be comparable to those found in previous work by elliott and johnston 2007 one advantage of the new estimates is that they are given by just one formula each for the un transformed and the transformed integrals rather than the much larger set of formulae in the previous work another advantage is that the new method applies over a much larger range of values than the previous method

estimation under unknown correlation covariance intersection revisited addresses the problem of obtaining a consistent estimate or upper bound of the covariance matrix when combining two quantities with unknown correlation the combination is defined linearly with two gains when the gains are chosen a priori a family of consistent estimates is presented in the note the member in this family having minimal trace is said to be family optimal when the gains are to be optimized in order to achieve minimal trace of the family optimal estimate of the covariance matrix it is proved that the global optimal solution is actually given by the covariance intersection algorithm which conducts the search only along a one dimensional curve in the n squared dimensional space of combination gains

the rayleigh equations for a multi sinusoidal periodic surface it was shown by purcell j acoust soc am 100 2919 2936 1996 that the rayleigh equations in the fourier domain for the reflection coefficients for scattering of a plane wave from a pressure release sinusoid are valid if the maximum slope of the sinusoid kd 0 6627 this current work finds the corresponding constraint sufficient for the validity of rayleigh s equations for a more general periodic surface consisting of a finite sum of sinusoids the mathematical basis of the derivation of the rayleigh equations from the helmholtz integral formula is a fourier series given by oberhettinger unlike the single sinusoid case developed by purcell referenced above the analysis of the general periodic surface given here requires an analytic continuation argument in addition a set of infinite linear equations of the second kind is derived for the reflection coefficients for the general periodic surface this guarantees that the truncation solutions for the reflection coefficients converge and are unique the matrix elements involved in these equations of the second kind require the numerical evaluation of a finite integral a generalization of bessel s integral for the integer index bessel functions and all calculations required can be performed by desktop computing

on the optimality of conditional expectation as a bregman predictor we consider the problem of predicting a random variable x from observations denoted by a random variable z it is well known that the conditional expectation e x z is the optimal l sup 2 predictor also known as the least mean square error predictor of x among all borel measurable functions of z in this orrespondence we provide necessary and sufficient conditions for the general loss functions under which the conditional expectation is the unique optimal predictor we show that e x z is the optimal predictor for all bregman loss functions blfs of which the l sup 2 loss function is a special case moreover under mild conditions we show that the blfs are exhaustive i e if for every random variable x the infimum of e f x y over all constants y is attained by the expectation e x then f is a blf

taylor expansions for singular kernels in the boundary element method the problem treated is the integration of singular functions which arise in three dimensional isoparametric formulations of boundary integral equations a taylor expansion in the local parametric co ordinates is developed for the singular integrand so allowing singular terms to be integrated in closed form even for curved surface elements the remainder integral obtained by subtracting out the worst singularities is integrated by repeated gaussian quadrature two groups of tests are presented first the accuracy of the integrations has been checked for plane parallelograms for which exact solutions have been developed and for curved elements on a sphere secondly results from complete boundary element calculations based on point collocation have been compared with known analytical solutions to two problems zonal surface harmonics on a sphere and the capacitance of an ellipsoid the agreement obtained with few degrees of freedom suggests that errors which have previously been attributed to point collocation might have arisen in the numerical integration

a self adaptive co ordinate transformation for efficient numerical evaluation of general boundary element integrals almost all general purpose boundary element computer packages include a curved geometry modelling capability thus numerical quadrature schemes play an important role in the efficiency of programming the technique the present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two dimensional axisymmetric and three dimensional applications emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of gaussian quadrature scheme s within the near singularity range the procedure can easily be implemented into existing be codes and presents the important feature of being self adaptive i e it produces a variable lumping of the gauss stations toward the singularity depending on the minimum distance from the source point to the element the self adaptiveness of the scheme also makes it inactive when not useful large source distances which makes it very safe for general usage

high level primitives for recursive maximum likelihood estimation this paper proposes a high level language constituted of a small number of primitives and macros for describing recursive maximum likelihood ml estimation algorithms this language is applicable to estimation problems involving linear gaussian models or processes taking values in a finite set the use of high level primitives allows the development of highly modular ml estimation algorithms based on simple numerical building blocks the primitives which correspond to the combination of different measurements the extraction of sufficient statistics and the conversion of the status of a variable from unknown to observed or vice versa are first defined for linear gaussian relations specifying mixed deterministic stochastic information about the system variables these primitives are used to define other macros and are illustrated by deriving new filtering and smoothing algorithms for linear descriptor systems the primitives are then extended to finite state processes and used to implement the viterbi ml state sequence estimator for a hidden markov model

distributed bayesian estimation of linear models with unknown observation covariances in this paper we address the problem of distributed bayesian estimation in networks of agents over a given undirected graph the agents observe data represented by a general linear model with unknown covariance matrices the agents try to reach consensus on the belief on the unknown linear parameters based on their private signals and information provided by their neighbors the belief is defined by the posterior distribution of the parameters after deriving the bayesian belief held by a fictitious fusion center we present a consensus based solution where the agents reach the belief of the fusion center according to our scheme at every time instant each agent carries out three operations a receives private noisy measurements b exchanges information about its belief with its neighbors and c updates its belief with the new information we show that with the proposed method the kullback leibler divergence between the beliefs of the agents and the fusion center converges to zero we demonstrate the performance of the method by computer simulations

non singular boundary integral equation implementation the basis of the boundary integral equation bie development is the singular field solution for the kelvin point load problem the presence of the mathematical singularity in an otherwise non singular problem has created over the years a variety of numerical coping strategies the current paper extends some of the earlier works in a simple manner that eliminates the mathematical singularity through analytical integration of the critical terms the resulting formulation is fully non singular and is shown to be amenable to simple low order gaussian integration the critical class of problems involving thin sections and or highly graded bie meshes now can be solved without previous problems and concerns the accuracy of the numerical integrations used in creating the linear bie equations extension of the formulation approach to remove hypersingular formulation problems in fracture mechanics is seen to be a future beneficiary of the semi analytical bie implementation reported herein

analysis of shell like structures by the boundary element method based on 3 d elasticity formulation and verification in this paper the boundary element method bem for 3 d elastostatic problems is studied for the analysis of shell or shell like structures it is shown that the conventional boundary integral equation cbie for 3 d elasticity does not degenerate when applied to shell like structures contrary to the case when it is applied to crack like problems where it does degenerate due to the closeness of the two crack surfaces the treatment of the nearly singular integrals which is a crucial step in the applications of bies to thin shapes is presented in detail to verify the theory numerical examples of spherical and ellipsoidal vessels are presented using the bem approach developed in this paper it is found that the system of equations using the cbie is well conditioned for all the thickness studied for the vessels the advantages disadvantages and potential applications of the proposed bem approach to shell like structures as compared with the fem regarding modelling and accuracy are discussed in the last section applications of this bem approach to shell like structures with non uniform thickness stiffeners and layers will be reported in a subsequent paper 1998 john wiley sons ltd

a semi analytical algorithm for the evaluation of the nearly singular integrals in three dimensional boundary element methods the nearly singular integrals occur in the boundary integral equations when the source point is close to an integration element as compared to its size but not on the element in this paper the concept of a relative distance from a source point to the boundary element is introduced to describe possible influence of the singularity of the integrals then a semi analytical algorithm is proposed for evaluating the nearly strongly singular and hypersingular integrals in the three dimensional bem by using integration by parts the nearly singular surface integrals on the elements are transformed to a series of line integrals along the contour of the element the singular behavior which appears as factor is separated from remaining regular integrals consequently standard numerical quadrature can provide very accurate evaluation of the resulting line integrals the semi analytical algorithm is applied to analyzing the three dimensional elasticity problems such as very thin walled structures meanwhile the displacements and stresses at the interior points very close to its bounding surface are also determined efficiently the results of the numerical investigation demonstrate the accuracy and effectiveness of the algorithm

distributed moving horizon estimation for linear constrained systems this paper presents a novel distributed estimation algorithm based on the concept of moving horizon estimation under weak observability conditions we prove convergence of the state estimates computed by any sensors to the correct state even when constraints on noise and state variables are taken into account in the estimation process simulation examples are provided in order to show the main features of the proposed method

a tutorial on the geometric analysis of linear time invariant implicit systems abstract a background of recent work in nonregular and regular implicit systems of the form e x ax bu is provided then the output nulling unknown input and composite subspaces are defined for singular systems with recursions given for their computation inner subspaces that is those in the domain of e and a are distinguished from outer subspaces those in the codomain of e and a the notions of composite preimage and composite image are introduced the result is a framework that unifies some of the recent work in the geometric theory of implicit systems system properties are discussed for both regular and nonregular systems and duality is investigated

three dimensional stress analysis of thin structures using a boundary element method with sinh transformation for nearly singular integrals abstract in this work a three dimensional 3d boundary element method was established with an efficient nonlinear coordinate transformation scheme namely sinh transformation to evaluate nearly singular integrals in boundary integral formulations second order quadrilateral surface elements were developed based on this method to accurately describe the geometry of thin structures the elastic behaviors of selected thin structures were then computed by using the 3d boundary element model to demonstrate the accuracy and efficiency of this approach a number of testing examples i e the 3d kirsch problem the thin spherical shell problem the ellipsoidal vessel problem with non uniform thickness and the hollow circular cylinder problem were numerically studied to test the established method remarkable accuracy and efficiency were found in the developed approach through the comparison to the numerical results and analytical solutions reported in the literature

a sinh transformation for evaluating nearly singular boundary element integrals an implementation of the boundary element method requires the accurate evaluation of many integrals when the source point is far from the boundary element under consideration a straightforward application of gaussian quadrature suffices to evaluate such integrals when the source point is on the element the integrand becomes singular and accurate evaluation can be obtained using the same gaussian points transformed under a polynomial transformation which has zero jacobian at the singular point a class of integrals which lies between these two extremes is that of nearly singular integrals here the source point is close to but not on the element and the integrand remains finite at all points however instead of remaining flat the integrand develops a sharp peak as the source point moves closer to the element thus rendering accurate evaluation of the integral difficult this paper presents a transformation based on the sinh function which automatically takes into account the position of the projection of the source point onto the element which we call the nearly singular point and the distance from the source point to the element the transformation again clusters the points towards the nearly singular point but does not have a zero jacobian implementation of the transformation is straightforward and could easily be included in existing boundary element method software it is shown that for the two dimensional boundary element method several orders of magnitude improvement in relative error can be obtained using this transformation compared to a conventional implementation of gaussian quadrature asymptotic estimates for the truncation errors are also quoted copyright 2004 john wiley sons ltd

an improved exponential transformation for nearly singular boundary element integrals in elasticity problems abstract this paper presents an improved exponential transformation for nearly singular boundary element integrals in elasticity problems the new transformation is less sensitive to the position of the projection point compared with the original transformation in our work the conventional distance function is modified into a new form in the polar coordinate system based on the refined distance function an improved exponential transformation is proposed in the polar coordinate system moreover to perform integrations on irregular elements an adaptive integration scheme considering both the element shape and the projection point associated with the improved transformation is proposed furthermore when the projection point is located outside the integration element another nearest point is introduced to subdivide the integration elements into triangular or quadrilateral patches of fine shapes numerical examples are presented to verify the proposed method results demonstrate the accuracy and efficiency of our method

an isogeometric boundary element method using adaptive integral method for 3d potential problems due to the merits of exact geometrical representation high accuracy no meshing process and only the boundary description of the problem etc the isogeometric boundary element method i e igabem has achieved rapid development in this paper based on the upper bound of the relative error of the gaussian quadrature formula we presented a 3d igabem using adaptive integration method for potential problems this method offers a number of key improvements compared with conventional igabem firstly the boundary element integrations can be computed easily and effectively at optimal computational cost secondly the adaptive algorithm can cope with the common situation where the sizes of adjacent cells are significantly different moreover the presented method can compute the nearly singular integrals easily owing to the use of subdivision technique to accurately evaluate the singular integrals appearing in our method the power series expansion method is employed the integration surface is on the real surface of the model rather than the interpolation surface i e no geometrical errors thus the value of integral is more accurate than the traditional boundary element method which can improve the computation accuracy of the igabem numerical tests show that the presented method has good performance in both exactness and convergence a general method is proposed to calculate the nearly singular integrals appearing in the 3d igabem the boundary element integrations can be computed easily and effectively at optimal computational cost the adaptive algorithm can be used to cope with the common situation where the sizes of adjacent cells are significantly different the power series expansion method is expanded to compute the singular integrals appearing in 3d igabem

derivation of the phd and cphd filters based on direct kullback leibler divergence minimization in this paper we provide novel derivations of the probability hypothesis density phd and cardinalised phd cphd filters without using probability generating functionals or functional derivatives we show that both the phd and cphd filters fit in the context of assumed density filtering and implicitly perform kullback leibler divergence kld minimizations after the prediction and update steps we perform the kld minimizations directly on the multitarget prediction and posterior densities

convergence speed in distributed consensus and averaging we study the convergence speed of distributed iterative algorithms for the consensus and averaging problems with emphasis on the latter we first consider the case of a fixed communication topology we show that a simple adaptation of a consensus algorithm leads to an averaging algorithm we prove lower bounds on the worst case convergence time for various classes of linear time invariant distributed consensus methods and provide an algorithm that essentially matches those lower bounds we then consider the case of a time varying topology and provide a polynomial time averaging algorithm

multi patch nonsingular isogeometric boundary element analysis in 3d abstract a multi patch nonsingular isogeometric boundary element method igabem for 3d problems is presented that provides accurate solutions for multi patch igabem in order to conveniently implement this method based on the greville abscissae a new collocation method moves the first and the last collocation points of each parametric direction inside of their patches and a simple method for merging equations handles the extra equations the numerical results verify the accuracy and efficiency of the present method by comparing it to the conventional igabem

an unsteady 3d isogeometrical boundary element analysis applied to nonlinear gravity waves abstract in this paper we describe a three dimensional isogeometric analysis based on the boundary element method iga bem in the time domain we show the capabilities and accuracy of the method for the simulation of non linear gravity waves the flow is assumed to be inviscid and irrotational and this leads to a mixed boundary value problem governed by the laplace s equation the boundary integral equation is solved at each time step and the time marching scheme is performed with a fourth order runge kutta method the hydrodynamic force is calculated with an auxiliary boundary equation in the simulations the analysis suitable t spline and nurbs basis are used to approximate both the geometry and the bem variables in the context of the bezier extraction framework the main advantages of this approach are 1 the control of the continuity and smoothness of the t spline and nurbs basis which makes the model numerically stable without the need of artificial smooth techniques 2 the high geometrical approximation of the non rational splines 3 the refinement capabilities without affecting the geometry and bem variables and 4 and the direct integration with computer aided geometrical design tools some numerical benchmark examples are analysed to demonstrate the accuracy and the stability of the method in addition we report simulations of waves generated by the movement of submerged foils which have implications in some wave generator systems installed in surf parks

regularization of hypersingular and nearly singular integrals in the potential theory and elasticity both the hypersingular and nearly singular integrals which appear in the hypersingular boundary integralequations and integral representations of the secondary fields respectively are regularized by the application of the superposition principle two kinds of the non singular formulations namely those with the strongly singular and weakly singular kernels are presented in this paper the formulations are given in terms of the relevant boundary quantities and the collocation at element junctions is possible two and three dimensional problems are analysed simultaneously in a unique way for either internal or external problems of the potential theory and elasticity

multiple window moving horizon estimation long horizon lengths in moving horizon estimation are desirable to reach the performance limits of the full information estimator however the conventional mhe technique suffers from a number of deficiencies in this respect first the problem complexity scales at least linearly with the horizon length selected which restrains from selecting long horizons if computational limitations are present second there is no monitoring of constraint activity inactivity which results in conducting redundant constrained minimizations even when no constraints are active in this study we develop a multiple window moving horizon estimation strategy mw mhe that exploits constraint inactivity to reduce the problem size in long horizon estimation problems the arrival cost is approximated using the unconstrained full information estimator arrival cost to guarantee stability of the technique a new horizon length selection criterion is developed based on the sensitivity between remote states in time the development will be in terms of general causal descriptor systems which includes the standard state space representation as a special case the potential of the new estimation algorithm will be demonstrated with an example showing a significant reduction in both computation time and numerical errors compared to conventional mhe

a general algorithm for evaluating nearly singular integrals in anisotropic three dimensional boundary element analysis abstract this paper presents a new general method for the evaluation of nearly singular boundary element integrals arising in anisotropic three dimensional 3d boundary element analysis it is shown that the original nearly singular integrals can be transformed into using a sinh function an element by element sum of regular integrals each one expressed in terms of intrinsic local coordinates as a consequence the actual computation can be performed by using standard n n gaussian quadrature and the procedure can be easily included in any existing computer code this new method has full generality and therefore can be applied to a wide class of integrals the numerical results demonstrate the accuracy and efficiency of the method along with its insensitivity to the location of the nearly singular points it is shown that several orders of magnitude improvement in relative errors can be obtained using this transformation when compared to a straightforward implementation of gaussian quadrature

filtering and lqg problems for discrete time stochastic singular systems discrete time stochastic singular systems are discussed filtering and linear quadratic gaussian lqg problems are considered the problems are first transformed into the normal form via state augmentation and then solved by utilizing standard results for nonsingular systems the linear unbiased least squares state estimation algorithm and the optimal control law for the lqg problem are given the order of the filtering algorithm obtained in this way is not much increased moreover this algorithm allows the presence of some kinds of control inputs

kullback leibler average consensus on probability densities and distributed state estimation with guaranteed stability this paper addresses distributed state estimation over a sensor network wherein each node equipped with processing communication and sensing capabilities repeatedly fuses local information with information from the neighbors estimation is cast in a bayesian framework and an information theoretic approach to data fusion is adopted by formulating a consensus problem on the kullback leibler average of the local probability density functions pdfs to be fused exploiting such a consensus on local posterior pdfs a novel distributed state estimator is derived it is shown that for a linear system the proposed estimator guarantees stability i e mean square boundedness of the state estimation error in all network nodes under the minimal requirements of network connectivity and system observability and for any number of consensus steps finally simulation experiments demonstrate the validity of the proposed approach

a boundary face method for potential problems in three dimensions this work presents a new implementation of the boundary node method bnm for numerical solution of laplace s equation by coupling the boundary integral equations and the moving least squares mls approximation the bnm is a boundary type meshless method however it still uses the standard elements for boundary integration and approximation of the geometry thus loses the advantages of the meshless methods in our implementation here called the boundary face method the boundary integration is performed on boundary faces which are represented in parametric form exactly as the boundary representation data structure in solid modeling the integrand quantities such as the coordinates of gauss integration points jacobian and out normal are calculated directly from the faces rather than from elements in order to deal with thin structures a mixed variable interpolation scheme of 1 d mls and lagrange polynomial for long and narrow faces an adaptive integration scheme for nearly singular integrals has been developed numerical examples show that our implementation can provide much more accurate results than the bnm and keep reasonable accuracy in some extreme cases such as very irregular distribution of nodes and thin shells copyright 2009 john wiley sons ltd

fusion of labeled rfs densities with minimum information loss this paper addresses fusion of labeled random finite set lrfs densities according to the criterion of minimum information loss mil the mil criterion amounts to minimizing the weighted sum of kullback leibler divergences klds with the fused density appearing as righthand argument of the klds the optimal fused density following the mil rule is the linear opinion pool of local ones however such results cannot be directly applied to the marginalized delta generalized labeled multi bernoulli m delta glmb and labeled multi bernoulli lmb densities since the resulting fused densities are not belonging to the same family of local ones thus cannot be adopted in the context of bayesian filtering which requires the conjugacy of prior in order to overcome such difficulties when lrfs densities are m delta glmb or lmb the mil rule is further elaborated by imposing the constraint that the fused density be in the same family of local ones the resulting fusion rules are derived in closed form and the error of replacing the optimal fused density with the best m delta glmb lmb one is theoretically analyzed the derivation of mil fusion of m delta glmb lmb densities is based on the assumption that their label spaces have been matched which however cannot be satisfied in the majority of practical applications it is shown theoretically that label matching can be solved as a separate problem with respect to lrfs density fusion by resorting to the mil criterion finally the performance of the proposed fusion approach is assessed via simulation experiments concerning distributed multitarget tracking dmt on a sensor network

a general algorithm for the numerical evaluation of nearly singular integrals on 3d boundary element a general numerical method is proposed to compute nearly singular integrals arising in the boundary integral equations bies the method provides a new implementation of the conventional distance transformation technique to make the result stable and accurate no matter where the projection point is located the distance functions are redefined in two local coordinate systems a new system denoted as a b is introduced here firstly its implementation is simpler than that of the polar system and it also performs efficiently then a new distance transformation is developed to remove or weaken the near singularities to perform integration on irregular elements an adaptive integration scheme is applied numerical examples are presented for both planar and curved surface elements the results demonstrate that our method can provide accurate results even when the source point is very close to the integration element and can keep reasonable accuracy on very irregular elements furthermore the accuracy of our method is much less sensitive to the position of the projection point than the conventional method

a new treatment of rough surface scattering this paper treats the problem of the scattering of a narrow beam at a randomly rough surface where the height distribution is gaussian and the correlation of heights is gaussian the field at the surface is assumed to satisfy a dirichlet boundary condition the problem is formulated using the standard integral equation approach in the case when the rms height is very large numerical solution of this equation for a realization of the surface involves the solution of a very large matrix problem particularly if the beam is scattered to other parts of the surface that are at a considerable distance from the initial illumination here we provide a straightforward technique motivated by ray theory that allows only those parts of the surface that are actually illuminated at any stage to be treated thus for the first reflection of the beam one solves an integral equation over the initially illuminated area this solution is used to determine the parts of the surface which give rise to doubly scattered waves and one then solves the integral equation over the newly illuminated area and so on until all reflections have been accounted for this procedure can be carried out with no explicit reference to any ray model working simply with the discrete matrix form of the integral equation in particular for one dimensional surface variation a strategy of successive sweeps from left to right and back again for a beam incident from the left is shown to be successful any standard iterative or direct solution technique can be used for the sequence of sub problems so introduced the general method is also applicable to scattering from surfaces varying in two dimensions

mean square state estimation for sensor networks this paper deals with mean square state estimation over sensor networks with a fixed topology attention is focused on designing local stationary state estimators with a general structure while accounting for the network communication topology two estimator design approaches are proposed one is based on the observability gramian and the other on the controllability gramian the computation of the estimator state space matrices is recast as off line convex optimization problems and requires the system asymptotic stability and global knowledge of the network topology convergence of the estimation error variance is ensured at each network node and a guaranteed performance in the mean square sense is achieved the proposed approaches are also extended for designing robust filters to handle polytopic type parameter uncertainty

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example