geometric quantization of dirac manifolds we extend a prequantization procedure to dirac manifolds by using singular distributions obtained from 2 cocycles associated with dirac structures given a dirac manifold m d we describe a prequantization formula in terms of a lie algebroid connection and show that it is a representation of a poisson algebra consisting of admissible functions on m d on the space of global sections of a hermitian line bundle over m if and only if the curvature derived from the lie algebroid connection is represented by a skew symmetric operation which is naturally defined for m d moreover we describe a necessary and sufficient condition for the prequantization formula to be the representation in terms of a lie algebroid cohomology we introduce the notion of a polarization for m d and construct a representation of a subalgebra of admissible functions lastly we discuss procedures for quantization in two cases where m is compact and where m is not compact

new approach to information fusion steady state kalman filtering by the modern time series analysis method based on the autoregressive moving average arma innovation model a unified and general information fusion steady state kalman filtering approach is presented for the general multisensor systems with different local dynamic models and correlated noises it can handle the filtering smoothing and prediction fusion problems for state or signal the optimal fusion rule weighted by matrices is re derived as a weighted least squares wls fuser and is reviewed an optimal fusion rule weighted by diagonal matrices is presented which is equivalent to the optimal fusion rule weighted by scalars for components and it realizes a decoupled fusion the new algorithms of the steady state kalman estimator gains are presented in order to compute the optimal weights the formulas of computing the cross covariances among local estimation errors by lyapunov equations are presented the exponential convergence of the iterative solution of lyapunov equation is proved it is proved that the optimal fusion estimators under three weighted fusion rules are locally optimal but are globally suboptimal the proposed steady state kalman fusers can reduce the on line computational burden and are suitable for real time applications a simulation example for the 3 sensor steady state kalman tracking fusion estimators shows their effectiveness and correctness and gives the accuracy comparison of the fusion rules

self tuning decoupled information fusion wiener state component filters and their convergence for the multisensor systems with unknown noise variances using the modern time series analysis method based on on line identification of the moving average ma innovation models and based on the solution of the matrix equations for correlation function the on line estimators of the noise variances are obtained and under linear minimum variance optimal information fusion criterion weighted by scalars for state components a class of self tuning decoupled fusion wiener filters is presented it realizes the self tuning decoupled local wiener filters and self tuning decoupled fused wiener filters for the state components a new concept of convergence in a realization is presented which is weaker than the convergence with probability one the dynamic error system analysis desa method is presented by which the problem of convergence in a realization for self tuning fusers is transformed into the stability problems of non homogeneous difference equations and the decision criterions of the stability are also presented it is strictly proved that if the parameter estimation of the ma innovation models is consistent and if the measurement process is bounded in a realization or with probability one then the self tuning fusers will converge to the optimal fusers in a realization or with probability one so that they have the asymptotic optimality they can deal with the systems with the non stationary or gaussian measurement processes they can reduce the computational burden and are suitable for real time applications a simulation example for a target tracking system with 3 sensor shows their effectiveness

regularity of constraints in the minkowski space yang mills theory for yang mills theory in the minkowski space it is proved that the constraint set is a smooth submanifold of the phase space consisting of square integrable cauchy data

letter to the editor on the conditions for the coincidence of two cubic bezier curves in a recent article wang et al 2 derive a necessary and sufficient condition for the coincidence of two cubic bezier curves with non collinear control points the condition reads that their control points must be either coincident or in reverse order we point out that this uniqueness of the control points for polynomial cubics is a straightforward consequence of a previous and more general result of barry and patterson namely the uniqueness of the control points for rational bezier curves moreover this uniqueness applies to properly parameterized polynomial curves of arbitrary degree

projective and affine symmetries and equivalences of rational and polynomial surfaces abstract it is known that proper parameterizations of rational curves in reduced form are unique up to bilinear reparameterizations i e projective transformations of its parameter domain this observation has been used in a series of papers by alcazar et al to formulate algorithms for detecting euclidean equivalences and symmetries as well as similarities we generalize this approach to projective equivalences of rationally parametrized surfaces more precisely we observe that a birational base point free parameterization of a surface is unique up to projective transformations of the domain furthermore we use this insight to find all projective equivalences between two given surfaces in particular we formulate a polynomial system of equations whose solutions specify the projective equivalences i e the reparameterizations associated with them furthermore we investigate how this system simplifies for the special case of affine equivalences for polynomial surfaces and how we can use our method to detect projective symmetries of surfaces this method can be used for classifying the generic cases of quadratic surfaces

sequential covariance intersection fusion kalman filter for multisensor system with unknown cross covariances among local estimation errors the batch covariance intersection bci fusion estimation algorithm requires the optimization of a multi dimensional nonlinear cost function which yields a larger computational burden and computational complexity a fast sequential covariance intersection sci kalman filtering algorithm is presented in this paper which only requires to solve the optimization problem of several one dimensional nonlinear cost functions it is equivalent to several two sensor covariance intersection ci kalman fusers and is a recursive two sensor ci kalman fuser its accuracy depends on the orders of sensors it is proved that the sci fuser is consistent and its accuracy is higher than that of each local estimator and is lower than that of the optimal kalman fuser with known cross covariances the geometric interpretation of accuracy relations based on the covariance ellipses is given and the properties of the covariance ellipses are rigorously proved two monte carlo simulation examples show the effectiveness of the proposed results show that the accuracies of the sci fusers are not very sensitive with respect to the orders of sensors and show that its actual accuracy is close to that of the optimal kalman fuser in general cases and its robust accuracy is close to that of the bci fuser so it has good performances

geometric quantization and multiplicities of group representations the heisenberg uncertainty principle says that it is impossible to determine simultaneously the position and momentum of a quantum mechanical particle this can be rephrased as follows the smallest subsets of classical phase space in which the presence of a quantum mechanical particle can be detected are its lagrangian submanifolds for this reason it makes sense to regard the lagrangian submanifolds of phase space as being its true points see weinstein 17 now let g be a compact lie group and g x x x a hamiltonian action of g on x see w for definitions it is well known that the fixed points of this action form a symplectic submanifold of x see for instance guillemin and sternberg 5 however what can one say about the fixed points of g we will show that they are also the points of a symplectic manifold xc this manifold is the marsden weinstein reduction of x with respect to the zero orbit in g and will be described in sect 2 it was introduced in a completely different context fl om ours by marsden and weinstein 12 problems in classical mechanics can often be reduced to the study of hamiltonian systems on symplectic manifolds and problems in quantum mechanics to the study of linear operators on hilbert space this fact has inspired a number of efforts to quantize symplectic geometry by devising schemes for associating hilbert space to symplectic manifolds the no go theorems of groenwald and van hove impose some embarrassing limitations on all such schemes however it seems to be a useful idea heuristically to think of every symplectic manifold x a ic 1 as being symbiotically associated with a hilbert space xq a t in such a way that the classical observables on the first space correspond to quantum observables on the second space the heuristics further suggests that if g is a group of symmetries of x la i j it should also be a group of symmetries of xq a tum in this heuristic spirit we will state the main conjecture of this paper

linearization stability and signorini series for the traction problems in elastostatics this paper uses previous results of chillingworth marsden and wan on symmetry and bifurcation for the traction problem in three dimensional elastostatics to establish new results on the signorini expansion we show that the signorini compatibility conditions are necessary and sufficient for linearization stability and analogies with results known for other field theories are pointed out under an explicit non degeneracy condition a new series expansion is given in which successive terms are inductively determined in pairs rather than singly our results include as special cases classical results of signorini tolotti and stopelli

optimal linear estimation fusion i unified fusion rules this paper deals with data or information fusion for the purpose of estimation three estimation fusion architectures are considered centralized distributed and hybrid a unified linear model and a general framework for these three architectures are established optimal fusion rules based on the best linear unbiased estimation blue the weighted least squares wls and their generalized versions are presented for cases with complete incomplete or no prior information these rules are more general and flexible and have wider applicability than previous results for example they are in a unified form that is optimal for all of the three fusion architectures with arbitrary correlation of local estimates or observation errors across sensors or across time they are also in explicit forms convenient for implementation the optimal fusion rules presented are not limited to linear data models illustrative numerical results are provided to verify the fusion rules and demonstrate how these fusion rules can be used in cases with complete incomplete or no prior information

symmetry and bifurcations of momentum mappings the zero set of a momentum mapping is shown to have a singularity at each point with symmetry the zero set is diffeomorphic to the product of a manifold and the zero set of a homogeneous quadratic function the proof uses the kuranishi theory of deformations among the applications it is shown that the set of all solutions of the yang mills equations on a lorentz manifold has a singularity at any solution with symmetry in the sense of a pure gauge symmetry similarly the set of solutions of einstein s equations has a singularity at any solution that has spacelike killing fields provided the spacetime has a compact cauchy surface

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

detecting symmetries in polynomial bezier curves in a recent article alcazar 2014 presents algorithms for detecting central and mirror symmetries in planar polynomial curves expressed with proper parameterization in the monomial i e power basis however for practical purposes in computer graphics and cagd the usual choice is the bernstein bezier representation because of its superior numerical and geometric characteristics we point out that in this form and for properly parameterized curves detecting symmetry amounts to simply checking that the bezier points exhibit pairwise symmetry this result is a direct consequence of well known properties of the bezier representation namely its symmetry affine invariance and uniqueness for proper parameterizations detecting the existence of a symmetric segment in a bezier curve also amounts to a simple task by analysing the last non vanishing derivatives finally these results carry over in a straightforward manner to symmetries in euclidean space

the structure of the space of homogeneous yang mills fields the structure of the space of solutions of yang mills equations is examined for solutions that are required to have a specified set of infinitesimal space time symmetries it is shown that when the set consists of killing vector fields which are tangent to a compact spacelike cauchy surface the space is a smooth ilh manifold near each solution that has only trivial gauge symmetries

orbifolds as configuration spaces of systems with gauge symmetries in systems like yang mills or gravity theory which have a symmetry of gauge type neither phase space nor configuration space is a manifold but rather an orbifold with singular points corresponding to classical states of non generically higher symmetry the consequences of these symmetries for quantum theory are investigated first a certain orbifold configuration space is identified then the schrodinger equation on this orbifold is considered as a typical case the schrodinger equation on double cones over riemannian manifolds is discussed in detail as a problem of selfadjoint extensions a marked tendency towards concentration of the wave function around the singular points in configuration space is observed which generically even reflects itself in the existence of additional bound states and can be interpreted as a quantum mechanism of symmetry enhancement

b spline contour representation and symmetry detection the detection of edges is only one of many steps in the understanding of images further processing necessarily involves grouping operations between contours we present a representation of edge contours by approximating b splines and show that such a representation facilitates the extraction of symmetries between contours our representation is rich compact stable and does not critically depend on feature extraction we turn our attention to the detection of three types of symmetries skew symmetries and parallel symmetries which have proven to be of great importance in inferring shape from contour and smooth local symmetries which have been used for planar shape description we show that our representation facilitates the computation of these symmetries

geometric and algebraic reduction for singular momentum maps this paper concerns the reduction of singular constraint sets of symplectic manifolds it develops a geometric reduction procedure as well as continues the work of sniatycki and patrick on reduction a la dirac the relationships among the dirac geometric and sniatycki weinstein algebraic reduction procedures are studied primary emphasis is placed on the case where the constraints are given by the vanishing of a singular momentum map associated to the hamiltonian action of a compact lie group specifically an explicit local normal form is given for the momentum map which is used to show that these various reductions are all well defined and a necessary and sufficient condition for them to agree is derived related conditions are investigated and shown to be sufficient in the case of torus actions numerous examples are computed illustrating the results some discussion and examples are given for the noncompact case

detecting similarity of rational plane curves a novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity which is a central question in pattern recognition as a by product it finds all such similarities and the particular case of equal curves yields all symmetries a complete theoretical description of the method is provided and the method has been implemented and tested in the sage system for curves of moderate degrees

coisotropic regularization of singular lagrangians we present an alternative approach to the usual treatments of singular lagrangians it is based on a hamiltonian regularization scheme inspired on the coisotropic embedding of presymplectic systems a lagrangian regularization of a singular lagrangian is a regular lagrangian defined on an extended velocity phase space that reproduces the original theory when restricted to the initial configuration space a lagrangian regularization does not always exists but a family of singular lagrangians is studied for which such a regularization can be described explicitly these regularizations turn out to be essentially unique and provide an alternative setting to quantize the corresponding physical systems these ideas can be applied both in classical mechanics and field theories several examples are discussed in detail

poisson reduction and quantization for the n 1 photon for a dynamical system in which the constraints are given by the vanishing of a singular momentum map j reduction in the usual group theoretic sense may not be possible nonetheless one may still reduce j 1 0 at least on the level of poisson algebras an example of such a singular constrained system is the n 1 photon that is a massless spinless particle in n 1 dimensional minkowski space time we apply the generalized reduction procedure to the n 1 photon explicitly constructing the poisson algebra of gauge invariant observables this technique also enables us to completely analyze the effects of the singularities in j 1 0 on the system we then quantize obtaining results which are in agreement with a quantization of the extended phase space and the subsequent imposition of the constraint

symmetry and bifurcation in three dimensional elasticity part i in part i of this paper chillingworth marsden and wan 1982 hereafter referred to as 1 we reformulated the traction problem in elastostatics in various forms gave a classification of loads and gave complete analysis of solutions of the traction problem that are nearly stress free for loads near loads of type 0 and type 1 this part develops the basic theory as well as giving an analysis of solutions for loads of types 2 3 and 4 it includes a count of the numbers of solutions and an analysis of their stability and the structural stability of the bifurcation diagrams we begin in section 2 with a derivation of a potential formulation of the problem on so 3 the second order potential used in 1 can be recovered as a special case it follows from this that the traction problem always has at least four solutions at least one of which is neutrally stable for loads of type 0 we showed in 1 that there are exactly four solutions near so 3 for the other types there can be many more up to 40 section 3 4 and 5 examine types 2 3 and 4 respectively in a manner analogous to our treatment of types 0 and 1 in 1 loads of type 3 and 4 have some special features already studied in the literature in connection with parallel loads these special features will be discussed and other connections with the existing literature will be made at appropriate points throughout the paper

the quantum theory of second class constraints kinematics the problem of second class quantum constraints is here set up in the context ofc algebras utilizing the connection with state conditions as given by the heuristic quantization rules that is a constraint set is said to be first class if all its members can satisfy the same state condition and second class otherwise several heuristic models are examined and they all agree with this definition given then a second class constraint set we separate out its first class part as all those constraints which are compatible with the others and we propose an algebraic construction for imposition of the constraints this construction reduces to the normal one when the constraints are first class moreover the physical automorphisms assumed as conserving the constraints will also respect this construction the final physical algebra obtained is free of constraints gauge invariant unital and with the right choice simple thisc algebra also contains a factor algebra of the usual observables i e the commutator algebra of the constraints the general theory is applied to two examples the elimination of a canonical pair from a boson field theory as in the two dimensional anomalous chiral schwinger model of rajaraman 14 and the imposition of quadratic second class constraints on a linear boson field theory

reduction of hamiltonian systems with symmetry abstract this paper presents an alternative phase space reduction process for hamiltonian systems with symmetry using a lie algebra of infinitesimal symmetries instead of a lie group of symmetries this approach avoids the use of the various conditions on the action of the group or of the isotropy subgroup necessary for the usual construction of a reduced phase space quotient with a globally defined symplectic manifold structure the existence of such a reduced phase space is proved without recourse to the existence of an equivariant moment map instead it is assumed that the orbits of the action associated to the lie algebra can be described as the level sets of some analytic map an assumption that holds in many of the known examples the relation between the two reduction processes is discussed in particular some cases where the marsden weinstein process leads to a quotient space which is not a smooth manifold are shown to be amenable to the method now proposed the natural control theoretic interpretation of the techniques used is also discussed

on the quantization of presymplectic dynamical systems via coisotropic imbeddings we study certain aspects of the problem of quantizing a presymplectic dynamical system such a system is quantized by imbedding the presymplectic manifoldm under consideration into a symplectic manifoldx and then geometrically quantizing the latter it is known that this procedure will yield consistent results provided the imbeddingm x is coisotropic we show that such imbeddings always exist and are locally unique furthermore we investigate the extent to which the resulting quantum dynamics is independent of the choice of coisotropic imbedding that is we examine to what extent the presymplectic phase spacem determines the quantum representation space and the quantization of observables the quantization is carried out within the geometric quantization framework of kostant and souriau

covariance intersection for partially correlated random vectors this paper generalizes the well known covariance intersection algorithm for distributed estimation and information fusion of random vectors our focus will be on partially correlated random vectors this is motivated by the restriction of the standard covariance intersection algorithm which treats all random vectors with arbitrary cross correlations and the restriction of the classical kalman filter which requires complete knowledge of the cross correlations we first give a result to characterize the conservatism of the standard covariance intersection algorithm we then generalize the covariance intersection algorithm to two random vectors with a given correlation coefficient bound and show in what sense the resulting covariance bound is tight finally we generalize the notion of correlation coefficient bound to multiple random vectors and provide a covariance intersection algorithm for this general case our results will make the already popular covariance intersection more applicable and more accurate for distributed estimation and information fusion problems

stratification of the orbit space in gauge theories the role of nongeneric strata gauge theory is a theory with constraints and for that reason the space of physical states is not a manifold but a stratified space orbifold with singularities the classification of strata for smooth and generalized connections as well as the formulation of the physical space as the zero set of a momentum map is reviewed several important features of nongeneric strata are discussed and new results are presented suggesting an important role for these strata as concentrators of the measure in ground state functionals and as a source of multiple structures in low lying excitations

efficient detection of symmetries of polynomially parametrized curves we present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations the algorithms are based on the existence of a linear relationship between two proper polynomial parametrizations of the curve which leads to a triangular polynomial system with complex unknowns that can be solved in a very fast way in particular curves parametrized by polynomials of serious degrees can be analyzed in a few seconds in our analysis we provide a good number of theoretical results on symmetries of polynomial curves algorithms for detecting rotation and mirror symmetry and closed formulas to determine the symmetry center and the symmetry axis when they exist a complexity analysis of the algorithms is also given

on the fusion of imprecise uncertainty measures using belief structures our interest is in the fusion of information from multiple sources when the information provided by the individual sources is expressed in terms of an imprecise uncertainty measure we observe that the dempster shafer belief structure provides a framework for the representation of a wide class of imprecise uncertainty measures we then discuss the fusion of multiple dempster shafer belief structures using the dempster rule and note the problems that can arise when using this fusion method because of the required normalization in the face of conflicting focal elements we then suggest some alternative approaches fusing multiple belief structures that avoid the need for normalization

decentralized data fusion with inverse covariance intersection in distributed and decentralized state estimation systems fusion methods are employed to systematically combine multiple estimates of the state into a single more accurate estimate an often encountered problem in the fusion process relates to unknown common information that is shared by the estimates to be fused and is responsible for correlations if the correlation structure is unknown to the fusion method conservative strategies are typically pursued as such the parameterization introduced by the ellipsoidal intersection method has been a novel approach to describe unknown correlations though suitable values for these parameters with proven consistency have not been identified yet in this article an extension of ellipsoidal intersection is proposed that guarantees consistent fusion results in the presence of unknown common information the bound used by the novel approach corresponds to computing an outer ellipsoidal bound on the intersection of inverse covariance ellipsoids as a major advantage of this inverse covariance intersection method fusion results prove to be more accurate than those provided by the well known covariance intersection method 2017 elsevier ltd

reduction theory and the lagrange routh equations reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of euler jacobi lagrange hamilton routh poincare and others the modern vision of mechanics includes besides the traditional mechanics of particles and rigid bodies field theories such as electromagnetism fluid mechanics plasma physics solid mechanics as well as quantum mechanics and relativistic theories including gravity symmetries in these theories vary from obvious translational and rotational symmetries to less obvious particle relabeling symmetries in fluids and plasmas to subtle symmetries underlying integrable systems reduction theory concerns the removal of symmetries and their associated conservation laws variational principles along with symplectic and poisson geometry provide fundamental tools for this endeavor reduction theory has been extremely useful in a wide variety of areas from a deeper understanding of many physical theories including new variational and poisson structures to stability theory integrable systems as well as geometric phases this paper surveys progress in selected topics in reduction theory especially those of the last few decades as well as presenting new results on non abelian routh reduction we develop the geometry of the associated lagrange routh equations in some detail the paper puts the new results in the general context of reduction theory and discusses some future directions

covariant geometric quantization of nonrelativistic time dependent mechanics we provide geometric quantization of the vertical cotangent bundle v q q r equipped with the canonical poisson structure and treated as a momentum phase space of nonrelativistic time dependent mechanics we show that this quantization is equivalent to fiberwise quantization of symplectic fibers of v q r and that the quantum algebra of time dependent mechanics is an instantwise algebra quantization of the classical evolution equation defines a connection on this instantwise algebra and describes quantum evolution in time dependent mechanics as a parallel transport

algebraic structure of the gradient holonomic algorithm for lax integrable nonlinear dynamical systems ii the reduction via dirac and canonical quantization procedure the generalized theory of the r structure on affine operator lie algebras is used to construct a complete theory of lax integrable nonlinear dynamical systems in multidimensions the operator bi hamiltonian structures and their functional reductions are discussed in great detail in the examples of operator korteweg de vries and benney kaup dynamical systems as an important by product of the developed algebraic theory the dirac canonical quantization problem is solved almost completely for the neumann bogoliubov type oscillatory dynamical system on spheres associated via moser with the spectral moment map on an affine associative metrized lie coalgebra with a one parameter gauge two cocycle some remarks are given on the problem of extending the developed algebraic theory to the case of lax integrable dynamical systems on discrete manifolds

clebsch lagrange variational principle and geometric constraint analysis of relativistic field theories inspired by the clebsch optimal control problem we introduce a new variational principle that is suitable for capturing the geometry of relativistic field theories with constraints related to a gauge symmetry its special feature is that the lagrange multipliers couple to the configuration variables via the symmetry group action the resulting constraints are formulated as a condition on the momentum map of the gauge group action on the phase space of the system we discuss the hamiltonian picture and the reduction in the gauge symmetry by stages in this geometric setting we show that the yang mills higgs action and the einstein hilbert action fit into this new framework after a 1 3 splitting moreover we recover the gaus constraint of yang mills higgs theory and the diffeomorphism constraint of general relativity as momentum map constraints inspired by the clebsch optimal control problem we introduce a new variational principle that is suitable for capturing the geometry of relativistic field theories with constraints related to a gauge symmetry its special feature is that the lagrange multipliers couple to the configuration variables via the symmetry group action the resulting constraints are formulated as a condition on the momentum map of the gauge group action on the phase space of the system we discuss the hamiltonian picture and the reduction in the gauge symmetry by stages in this geometric setting we show that the yang mills higgs action and the einstein hilbert action fit into this new framework after a 1 3 splitting moreover we recover the gaus constraint of yang mills higgs theory and the diffeomorphism constraint of general relativity as momentum map constraints

constraints reduction and quantization theorems are proved that establish the unitary equivalence of the extended and reduced phase space quantizations of a constrained classical system with symmetry several examples are presented

robust weighted fusion time varying kalman smoothers for multisensor system with uncertain noise variances this paper addresses the design of robust weighted fusion time varying kalman smoothers for multisensor time varying system with uncertain noise variances by the augmented state approach according to the minimax robust estimation principle and the unbiased linear minimum variance ulmv optimal estimation rule the six robust weighted fusion time varying kalman smoothers are presented based on the worst case conservative system with the conservative upper bounds of noise variances the actual smoothing error variances of each fuser are guaranteed to have a minimal upper bound for all admissible uncertainties their robustness is proved by the lyapunov equation approach their robust accuracy relations are analyzed and proved specially the corresponding steady state robust kalman smoothers are also presented for multisensor time invariant system and the convergence in a realization between the time varying and steady state robust kalman smoothers is proved by the dynamic error system analysis desa method and dynamic variance error system analysis dvesa method a simulation example is given to verify the robustness and robust accuracy relations

reduced phase space quotienting procedure for gauge theories we present a reduction procedure for gauge theories based on quotienting out the kernel of the presymplectic form in configuration velocity space local expressions for a basis of this kernel are obtained using phase space procedures the obstructions to the formulation of the dynamics in the reduced phase space are identified and circumvented we show that this reduction procedure is equivalent to the standard dirac method as long as the dirac conjecture holds that the dirac hamiltonian containing the primary first class constraints with their lagrange multipliers can be enlarged to an extended dirac hamiltonian which includes all first class constraints without any change of the dynamics the quotienting procedure is always equivalent to the extended dirac theory even when it differs from the standard dirac theory the differences occur when there are ineffective constraints and in these situations we conclude that the standard dirac method is preferable at least for classical theories an example is given to illustrate these features as well as the possibility of having phase space formulations with an odd number of physical degrees of freedom

singular angular momentum mappings we algebraically reduce the system consisting of a nonrelativistic particle moving in r with vanishing angular momentum after analyzing the conical structure of the constraint set 1 0 we use algebraic geometric techniques to explicitly construct the reduced poisson algebra of rotationally invariant observables this procedure enables us to completely identify the effects of the singularity in j 0 on the system we then group theoretically reduce the system and compare our results with those obtained algebraically

nonlinear weighted measurement fusion unscented kalman filter with asymptotic optimality for the general nonlinear systems a universal weighted measurement fusion wmf algorithm is presented via the taylor series expansion method based on the proposed fusion algorithm and the well known unscented kalman filter ukf the wmf ukf is presented it is proven that the proposed wmf ukf asymptotically approaches to the centralized measurement fusion ukf cmf ukf with the increase of the order of taylor series expansion so it has the asymptotical global optimality we find that wmf ukf has less computational cost than the cmf ukf does with the increase of the number of sensors two examples are given to show the effectiveness of the proposed algorithms

a variational bayesian approach to robust sensor fusion based on student t distribution in this paper a robust sensor fusion method is proposed where the measurement noise is modeled by a student t distribution the student t distribution has a heavy tail compared to the gaussian distribution and is robust to outliers we formulate sensor fusion as a state space estimation problem in the bayesian framework both batch and recursive variational bayesian vb algorithms are developed to perform this non gaussian state space estimation problem to obtain the fusion results computer simulations show that the proposed approach has an improved fusion performance and a lower computation cost compared to methods based on gaussian and finite gaussian mixture models

covariance intersection based image fusion technique with application to pansharpening in remote sensing image fusion of multi spectral images and panchromatic images has been widely applied to imaging sensors multi spectral images are rich in spectral information whereas panchromatic images have relatively higher spatial resolution in this paper we consider the image fusion as an estimation problem that is to estimate the ideal scene of multi spectral images at the resolution of panchromatic images we propose a method of combining the covariance intersection ci principle with the expectation maximization em algorithm to develop a novel image fusion approach in contrast to other fusion methods the proposed scheme takes cross correlation among data sources into account and thus provides consistent and accurate estimates through convex combinations since the covariance information is usually unknown in practice the em method is employed to provide a maximum likelihood estimate mle of the covariance matrix real multi spectral and panchromatic images are used to evaluate the effectiveness of the proposed em ci method the proposed algorithm is found to preserve both the spectral information of the multi spectral image and the high spatial resolution information of the panchromatic image more effectively than the conventional image fusion techniques

an order insensitive sequential fast covariance intersection fusion algorithm the proposed sfci fusion algorithm can handle the problem of unknown cross correlation in local estimation errors the fusion accuracy of the proposed algorithm is not relevant to the fusion orders i e all fusion nodes can acquire identical result the fusion coefficients are straightforward to calculate owing to not require optimizing nonlinear cost function the proposed algorithm is computationally efficient and is therefore applicable for use in real time fusion systems in this article data cross correlation in distributed sensor system is investigated via an order insensitive sequential fast covariance intersection fusion algorithm among the existing approaches the common drawbacks are that the fusion results are sensitive to fusion orders and the computational burden is tremendous due to the optimization of multi dimensional nonlinear cost function in order to overcome these drawbacks a sequential fast covariance intersection sfci algorithm is presented the new fusion coefficients can be calculated straightforward by taking the reciprocal of the trace of the inverse variances as local fusion coefficients and using an iterative process for fusion step to revise the coefficient weight note that the proposed fusion algorithm is consistent and its accuracy is unrelated to the fusion order of the distributed system finally real radar data and simulation examples are provided to verify the effectiveness of the proposed algorithm