state estimation in stochastic hybrid systems with sparse observations in this note we study the problem of state estimation for a class of sampled measurement stochastic hybrid systems where the continuous state x satisfies a linear stochastic differential equation and noisy measurements y are taken at assigned discrete time instants the parameters of both the state and measurement equation depend on the discrete state q of a continuous time finite markov chain even in the fault detection setting we consider at most one transition for q is admissible the switch may occur between two observations whence it turns out that the optimal estimates cannot be expressed in parametric form and time integrations are unavoidable so that the known estimation techniques cannot be applied we derive and implement an algorithm for the estimation of the states x q and of the discrete state switching time that is convenient for both recursive update and the eventual numerical quadrature numerical simulations are illustrated

cone beam reconstruction using the backprojection of locally filtered projections this paper describes a flexible new methodology for accurate cone beam reconstruction with source positions on a curve or set of curves the inversion formulas employed by this methodology are based on first backprojecting a simple derivative in the projection space and then applying a hilbert transform inversion in the image space the local nature of the projection space filtering distinguishes this approach from conventional filtered backprojection methods this characteristic together with a degree of flexibility in choosing the direction of the hilbert transform used for inversion offers two important features for the design of data acquisition geometries and reconstruction algorithms first the size of the detector necessary to acquire sufficient data for accurate reconstruction of a given region is often smaller than that required by previously documented approaches in other words more data truncation is allowed second redundant data can be incorporated for the purpose of noise reduction the validity of the inversion formulas along with the application of these two properties are illustrated with reconstructions from computer simulated data in particular in the helical cone beam geometry it is shown that 1 intermittent transaxial truncation has no effect on the reconstruction in a central region which means that wider patients can be accommodated on existing scanners and more importantly that radiation exposure can be reduced for region of interest imaging and 2 at maximum pitch the data outside the tam danielsson window can be used to reduce image noise and thereby improve dose utilization furthermore the degree of axial truncation tolerated by our approach for saddle trajectories is shown to be larger than that of previous methods

efficient particle filtering for jump markov systems application to time varying autoregressions we present an efficient particle filtering method to perform optimal estimation in jump markov nonlinear systems jmss such processes consist of a mixture of heterogeneous models and possess a natural hierarchical structure we take advantage of these specificities in order to develop a generic filtering methodology for these models the method relies on an original and nontrivial combination of techniques that have been presented recently in the filtering literature namely the auxiliary particle filter and the unscented transform this algorithm is applied to the complex problem of time varying autoregressive estimation with an unknown time varying model order more precisely we develop an attractive and original probabilistic model that relies on a flexible pole representation that easily lends itself to interpretations we show that this problem can be formulated as a jms and that the associated filtering problem can be efficiently addressed using the generic methodology developed in this paper simulations demonstrate the performance of our method compared to standard particle filtering techniques

a factorization approach for cone beam reconstruction on a circular short scan in this paper we introduce a new algorithm for 3 d image reconstruction from cone beam cb projections acquired along a partial circular scan our algorithm is based on a novel exact factorization of the initial 3 d reconstruction problem into a set of independent 2 d inversion problems each of which corresponds to finding the object density on one single plane any such 2 d inversion problem is solved numerically using a projected steepest descent iteration scheme we present a numerical evaluation of our factorization algorithm using computer simulated cb data without and with noise of the forbild head phantom and of a disk phantom first we study quantitatively the impact of the reconstruction parameters on the algorithm performance next we present reconstruction results for visual assessment of the achievable image quality and provide for comparison results obtained with two other state of the art reconstruction algorithms for the circular short scan

brief paper design of h filter for markov jumping linear systems with non accessible mode information for markov jumping linear systems mjls it is often encountered that the jumping mode cannot be accessible for filtering therefore it is strongly desirable to design a filter which is independent of the jumping model in this paper a new deterministic filter design procedure is proposed which shows less conservatism than existing results the whole design procedure can be accomplished by solving a set of linear matrix inequalities lmis finally numerical examples are given to illustrate the effectiveness of the proposed approach

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

noise properties of chord image reconstruction recently there has been much progress in algorithm development for image reconstruction in cone beam computed tomography ct current algorithms including the chord based algorithms now accept minimal data sets for obtaining images on volume regions of interest rois thereby potentially allowing for reduction of x ray dose in diagnostic ct as these developments are relatively new little effort has been directed at investigating the response of the resulting algorithm implementations to physical factors such as data noise in this paper we perform an investigation on the noise properties of roi images reconstructed by using chord based algorithms for different scanning configurations we find that for the cases under study the chord based algorithms yield images with comparable quality additionally it is observed that in many situations large data sets contain extraneous data that may not reduce the roi image variances

mode independent cal h _ infty filters for markovian jump linear systems this note addresses the problem of hinfin filtering for continuous time linear systems with markovian jumping parameters the main contribution of the note is to provide a method for designing an asymptotically stable linear time invariant hinfin filter for systems where the jumping parameter is not accessible the cases where the transition rate matrix of the markov process is either exactly known or unknown but belongs to a given polytope are treated the robust hinfin filtering problem for systems with polytopic uncertain matrices is also considered and a filter design method based on a lyapunov function that depends on the uncertain parameters is developed the proposed filter designs are given in terms of linear matrix inequalities

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

optimization for limited angle tomography in medical image processing this paper aims to reduce the problems of incomplete data in computed tomography which happens frequently in medical image process and analysis e g when the high density region of objects can only be penetrated by x rays at a limited angular range as the projection data are available only in an angular range the incomplete data problem can be attributed to the limited angle problem which is an ill posed inverse problem image reconstruction based on total variation tv reduces the problem and gives better performance on edge preserving reconstruction however the artificial parameter can only be determined through considerable experimentation in this paper an effective tv objective function is proposed to reduce the inverse problem in the limited angle tomography this novel objective function provides a robust and effective reconstruction without any artificial parameter in the iterative processes using the tv as a multiplicative constraint the results demonstrate that this reconstruction strategy outperforms some previous ones

quasi exact filtered backprojection algorithm for long object problem in helical cone beam tomography exact reconstruction from axially truncated cone beam projections acquired with a helical vertex path is a challenging problem for which solutions are currently under investigation by some researchers this paper deals with a difficult class of this problem called the long object problem its purpose is to reconstruct a central region of interest roi of a long object when the helical path extends only a little bit above and below the roi by extending the authors recent approach based on the triangular decomposition of the grangeat formula the authors derive quasi exact reconstruction algorithms whose overall structure is of filtered backprojection fbp style unlike the previous similar approaches to the long object problem the proposed fbp algorithms do not require additional two circular scans at the ends of the helical path furthermore the algorithms require a significantly smaller detector area and achieve improved image quality even for a large pitch compared with the approximate feldkamp algorithms one drawback of the proposed algorithms is the computational time which is much longer than for the feldkamp algorithms the authors show some simulation results to demonstrate the performances of the proposed algorithms

sequential approximation of feasible parameter sets for identification with set membership uncertainty in this paper the problem of approximating the feasible parameter set for identification of a system in a set membership setting is considered the system model is linear in the unknown parameters a recursive procedure providing an approximation of the parameter set of interest through parallelotopes is presented and an efficient algorithm is proposed its computational complexity is similar to that of the commonly used ellipsoidal approximation schemes numerical results are also reported on some simulation experiments conducted to assess the performance of the proposed algorithm

uniqueness of gibbs state for nonideal gas in ℝ d the case of pair potentials we consider a classical gas of particles in d interacting via a pair potential we prove that in a given region of the plane where is the inverse temperature and is the chemical potential either the gibbs state is unique or it does not exist our method uses a version of the well known dobrushin uniqueness theorem adapted for lattice systems with a noncompact spin space and proved by dobrushin and pechersky the advantage of this version is that using it one needs to check dobrushin s contraction condition not for all boundary configurations but only for those that have spin values in some compact subset of the spin space

an ol n 3 primal interior point algorithm for convex quadratic programming we present a primal interior point method for convex quadratic programming which is based upon a logarithmic barrier function approach this approach generates a sequence of problems each of which is approximately solved by taking a single newton step it is shown that the method requires o sqrt n l iterations and o n3 5l arithmetic operations by using modified newton steps the number of arithmetic operations required by the algorithm can be reduced to o n3l

brief paper risk sensitive filtering for jump markov linear systems in this paper a risk sensitive multiple model filtering algorithm is derived using the reference probability methods first the approximation of the interacting multiple model imm algorithm is identified in the reference probability domain then the same type of approximation is used to derive the finite dimensional risk sensitive filtering algorithm the derived algorithm reduces to the imm filter when the risk sensitive parameter goes to zero and reduces to the risk sensitive filter for linear gauss markov systems when the number of models is unity the algorithm performs better in a simulated uncertain parameter scenario than the imm filter

set membership filtering with incomplete observations abstract this study addresses the set membership estimation problem for a class of discrete time varying systems with incomplete observations a set membership filter is developed and a recursive algorithm is proposed to calculate the state estimate ellipsoid which contains the true value to solve the problem that the conventional set membership filter cannot guarantee the stability when applied to discrete time varying systems with incomplete observations a quantitative analysis method about incomplete observations is developed and a tight bound of the estimation error is found based on interval analysis and some bounded noise assumptions in terms of bounded assumptions the relationship between the bound of estimated error and the data dropout rate is obtained if the data dropout rate is less than a maximal value the set membership filter is asymptotically stable the proposed filter is applied to a two state example to demonstrate the effectiveness of theoretical results

brief paper a set membership state estimation algorithm based on dc programming this paper presents a new approach to guaranteed state estimation for nonlinear discrete time systems with a bounded description of noise and parameters the sets of states that are consistent with the evolution of the system the measured outputs and bounded noise and parameters are represented by zonotopes dc programming and intersection operations are used to obtain a tight bound an example is given to illustrate the proposed algorithm

a general exact reconstruction for cone beam ct via backprojection filtration in this paper we prove a generalized backprojection filtration formula for exact cone beam image reconstruction with an arbitrary scanning locus our proof is independent of the shape of the scanning locus as long as the object is contained in a region where there is a chord through any interior point as special cases this generalized formula can be applied with cone beam scanning along nonstandard spiral and saddle curves as well as in an n pi window setting the algorithmic implementation and numerical results are described to support the correctness of our general claim

a switched imm extended viterbi estimator based algorithm for maneuvering target tracking this paper presents a new algorithm for tracking a maneuvering target modeled as a class of markov jump linear systems the proposed algorithm consists of two interacting multiple model extended viterbi imm ev algorithms coupled with proposed detection schemes for maneuver occurrences and terminations as well as for switching initializations combined performance strengths of the two imm ev algorithms are utilized via switching from one imm ev algorithm to the other appropriate design parameter values are derived for the detection schemes of maneuver occurrences and terminations the results demonstrate that the proposed algorithm can be a viable alternative to several well known tracking methods

linear minimum mean square error estimation for discrete time markovian jump linear systems the linear minimum mean square error estimator lmmse for discrete time linear systems subject to abrupt changes in the parameters modeled by a markov chain spl theta k spl epsiv 1 n is considered the filter equations are derived from geometric arguments in a recursive form resulting in an on line algorithm suitable for computer implementation the author s approach is based on estimating x k 1 sub spl theta k i instead of estimating directly x k the uncertainty introduced by the markovian jumps increases the dimension of the filter to n n 1 where n is the dimension of the state variable an example where the dimension of the filter can be reduced to n is presented as well as a numerical comparison with the imm filter

stochastic sampling algorithms for state estimation of jump markov linear systems jump markov linear systems are linear systems whose parameters evolve with time according to a finite state markov chain given a set of observations our aim is to estimate the states of the finite state markov chain and the continuous in space states of the linear system the computational cost in computing conditional mean or maximum a posteriori map state estimates of the markov chain or the state of the jump markov linear system grows exponentially in the number of observations we present three globally convergent algorithms based on stochastic sampling methods for state estimation of jump markov linear systems the cost per iteration is linear in the data length the first proposed algorithm is a data augmentation da scheme that yields conditional mean state estimates the second proposed scheme is a stochastic annealing sa version of da that computes the joint map sequence estimate of the finite and continuous states finally a metropolis hastings da scheme based on sa is designed to yield the map estimate of the finite state markov chain convergence results of the three above mentioned stochastic algorithms are obtained computer simulations are carried out to evaluate the performances of the proposed algorithms the problem of estimating a sparse signal developing from a neutron sensor based on a set of noisy data from a neutron sensor and the problem of narrow band interference suppression in spread spectrum code division multiple access cdma systems are considered

an inversion formula for cone beam reconstruction an analytic inversion formula allowing the reconstruction of a three dimensional object from x ray cone beams is given the formula is valid for the case where the source of the beams describes a bounded curve satisfying a set of weak conditions

direct reconstruction of cone beam data acquired with a vertex path containing a circle cone beam data acquired with a vertex path satisfying the data sufficiency condition of tuy can be reconstructed using exact filtered backprojection algorithms these algorithms are based on the application to each cone beam projection of a two dimensional 2 d filter that is nonstationary and therefore more complex than the one dimensional 1 d ramp filter used in the approximate algorithm of feldkamp davis and kress 1984 fdk we determine in this paper the general conditions under which the 2 d nonstationary filter reduces to a 2 d stationary filter and also give the explicit expression of the corresponding convolution kernel using this result and the redundancy of the cone beam data a composite algorithm is derived for the class of vertex paths that consist of one circle and some complementary subpath designed to guarantee data sufficiency in this algorithm the projections corresponding to vertex points along the circle are filtered using a 2 d stationary filter whereas the other projections are handled with a 2 d nonstationary filter the composite algorithm generalizes the method proposed by kudo and saito 1990 in which the circle data are processed with a 1 d ramp filter as in the fdk algorithm the advantage of the 2 d filter introduced in this paper is to guarantee that the filtered cone beam projections do not contain singularities in smooth regions of the object tests of the composite algorithm on simulated data are presented

state estimation for markovian jump linear systems with bounded disturbances in this paper we investigate the state estimation problem for a class of markovian jump linear systems mjlss in the presence of bounded polyhedral disturbances a set membership estimation algorithm is first proposed to find the smallest consistent set of all possible states which is shown to be expressed by a union of multiple polytopes the posterior probabilities of the system jumping modes are then estimated by introducing the lebesgue measure based on which the optimal point estimate is further provided moreover a similarity relationship for polytopes is defined and an approximate method is presented to calculate the minkowski sum of polytopes which can help reduce the computational complexity of the overall estimation algorithm

boolean percolation on doubling graphs we consider the discrete boolean model of percolation on weighted graphs satisfying a doubling metric condition we study sufficient conditions on the distribution of the radii of balls placed at the points of a bernoulli point process for the absence of percolation provided that the parameter of the underlying point process is small enough we exhibit three families of interesting graphs where the main result of this work holds finally we give sufficient conditions for ergodicity of the discrete boolean model of percolation

brief paper the minimal disturbance invariant set outer approximations via its partial sums this paper is concerned with outer approximations of the minimal disturbance invariant set mdis of a discrete time linear system with an additive set bounded disturbance the k step disturbance reachable sets minkowski partial sums are inner approximations of mdis that converge to mdis enlarged by a suitable scaling they can lead to outer approximations of mdis three families of approximations each based on partial sums are considered theoretical properties of the families are proved and interrelated algorithmic questions including error bounds are addressed the results are illustrated by computational data from several examples

formulation of four katsevich algorithms in native geometry we derive formulations of the four exact helical katsevich algorithms in the native cylindrical detector geometry which allow efficient implementation in modern computed tomography scanners with wide cone beam aperture also we discuss some aspects of numerical implementation

exact radon rebinning algorithm for the long object problem in helical cone beam ct this paper addresses the long object problem in helical cone beam computed tomography the authors present the phi method a new algorithm for the exact reconstruction of a region of interest roi of a long object from axially truncated data extending only slightly beyond the roi the phi method is an extension of the radon method published by kudo et al in phys in med and biol vol 43 p 2885 909 1998 the key novelty of the phi method is the introduction of a virtual object f sub spl phi x for each value of the azimuthal angle spl phi in the image space with each virtual object having the property of being equal to the true object f x in some roi spl omega sub m the authors show that for each spl phi one can calculate exact radon data corresponding to the two dimensional 2 d parallel beam projection of f sub spl phi x onto the meridian plane of angle spl phi given an angular range of length spl pi of such parallel beam projections the roi spl omega sub m can be exactly reconstructed because f x is identical to f sub spl phi x in spl omega sub m simulation results are given for both the radon method and the phi method indicating that 1 for the case of short objects the radon and phi methods produce comparable image quality 2 for the case of long objects the phi method delivers the same image quality as in the short object case while the radon method fails and 3 the image quality produced by the phi method is similar for a large range of pitch values

brief paper robust set membership state estimation application to underwater robotics this paper proposes a new observer for estimating the state vector of a nonlinear system this observer which is robust with respect to outliers assumes that the measurement errors as well as the number of outliers that could occur within a given time window are bounded the principle of the approach is to use interval analysis to deal properly with the nonlinearities involved in the system without any linearization or approximation and to propagate through the time in a forward and backward manner the assumptions made about outliers a test case related to the localization and control of an underwater robot is also proposed to illustrate the efficiency of the approach

exact recursive polyhedral description of the feasible parameter set for bounded error models a method is described which exactly characterizes the set of all the values of the parameter vector of a linear model that are consistent with bounded errors on the measurements it provides a parameterized expression of this set which can be used for robust control design or for optimizing any criterion over the set this approach is based on a new variant of the double description method for determining the edges of a polyhedral cone it can be used in real time and provides a suitable context for implementation on a computer whenever a new measurement modifies the set the characterization is updated the technique is illustrated with a simple example

event triggered state estimation for markovian jumping impulsive neural networks with interval time varying delays abstractthis paper investigates the event triggered state estimation problem of markovian jumping impulsive neural networks with interval time varying delays the purpose is to design a state estimator to estimate system states through available output measurements in the neural networks there are a set of modes which are determined by markov chain a markovian jumping time delay impulsive neural networks model is employed to describe the event triggered scheme and the network related behaviour such as transmission delay data package dropout and disorder the proposed event triggered scheme is used to determine whether the sampled state information should be transmitted the discrete delays are assumed to be time varying and belong to a given interval which means that the lower and upper bounds of interval time varying delays are available first we design a state observer to estimate the neuron states second based on a novel lyapunov krasovskii functional lkf with triple integral terms and us

percolation properties of the non ideal gas we estimate locations of the regions of the percolation and of the non percolation in the plane the poisson rate the inverse temperature for interacting particle systems in finite dimension euclidean spaces our results about the percolation and about the non percolation are obtained under different assumptions the intersection of two groups of the assumptions reduces the results to two dimension euclidean space 2 and to a potential function of the interactions having a hard core