adaptive control of linear systems with markov perturbations the stochastic model considered is a linear jump diffusion process x for which the coefficients and the jump processes depend on a markov chain z with finite state space first we study the optimal filtering and control problem for these systems with non gaussian initial conditions given noisy observations of the state x and perfect measurements of z we derive a new sufficient condition which ensures the existence and the uniqueness of the solution of the nonlinear stochastic differential equations satisfied by the output of the filter we study a quadratic control problem and show that the separation principle holds next we investigate an adaptive control problem for a state process x defined by a linear diffusion for which the coefficients depend on a markov chain the processes x and z being observed in independent white noises suboptimal estimates for the process x z and approximate control law are investigated for a large class of probability distributions of the initial state asymptotic properties of these filters and this control law are obtained upper bounds for the corresponding error are given

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

partial non gaussian state space summary in this paper we suggest the use of simulation techniques to extend the applicability of the usual gaussian state space filtering and smoothing techniques to a class of nongaussian time series models this allows a fully bayesian or maximum likelihood analysis of some interesting models including outlier models discrete markov chain components multiplicative models and stochastic variance models finally we discuss at some length the use of a non gaussian model to seasonally adjust the published money supply figures

on the stable set polytope of a series parallel graph we give a short proof of chvatal s conjecture that the nontrivial facets of the stable set polytope of a series parallel graph all come from edges and odd holes

extended object tracking using monte carlo methods this correspondence addresses the problem of tracking extended objects such as ships or a convoy of vehicles moving in urban environment two monte carlo techniques for extended object tracking are proposed an interacting multiple model data augmentation imm da algorithm and a modified version of the mixture kalman filter mkf of chen and liu called the mixture kalman filter modified mkfm the data augmentation da technique with finite mixtures estimates the object extent parameters whereas an interacting multiple model imm filter estimates the kinematic states position and speed of the manoeuvring object next the system model is formulated in a partially conditional dynamic linear pcdl form this affords us to propose two latent indicator variables characterizing respectively the motion mode and object size then an mkfm is developed with the pcdl model the imm da and the mkfm performance is compared with a combined imm particle filter imm pf algorithm with respect to accuracy and computational complexity the most accurate parameter estimates are obtained by the da algorithm followed by the mkfm and pf

the steiner tree polytope and related polyhedra we consider the vertex weighted version of the undirected steiner tree problem in this problem a cost is incurred both for the vertices and the edges present in the steiner tree we completely describe the associated polytope by linear inequalities when the underlying graph is series parallel for general graphs this formulation can be interpreted as a partial extended formulation for the steiner tree problem by projecting this formulation we obtain some very large classes of facet defining valid inequalities for the steiner tree polytope

facets with fixed defect of the stable set polytope the stable set polytope of a graph is the convex hull of the 0 1 vectors corresponding to stable sets of vertices to any nontrivial facet v v a v x v b of this polytope we associate an integer called the defect of the facet by v v a v 2b we show that for any fixed there is a finite collection of graphs called basis such that any graph with a facet of defect contains a subgraph which can be obtained from one of the graphs in the basis by a simple subdivision operation

state estimation for discrete time markov jump linear systems with time correlated measurement noise abstract in this paper the state estimation problem for discrete time markov jump linear systems affected by time correlated measurement noise is considered where the time correlated measurement noise is described by a linear system model with white noise as a result two algorithms are proposed to estimate the state of the system under consideration based on a measurement sequence the first algorithm is optimal in the sense of minimum mean square error which is obtained based on the measurement differencing method bayes rule and some results derived in this paper the second algorithm is a suboptimal algorithm obtained by using a lot of gaussian hypotheses the proposed suboptimal algorithm is finite dimensionally computable and does not increase computational and storage load with time computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm

identification of time varying systems in reproducing kernel hilbert spaces we consider a class of linear systems in state space form whose parameters evolve in time according to a continuous time gauss markov process our problem is to identify the system from a finite set of noisy output measurements we derive a connection between this problem and tikhonov regularization in reproducing kernel hilbert spaces relying upon this result conditions that ensure the existence of the maximum a posteriori estimate of the parameter trajectory are provided and an identification algorithm is worked out simulated data are used to test the goodness of the proposed approach

applying lehman s theorems to packing problems a 0 1 matrixa isideal if the polyhedronq a conv x qv a x 1 x 0 v denotes the column index set ofa is integral similarly a matrix isperfect ifp a conv x qv a x 1 x 0 is integral little is known about the relationship between these two classes of matrices we consider a transformation between the two classes which enables us to apply lehman s modified theorem about deletion minimal nonideal matrices to obtain new results about packing polyhedra this results in a polyhedral description for the stable set polytopes ofnear bipartite graphs the deletion of any neighbourhood produces a bipartite graph note that this class includes the complements of line graphs to date this is the only natural class besides the perfect graphs for which such a description is known for the graphs and their complements some remarks are also made on possible approaches to describing the stable set polyhedra of quasi line graphs and more generally claw free graphs these results also yield a new class oft perfect graphs

a monte carlo approach to nonnormal and nonlinear state space modeling abstract a solution to multivariate state space modeling forecasting and smoothing is discussed we allow for the possibilities of nonnormal errors and nonlinear functionals in the state equation the observational equation or both an adaptive monte carlo integration technique known as the gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework the methodology is a general strategy for obtaining marginal posterior densities of coefficients in the model or of any of the unknown elements of the state space missing data problems including the k step ahead prediction problem also are easily incorporated into this framework we illustrate the broad applicability of our approach with two examples a problem involving nonnormal error distributions in a linear model setting and a one step ahead prediction problem in a situation where both the state and observational equations are nonlinear and involve unknown parameters

stationary filter for linear minimum mean square error estimator of discrete time markovian jump systems we derive in this paper a stationary filter for the linear minimum mean square error estimator lmmse of discrete time markovian jump linear systems mjlss we obtain the convergence of the error covariance matrix of the lmmse to a stationary value under the assumption of mean square stability of the mjls and ergodicity of the associated markov chain it is shown that there exists a unique solution for the stationary riccati filter equation and moreover this solution is the limit of the error covariance matrix of the lmmse the advantage of this scheme is that it is very easy to implement and all calculations can be performed off line leading to a linear time invariant filter

rao blackwellized gaussian smoothing in this paper we consider rao blackwellization of linear substructures in sigma point based gaussian assumed density smoothers we derive marginalized prediction smoothing and update steps for the mixed linear nonlinear gaussian state space model as well as for a hierarchical model for both conventional and iterated posterior linearization gaussian smoothers the proposed method is evaluated in a numerical example and it is shown that the computational complexity is reduced considerably compared to non rao blackwellized gaussian smoothers for systems with high dimensional linear subspaces

on the cut polytope the cut polytopep c g of a graphg v e is the convex hull of the incidence vectors of all edge sets of cuts ofg we show some classes of facet defining inequalities ofp c g we describe three methods with which new facet defining inequalities ofp c g can be constructed from known ones in particular we show that inequalities associated with chordless cycles define facets of this polytope moreover for these inequalities a polynomial algorithm to solve the separation problem is presented we characterize the facet defining inequalities ofp c g ifg is not contractible tok 5 we give a simple characterization of adjacency inp c g and prove that for complete graphs this polytope has diameter one and thatp c g has the hirsch property a relationship betweenp c g and the convex hull of incidence vectors of balancing edge sets of a signed graph is studied

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

expectation maximization algorithms for map estimation of jump markov linear systems in a jump markov linear system the state matrix observation matrix and the noise covariance matrices evolve according to the realization of a finite state markov chain given a realization of the observation process the aim is to estimate the state of the markov chain assuming known model parameters computing conditional mean estimates is infeasible as it involves a cost that grows exponentially with the number of observations we present three expectation maximization em algorithms for state estimation to compute maximum a posteriori map state sequence estimates which are also known as bayesian maximum likelihood state sequence estimates mlses the first em algorithm yields the map estimate for the entire sequence of the finite state markov chain the second em algorithm yields the map estimate of the continuous state of the jump linear system the third em algorithm computes the joint map estimate of the finite and continuous states the three em algorithms optimally combine a hidden markov model hmm estimator and a kalman smoother ks in three different ways to compute the desired map state sequence estimates unlike the conditional mean state estimates which require computational cost exponential in the data length the proposed iterative schemes are linear in the data length

integer round up property for the chromatic number of some h perfect graphs we prove that every h perfect line graph and every t perfect claw free graph g has the integer round up property for the chromatic number for every non negative integral weight function c on the vertices of g the weighted chromatic number of g c can be obtained by rounding up its fractional relaxation as a corollary we obtain that the weighted chromatic number can be computed in polynomial time for these graphs finally we show a new example of a graph operation which preserves the integer round up property for the chromatic number and use it to provide a first example of a t perfect 3 colorable graph which does not have this property

gear composition of stable set polytopes and g perfection graphs obtained by applying the gear composition to a given graph h are called geared graphs we show how a linear description of the stable set polytope stab g of a geared graph g can be obtained by extending the linear inequalities defining stab h and stab he where he is the graph obtained from h by subdividing the edge e we also introduce the class of g perfect graphs i e graphs whose stable set polytope is described by nonnegativity inequalities rank inequalities lifted 5 wheel inequalities and some special inequalities called geared inequalities and g lifted inequalities we prove that graphs obtained by repeated applications of the gear composition to a given graph h are g perfect provided that any graph obtained from h by subdividing a subset of its simplicial edges is g perfect in particular we show that a large subclass of claw free graphs is g perfect

modal estimation in hybrid systems in hybrid systems estimation is made difficult by the nonlinear equations of state evolution several algorithms for generating an approximation to the conditional mean estimator have been proposed these are satisfactory in many cases but because of the way the observations are fused the estimate of the modal component of the state is often less good this paper proposes a novel algorithm for state estimation and compares it with some in current use

adaptive gaussian sum filter for nonlinear bayesian estimation a nonlinear filter is developed by representing the state probability density function by a finite sum of gaussian density kernels whose mean and covariance are propagated from one time step to the next using linear system theory methods such as extended kalman filter or unscented kalman filter the novelty in the proposed method is that the weights of the gaussian kernels are updated at every time step by solving a convex optimization problem posed by requiring the gaussian sum approximation to satisfy the fokker planck kolmogorov equation for continuous time dynamical systems and the chapman kolmogorov equation for discrete time dynamical systems the numerical simulation results show that updating the weights of different mixture components during propagation mode of the filter not only provides us with better state estimates but also with a more accurate state probability density function

iterative algorithms for state estimation of jump markov linear systems jump markov linear systems jmlss 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 in this paper we present original deterministic and stochastic iterative algorithms for optimal state estimation of jmlss the first stochastic algorithm yields minimum mean square error mmse estimates of the finite state space markov chain and of the continuous state of the jmls a deterministic and a stochastic algorithm are given to obtain the marginal maximum a posteriori mmap sequence estimate of the finite state markov chain finally a deterministic and a stochastic algorithm are derived to obtain the mmap sequence estimate of the continuous state of the jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problem of deconvolution of bernoulli gaussian bg processes and the problem of tracking a maneuvering target are addressed

on gibbs sampling for state space models summary we show how to use the gibbs sampler to carry out bayesian inference on a linear state space model with errors that are a mixture of normals and coefficients that can switch over time our approach simultaneously generates the whole of the state vector given the mixture and coefficient indicator variables and simultaneously generates all the indicator variables conditional on the state vectors the states are generated efficiently using the kalman filter we illustrate our approach by several examples and empirically compare its performance to another gibbs sampler where the states are generated one at a time the empirical results suggest that our approach is both practical to implement and dominates the gibbs sampler that generates the states one at a time

hybrid filtering for linear systems with non gaussian disturbances this paper is concerned with hybrid filtering of a non gaussian system coupled by a hidden switching process an optimal control approach is used to derive a finite dimensional recursive filter that is optimal in the sense of the most probable trajectory mpt estimate an approximate scheme is obtained when the probability distribution of the switching process converges to a limiting distribution which is often easier to obtain numerical examples are considered and computational experiments are reported in these examples our schemes outperform popular filtering schemes available in the literature

state and mode estimation for discrete time jump markov systems in this article we compute new state and mode estimation algorithms for discrete time gauss markov models whose parameter sets switch according to a known markov law an important feature of our algorithms is that they are based upon the exact filter dynamics computed in r j elliott f dufour and d sworder ieee trans automat control 41 1996 pp 1807 1810 the fundamental and well known obstacle in estimation of jump markov systems is managing the geometrically growing history of candidate hypotheses in our scheme we address this issue by proposing an extension of an idea due to viterbi our scheme maintains a fixed number of candidate paths in a history each identified by an optimal subset of estimated mode probabilities we compute finite dimensional suboptimal filters and smoothers which estimate the hidden state process and the mode probability our smoothers are based upon a duality between forward and backward dynamics further our smoothing algorithms are general and can be configured into the standard forms of fixed point fixed lag and fixed interval smoothers a computer simulation is included to demonstrate performance

maximum likelihood estimation of transition probabilities of jump markov linear systems this paper describes an online maximum likelihood estimator for the transition probabilities associated with a jump markov linear system jmls the maximum likelihood estimator is derived using the reference probability method which exploits an hypothetical probability measure to find recursions for complex expectations expectation maximization em procedure is utilized for maximizing the likelihood function in order to avoid the exponential increase in the number of statistics of the optimal em algorithm we make interacting multiple model imm type approximations the resulting method needs the mode weights of an imm filter with n3 components where n is the number of models in the jmls the algorithm can also supply base state estimates and covariances as a by product the performance of the estimator is illustrated on two simulated examples and compared to a recently proposed alternative

stable set polytopes for a class of circulant graphs we study the stable set polytope p gn for the graph gn with n nodes and edges i j with j in i 1 i 2 i 1 ldots n and where nodes n 1 and 1 resp n 2 and 2 are identified this graph coincides with the antiweb bar w n 3 a minimal linear system defining p gn is determined the system consists of certain rank inequalities with some number theoretic flavor a characterization of the vertices of a natural relaxation of p gn is also given

wavelet based sequential monte carlo blind receivers in fading channels with unknown channel statistics recently an adaptive bayesian receiver for blind detection in flat fading channels was developed by the present authors based on the sequential monte carlo methodology that work is built on a parametric modeling of the fading process in the form of a state space model and assumes the knowledge of the second order statistics of the fading channel in this paper we develop a nonparametric approach to the problem of blind detection in fading channels without assuming any knowledge of the channel statistics the basic idea is to decompose the fading process using a wavelet basis and to use the sequential monte carlo technique to track both the wavelet coefficients and the transmitted symbols a novel resampling based wavelet shrinkage technique is proposed to dynamically choose the number of wavelet coefficients to best fit the fading process under such a framework blind detectors for both flat fading channels and frequency selective fading channels are developed simulation results are provided to demonstrate the excellent performance of the proposed blind adaptive receivers

particle filters for state estimation of jump markov linear systems jump markov linear systems jmls are linear systems whose parameters evolve with time according to a finite state markov chain in this paper our aim is to recursively compute optimal state estimates for this class of systems we present efficient simulation based algorithms called particle filters to solve the optimal filtering problem as well as the optimal fixed lag smoothing problem our algorithms combine sequential importance sampling a selection scheme and markov chain monte carlo methods they use several variance reduction methods to make the most of the statistical structure of jmls computer simulations are carried out to evaluate the performance of the proposed algorithms the problems of on line deconvolution of impulsive processes and of tracking a maneuvering target are considered it is shown that our algorithms outperform the current methods

on claw free t perfect graphs a graph is called t perfect if its stable set polytope is defined by non negativity edge and odd cycle inequalities we characterise the class of all claw free t perfect graphs by forbidden t minors and show that they are 3 colourable moreover we determine the chromatic number of claw free h perfect graphs and give a polynomial time algorithm to compute an optimal colouring

a superposition principle for the kalman filter abstract in this paper decomposition formulas for the discrete time kalman filter are presented both the state estimate and the error covariance matrix are expressed as the sum of two terms the first being the estimate corresponding to zero initial conditions and the second being an explicit function of the initial values x 0 and p 0 the representation is updated in time by well behaved finite complexity matrix recursions and allows for a direct evaluation of the estimates for variable initial conditions applications to stochastic hybrid filtering are discussed

the matching theorems and coincidence theorems for generalized r kkm mapping in topological spaces abstract in this paper we present some new matching theorems with open cover and closed cover by using the generalized r kkm theorems l deng x xia generalized r kkm theorem in topological space and their applications j math anal appl 285 2003 679 690 in the topological spaces with property h as applications some coincidence theorems are established in topological spaces our results extend and generalize some known results

brief paper detection and estimation for abruptly changing systems the problem of state estimation and system structure detection for discrete stochastic dynamical systems with parameters which may switch among a finite set of values is considered the switchings are modelled by a markov chain with known transition probabilities a brief survey and a unified treatment of the existing suboptimal algorithms are provided the optimal algorithms require exponentially increasing memory and computations with time simulation results comparing the various suboptimal algorithms are presented

state estimation for discrete time markov jump linear systems with time correlated and mode dependent measurement noise abstract the state estimation problem for discrete time markov jump linear systems corrupted by time correlated and mode dependent measurement noise is considered where the time correlated and mode dependent measurement noise is described via a discrete time stochastic system with markov parameter and kronecker delta function by defining the measurement noise in this manner both time correlation and periodic step change caused by the change of system environment or structure can be embodied in the measurement noise a novel distributed measurement differencing method is applied to the problem of state estimation under consideration so that two algorithms are obtained using some results presented in this paper the first algorithm is optimal in the sense of minimum mean square error which can exactly compute the minimum mean square error estimate of system state the second algorithm is suboptimal and the suboptimality of the algorithm is caused by using some gaussian hypotheses the two proposed algorithms are recursive and the proposed suboptimal algorithm has a time independent complexity the performance of the proposed suboptimal algorithm is illustrated using computer simulations

the strong perfect graph theorem a graph g is perfect if for every induced subgraph h the chromatic number of h equals the size of the largest complete subgraph of h and g is berge if no induced subgraph of g is an odd cycle of length at least five or the complement of one the strong perfect graph conjecture berge 1961 asserts that a graph is perfect if and only if it is berge a stronger conjecture was made recently by conforti cornu ejols and vuiskovi c that every berge graph either falls into one of a few basic classes or admits one of a few kinds of separation designed so that a minimum counterexample to berge s conjecture cannot have either of these properties in this paper we prove both of these conjectures

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

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

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

antiweb wheel inequalities and their separation problems over the stable set polytopes a stable set in a graph g is a set of pairwise nonadjacent vertices the problem of finding a maximum weight stable set is one of the most basic hard problems an important approach to this problem is to formulate it as the problem of optimizing a linear function over the convex hull stab g of incidence vectors of stable sets since it is impossible unless co to obtain a concise characterization of stab g as the solution set of a system of linear inequalities it is a more realistic goal to find large classes of valid inequalities with the property that the corresponding separation problem given a point x find if possible an inequality in the class that x violates is efficiently solvable some known large classes of separable inequalities are the trivial edge cycle and wheel inequalities in this paper we give a polynomial time separation algorithm for the t antiweb inequalities of trotter we then introduce an even larger class in fact a sequence of classes of valid inequalities called t antiweb s wheel inequalities this class is a common generalization of the t antiweb inequalities and the wheel inequalities we also give efficient separation algorithms for them

dynamic conditional independence models and markov chain monte carlo methods abstract in dynamic statistical modeling situations observations arise sequentially causing the model to expand by progressive incorporation of new data items and new unknown parameters for example in clinical monitoring patients and data arrive sequentially and new patient specific parameters are introduced with each new patient markov chain monte carlo mcmc might be used for continuous updating of the evolving posterior distribution but would need to be restarted from scratch at each expansion stage thus mcmc methods are often too slow for real time inference in dynamic contexts by combining mcmc with importance resampling we show how real time sequential updating of posterior distributions can be effected the proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded such as when a patient dies or is discharged we apply the

some results on r kkm mappings and r kkm selections and their applications first some intersection theorems based on r kkm mappings are obtained and then their application to minimax inequalities is given

on a generalized class of minimax inequalities abstract some results on a generalized class of minimax inequalities based on the r i g h kkm mapping theorems in a g h space setting are presented the r i g h kkm mappings represent a new class of kkm mappings in g h spaces as well as in the interval spaces

sequential imputations and bayesian missing data problems abstract for missing data problems tanner and wong have described a data augmentation procedure that approximates the actual posterior distribution of the parameter vector by a mixture of complete data posteriors their method of constructing the complete data sets is closely related to the gibbs sampler both required iterations and similar to the em algorithm convergence can be slow we introduce in this article an alternative procedure that involves imputing the missing data sequentially and computing appropriate importance sampling weights in many applications this new procedure works very well without the need for iterations sensitivity analysis influence analysis and updating with new data can be performed cheaply bayesian prediction and model selection can also be incorporated examples taken from a wide range of applications are used for illustration

robust m ary detection filters and smoothers for continuous time jump markov systems in this paper we consider a dynamic m ary detection problem when markov chains are observed through a wiener process these systems are fully specified by a candidate set of parameters whose elements are a rate matrix for the markov chain and a parameter for the observation model further we suppose these parameter sets can switch according to the state of an unobserved markov chain and thereby produce an observation process generated by time varying jump stochastic parameter sets given such an observation process and a specified collection of models we estimate the probabilities of each model parameter set explaining the observation by defining a new augmented state process then applying the method of reference probability we compute matrix valued dynamics whose solutions estimate joint probabilities for all combinations of candidate model parameter sets and values taken by the indirectly observed state process these matrix valued dynamics satisfy a stochastic integral equation with a wiener process integrator using the gauge transformation techniques introduced by clark and a pointwise matrix product we compute robust matrix valued dynamics for the joint probabilities on the augmented state space in these new dynamics the observation wiener process appears as a parameter matrix in a linear ordinary differential equation rather than an integrator in a stochastic integral equation it is shown that these robust dynamics when discretised enjoy a deterministic upper bound which ensures nonnegative probabilities for any observation sample path in contrast no such upper bounds can be computed for taylor expansion approximations such as the euler maryauana and milstein schemes finally by exploiting a duality between causal and anticausal robust detector dynamics we develop an algorithm to compute smoothed mode probability estimates without stochastic integrations a computer simulation demonstrating performance is included

the boolean quadric polytope some characteristics facets and relatives we study unconstrained quadratic zero one programming problems havingn variables from a polyhedral point of view by considering the boolean quadric polytope qpn inn n 1 2 dimensions that results from the linearization of the quadratic form we show that qpn has a diameter of one descriptively identify three families of facets of qpn and show that qpn is symmetric in the sense that all facets of qpn can be obtained from those that contain the origin by way of a mapping the naive linear programming relaxation qpnlp of qpn is shown to possess the trubin property and its extreme points are shown to be 0 1 2 1 valued furthermore o n3 facet defining inequalities of qpn suffice to cut off all fractional vertices of qpnlp whereas the family of facets described by us has at least o 3n members the problem is also studied for sparse quadratic forms i e when several or many coefficients are zero and conditions are given for the previous results to carry over to this case polynomially solvable problem instances are discussed and it is shown that the known polynomiality result for the maximization of nonnegative quadratic forms can be obtained by simply rounding the solution to the linear programming relaxation in the case that the graph induced by the nonzero coefficients of the quadratic form is series parallel a complete linear description of the associated boolean quadric polytope is given the relationship of the boolean quadric polytope associated to sparse quadratic forms with the vertex packing polytope is discussed as well

on line inference for hidden markov models via particle filters we consider the on line bayesian analysis of data by using a hidden markov model where inference is tractable conditional on the history of the state of the hidden component a new particle filter algorithm is introduced and shown to produce promising results when analysing data of this type the algorithm is similar to the mixture kalman filter but uses a different resampling algorithm we prove that this resampling algorithm is computationally efficient and optimal among unbiased resampling algorithms in terms of minimizing a squared error loss function in a practical example that of estimating break points from well log data our new particle filter outperforms two other particle filters one of which is the mixture kalman filter by between one and two orders of magnitude

generalizations of cliques odd cycles and anticycles and their relation to independence system polyhedra padberg padberg m w 1973 on the facial structure of set packing polyhedra math programming5 199 215 has shown that if a graph g with vertex set v constitutes a clique odd cycle odd anticycle then the inequality x vxv 1 x vxv v 1 x vxv 2 defines a facet of pistg the convex hull of the incidence vectors of stable sets in g we generalize the concepts of cliques odd cycles and anticycles to arbitrary independence systems e i and show that the corresponding inequalities define facets of pi the convex hull of the incidence vectors of independent sets

gaussian sum particle filtering we use the gaussian particle filter to build several types of gaussian sum particle filters these filters approximate the filtering and predictive distributions by weighted gaussian mixtures and are basically banks of gaussian particle filters then we extend the use of gaussian particle filters and gaussian sum particle filters to dynamic state space dss models with non gaussian noise with non gaussian noise approximated by gaussian mixtures the non gaussian noise models are approximated by banks of gaussian noise models and gaussian mixture filters are developed using algorithms developed for gaussian noise dss models as a result problems involving heavy tailed densities can be conveniently addressed simulations are presented to exhibit the application of the framework developed herein and the performance of the algorithms is examined

exact hybrid filters in discrete time using the reference probability method and the change of measure in discrete time the state estimator problem is considered for linear systems observed in gaussian noise when the coefficients are functions of a noisily observed finite state markov chain the methods are new and finite dimensional filters are obtained however the number of statistics increases in time a numerical comparison of this filter with the interactive multiple model algorithm introduced by blom and bar shalom 1988 is given

progress on perfect graphs a graph is perfect if for every induced subgraph the chromatic number is equal to the maximum size of a complete subgraph the class of perfect graphs is important for several reasons for instance many problems of interest in practice but intractable in general can be solved efficiently when restricted to the class of perfect graphs also the question of when a certain class of linear programs always have an integer solution can be answered in terms of perfection of an associated graph

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

a blind particle filtering detector of signals transmitted over flat fading channels a new particle filtering detector pfd is proposed for blind signal detection over flat rayleigh fading channels whose model coefficients are unknown the detector employs a hybrid importance function and a mixture kalman filter it also incorporates an auxiliary particle filtering strategy with a smoothing kernel in the resampling step further by considering practical information of communication systems and the physical interpretation of the adopted second order autoregressive ar channel model a fully blind particle filtering implementation is developed the structure of the proposed pfd can be easily adapted to other system requirements simulations are provided that demonstrate the performance of the new pfd

wheel inequalities for stable set polytopes we introduce new classes of valid inequalities called wheel inequalities for the stable set polytopepg of a graphg each wheel configuration gives rise to two such inequalities the simplest wheel configuration is an odd subdivisionw of a wheel and for these we give necessary and sufficient conditions for the wheel inequality to be facet inducing forpw generalizations arise by allowing subdivision paths to intersect and by replacing the hub of the wheel by a clique the separation problem for these inequalities can be solved in polynomial time

particle filtering for partially observed gaussian state space models summary solving bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data has many applications for dynamic models a large number of algorithms based on particle filtering methods also known as sequential monte carlo algorithms have recently been proposed to solve these problems we propose a special particle filtering method which uses random mixtures of normal distributions to represent the posterior distributions of partially observed gaussian state space models this algorithm is based on a marginalization idea for improving efficiency and can lead to substantial gains over standard algorithms it differs from previous algorithms which were only applicable to conditionally linear gaussian state space models computer simulations are carried out to evaluate the performance of the proposed algorithm for dynamic tobit and probit models

local momentum autoregression and the modeling of interest rate term structure abstract a parsimonious autoregressive model that is globally mean reverting but locally driven by momentum is proposed the local momentum autoregression lm ar model carries one extra parameter and depending on the sign of this extra parameter it can be either local momentum preserving or momentum building the lm ar model is motivated by observing us interest rate movement over many decades which over a long time span seems to mean revert but over a period of several months or years can actually exhibit a momentum like behavior we use the lm ar model with a stochastic central tendency factor as the dominant global risk factor in interest rates and add a local variation component of the standard mean reverting type to create a 3 factor risk environment we then derive its corresponding term structure model and empirically implement the model on us interest rates of seven maturities from january 1954 to december 2013 on a weekly frequency to establish the presence of local momentum building

conditional densities for continuous time nonlinear hybrid systems with applications to fault detection continuous time nonlinear stochastic differential state and measurement equations all of which have coefficients capable of abrupt changes at a random time are considered finite state jump markov chains are used to model the changes conditional probability densities which are essential in obtaining filtered estimates for these hybrid systems are then derived they are governed by a coupled system of stochastic partial differential equations when the q matrix of the markov chain is either lower or upper diagonal it is shown that the system of conditional density equations is finite dimensional computable these findings are then applied to a fault detection problem to compute state estimates that include the failure time

silverman algorithm and the structure of discrete time stochastic systems abstract it is a well known yet poorly understood fact that contrary to the continuous time case the same discrete time process y can be represented by minimal linear models see 1 1a 1 1b below which may either have a non singular or a singular d matrix in fact models with d 0 have been commonly used in the statistical literature on the other hand for models with a singular d matrix the riccati difference equation of kalman filtering involves in general the pseudo inversion of a singular matrix this cheap filtering problem dual to the better known cheap control problem has been studied for several decades in connection with the so called invariant directions of the riccati equation for a singular d a reduction of the order of the riccati equation is in general possible the reasons for such a reduction do not seem to be completely clear either in this paper we provide an explanation of this phenomenon from the classical point of view of zero flipping among minimal spectral factors changing d s occurs whenever zeros are flipped from z to their reciprocals at z 0 it is well known that for finite zeros the zero flipping process takes place by multiplication of the underlying spectral factor by a suitable rational all pass matrix function for infinite zeros zero flipping is implemented by a dual version of the silverman structure algorithm using this interpretation we derive a new algorithm for filtering of non regular processes based on a reduced order riccati equation we also obtain a precise characterization of the reduction of the order of the riccati equation which is afforded by zeros either at z or at the origin this order reduction has traditionally been associated with the study of invariant directions a point of view which as we show does not capture the essence of the phenomenon

filtering via simulation auxiliary particle filters this article analyses the recently suggested particle approach to filtering time series we suggest that the algorithm is not robust to outliers for two reasons the design of the simulators and the use of the discrete support to represent the sequentially updating prior distribution here we tackle the first of these problems

on hybrid state estimation for stochastic hybrid systems this paper considers the state estimation problem for the general continuous time stochastic hybrid system shs which has various applications defined on the hybrid state space the shs has the interacting discrete dynamics and continuous dynamics subject to various uncertainties the hybrid state estimation problem is to estimate both the continuous state and the discrete state of the shs with the information given by a continuous time observation process in this paper the hybrid state estimation problem is mathematically formulated and the corresponding filtering equations that are stochastic partial differential equations are derived to describe the evolution of the hybrid state estimates conditioned on the observation history a numerical algorithm based on a finite difference approach is proposed to solve the filtering equations a markov chain mc is constructed on the descretized hybrid state space to approximate the infinitesimal generator of the shs and then hybrid state estimation for the shs is reduced to estimating the state of the mc it is proved that the state estimation results of the mc converge to the solution to the filtering equations as the constructed mc converges to the shs an illustrative example of aircraft tracking is used to demonstrate the performance of the proposed algorithm

the calculation of posterior distributions by data augmentation comment a noniterative sampling importance resampling alternative to the data augmentation algorithm for creating a few imputations when fractions of missing information are modest the sir algorithm

fractional and integral colourings letg v e be an undirected graph andc any vector in v g denote by gc resp gc the chromatic number resp fractional chromatic number ofg with respect toc we study graphs for which gc gc 1 we show that for the class of graphs satisfying gc gc a class generalizing perfect graphs an analogue of the duplication lemma does not hold we also describe a 2 vertex cut decomposition procedure related to the integer decomposition property we use this procedure to show that gc gc for series parallel graphs and gc gc 1 for graphs that do not have the 4 wheel as a minor

discrete time estimation of a markov chain with marked point process observations application to markovian jump filtering in this paper various discrete time estimation problems are studied for a finite and homogeneous markov chain observed by a marked point process these problems which could have significant applications in target tracking manufacturing or communication theory have never been studied in the literature the quantities to be estimated are the state the number of jumps and the occupation times the identification of the chain transition matrix is also addressed via an expectation maximization procedure solutions in the sense of the conditional distribution are obtained by a change of probability measure and are shown to have convenient recursive forms the efficiency of this new approach for sensor modeling is illustrated by the study of a linear markovian jump filtering problem where in addition to a classical state observation a mode markov point process observation is assumed a numerical example is given

an application of the lovasz schrijver m k k operator to the stable set problem although the lift and project operators of lovasz and schrijver have been the subject of intense study their m k k operator has received little attention we consider an application of this operator to the stable set problem we begin with an initial linear programming lp relaxation consisting of clique and non negativity inequalities and then apply the operator to obtain a stronger extended lp relaxation we discuss theoretical properties of the resulting relaxation describe the issues that must be overcome to obtain an effective practical implementation and give extensive computational results remarkably the upper bounds obtained are sometimes stronger than those obtained with semidefinite programming techniques

image enhanced multiple model tracking we consider tracking algorithms for manoeuvring targets when the observations include extra information on the current operating mode of the target obtained from an image sensor the target is modelled as a markov jump linear system and the image based observations form a discrete time point process we derive the optimal minimum mean square error filtered estimate which intrinsically fuses the image based and primary observations this optimal filter is computationally prohibitive but provides the basis for a clear understanding of various suboptimal approaches we propose the image enhanced imm filter as a practical alternative which retains many desirable properties of the optimal filter and outperforms existing image enhanced tracking algorithms over a broad range of operating scenarios

kalman filtering for linear systems with coefficients driven by a hidden markov jump process abstract we present an explicit algorithm for the solution of the nonlinear filtering problem concerning a linear partially observed diffusion type model where the coefficients are driven by a hidden markov jump process of which one can observe the occurrence of a jump the recursive filter is of a branching type with its finite dimension growing for each jump of the hidden markov process

particle filter with a mode tracker for visual tracking across illumination changes in this correspondence our goal is to develop a visual tracking algorithm that is able to track moving objects in the presence of illumination variations in the scene and that is robust to occlusions we treat the illumination and motion x y translation and scale parameters as the unknown state sequence the observation is the entire image and the observation model allows for occasional occlusions modeled as outliers the nonlinearity and multimodality of the observation model necessitate the use of a particle filter pf due to the inclusion of illumination parameters the state dimension increases thus making regular pfs impractically expensive we show that the recently proposed approach using a pf with a mode tracker can be used here since even in most occlusion cases the posterior of illumination conditioned on motion and the previous state is unimodal and quite narrow the key idea is to importance sample on the motion states while approximating importance sampling by posterior mode tracking for estimating illumination experiments demonstrate the advantage of the proposed algorithm over existing pf based approaches for various face and vehicle tracking we are also able to detect illumination model changes e g those due to transition from shadow to sunlight or vice versa by using the generalized expected log likelihood statistics and successfully compensate for it without ever loosing track

almost all webs are not rank perfect graphs with circular symmetry called webs are crucial for describing the stable set polytopes of two larger graph classes quasi line graphs 8 12 and claw free graphs 7 8 providing a complete linear description of the stable set polytopes of claw free graphs is a long standing problem 9 ben rebea conjectured a description for quasi line graphs see 12 chudnovsky and seymour 2 verified this conjecture recently for quasi line graphs not belonging to the subclass of fuzzy circular interval graphs and showed that rank facets are required in this case only fuzzy circular interval graphs contain all webs and even the problem of finding all facets of their stable set polytopes is open so far it is only known that stable set polytopes of webs with clique number 3 have rank facets only 5 17 while there are examples with clique number 4 having non rank facets 10 12 15

blind deconvolution via sequential imputations abstract the sequential imputation procedure is applied to adaptively and sequentially reconstruct discrete input signals that are blurred by an unknown linear moving average channel and contaminated by additive gaussian noises a problem known as blind deconvolution in digital communication a rejuvenation procedure for improving the efficiency of sequential imputation is introduced and theoretically justified the proposed method does not require the channel to be nonminimum phase and can be used in real time signal restoration two simulated systems are studied to illustrate the proposed method our result shows that the ideas of multiple imputations and flexible simulation techniques are as powerful in engineering as in survey sampling

covariance structure of the gibbs sampler with applications to the comparisons of estimators and augmentation schemes summary we study the covariance structure of a markov chain generated by the gibbs sampler with emphasis on data augmentation when applied to a bayesian missing data problem the gibbs sampler produces two natural approximations for the posterior distribution of the parameter vector the empirical distribution based on the sampled values of the parameter vector and a mixture of complete data posteriors we prove that rao blackwellization causes a one lag delay for the autocovariances among dependent samples obtained from data augmentation and consequently the mixture approximation produces estimates with smaller variances than the empirical approximation the covariance structure results are used to compare different augmentation schemes it is shown that collapsing and grouping random components in a gibbs sampler with two or three components usually result in more efficient sampling schemes

inference and model choice for sequentially ordered hidden markov models summary the system equation of a hidden markov model is rewritten to label the components by order of appearance and to make explicit the random behaviour of the number of components mt we argue that this reformulation is often a good way to achieve identifiability as it facilitates the interpretation of the posterior density and the estimation of the number of components that have appeared in a given sample we develop a sequential monte carlo algorithm for estimating the reformulated model which relies on particle filtering and gibbs sampling our algorithm has a computational cost that is similar to that of a markov chain monte carlo sampler and is much less likely to be affected by label switching i e the possibility of becoming trapped in a local mode of the posterior density the extension to transdimensional priors is also considered the approach is illustrated by two real data examples

a generalization of antiwebs to independence systems and their canonical facets we consider independence system polytopes i e polytopes whose extreme points are the incidence vectors of the sets of an independence system we first give a sufficient condition for recognizing boolean facets then the notion of antiweb introduced by trotter for graphs is generalized to independence systems and used for obtaining canonical facets of the associated polytopes we also point out how our results relate with known ones for knapsack set covering and matroid polytopes

exact bayesian filter and joint imm coupled pda tracking of maneuvering targets from possibly missing and false measurements this paper represents the problem of tracking multiple maneuvering targets from possibly missing and false measurements as one of filtering for a jump linear descriptor system with stochastic i i d coefficients this particular representation serves as an instrument in the characterization of the exact bayesian filter subsequently novel finite dimensional filter algorithms are developed through introducing approximations to the exact bayesian solution one filter approximation assumes conditionally gaussian density of the joint target state given the joint target maneuver mode and the algorithm is referred to as joint imm coupled pda jimmcpda the specialty of this filter algorithm is that both the imm step and the pda step are performed jointly over the modes and states of all targets subsequently the cpda track coalescence avoiding hypothesis pruning approach of blom bloem 2000 probabilistic data association avoiding track coalescence ieee transactions of automatic control 45 247 259 is extended to bring the joint target modes into account the resulting filter algorithm is referred to as track coalescence avoiding joint imm coupled pda the two novel algorithms are compared to immjpda and immpda through monte carlo simulations

mixture kalman filters in treating dynamic systems sequential monte carlo methods use discrete samples to represent a complicated probability distribution and use rejection sampling importance sampling and weighted resampling to complete the on line filtering task we propose a special sequential monte carlo method the mixture kalman filter which uses a random mixture of the gaussian distributions to approximate a target distribution it is designed for on line estimation and prediction of conditional and partial conditional dynamic linear models which are themselves a class of widely used non linear systems and also serve to approximate many others compared with a few available filtering methods including monte carlo methods the gain in efficiency that is provided by the mixture kalman filter can be very substantial another contribution of the paper is the formulation of many non linear systems into conditional or partial conditional linear form to which the mixture kalman filter can be applied examples in target tracking and digital communications are given to demonstrate the procedures proposed

a low complexity sequential monte carlo algorithm for blind detection in mimo systems in statistical signal processing the sequential monte carlo smc method is powerful and can approach the theoretical optima however its computational complexity is usually very high especially in multiple input multiple output mimo systems this paper presents a new low complexity smc lc smc algorithm for blind detection in mimo systems the main idea of which is to shrink the sampling space via channel estimation which is initialized using the first differentially modulated symbol and then updated using the monte carlo samples since the a posteriori probability of the transmitted symbols can be calculated separately by each transmit antenna the proposed lc smc algorithm is not only computationally efficient as compared to the original smc whose complexity grows exponentially with the number of transmit antennas but also makes blind turbo receiver more feasible for multilevel phase modulations simulation results are presented to demonstrate the effectiveness of the lc smc algorithm

strong lift and project cutting planes for the stable set problem a great deal of research has been focusing since the early seventies on finding strong relaxations for the stable set problem polyhedral combinatorics techniques have been at first developed to strengthen the natural linear formulation afterward strong semidefinite programming relaxations have been deeply investigated nevertheless the resulting integer programming ip algorithms cannot be regarded as being quite successful in practice as most of the relaxations give rise to one out of two extreme situations either provide weak bounds at low computational cost or give good bounds sometimes excellent but too demanding to compute in this paper we present a method to bridge such a gap in particular a new lift and project relaxation is obtained by a problem specific variant of the lifting operator m k k by lovasz and schrijver combined with benders decomposition this yields strong cutting planes generated by solving a cut generating linear program an extensive computational experience shows that embedding these cuts in a branch and cut framework significantly reduces the size of the enumeration trees as well as the cpu times with respect to state of the art ip algorithms

clique circulants and the stable set polytope of fuzzy circular interval graphs in this paper we give a complete and explicit description of the rank facets of the stable set polytope for a class of claw free graphs recently introduced by chudnovsky and seymour proceedings of the bristish combinatorial conference 2005 called fuzzy circular interval graphs the result builds upon the characterization of minimal rank facets for claw free graphs by galluccio and sassano j combinatorial theory 69 1 38 2005 and upon the introduction of a superclass of circulant graphs that are called clique circulants the new class of graphs is invetigated in depth we characterize which clique circulants c are facet producing i e are such that sum v in v c x v leq alpha c is a facet of stab c thus extending a result of trotter discrete math 12 373 388 1975 for circulants we show that a simple clique family inequality oriolo discrete appl math 132 2 185 201 2004 may be associated with each clique circulant c subseteq g when g is fuzzy circular interval we show that these inequalities provide all the rank facets of stab g if g is a fuzzy circular interval graph moreover we conjecture that in this case they also provide all the non rank facets of stab g and offer evidences for this conjecture