recursive maximum likelihood identification of jump markov nonlinear systems we present an online method for joint state and parameter estimation in jump markov non linear systems jmnls state inference is enabled via the use of particle filters which makes the method applicable to a wide range of non linear models to exploit the inherent structure of jmnls we design a rao blackwellized particle filter rbpf where the discrete mode is marginalized out analytically this results in an efficient implementation of the algorithm and reduces the estimation error variance the proposed rbpf is then used to compute recursively in time smoothed estimates of complete data sufficient statistics together with the online expectation maximization algorithm this enables recursive identification of unknown model parameters including the transition probability matrix the method is also applicable to online identification of jump markov linear systems jmls the performance of the method is illustrated in simulations and on a localization problem in wireless networks using real data

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

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

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

transient fokker planck kolmogorov equation solved with smoothed particle hydrodynamics method summary probabilistic theories aim at describing the properties of systems subjected to random excitations by means of statistical characteristics such as the probability density function pdf the time evolution of the pdf of the response of a randomly excited deterministic system is commonly described with the transient fokker planck kolmogorov fpk equation the fpk equation is a conservation equation of a hypothetical or abstract fluid which models the transport of probability this paper presents a generalized formalism for the resolution of the transient fpk equation by using the well known mesh free lagrangian method smoothed particle hydrodynamics numerical implementation shows notable advantages of this method in an unbounded state space 1 the conservation of total probability in the state space is explicitly written 2 no artifact is required to manage far field boundary conditions 3 the positivity of the pdf is ensured and 4 the extension to higher dimensions is straightforward furthermore thanks to the moving particles this method is adapted for a large kind of initial conditions even slightly dispersed distributions the fpk equation is solved without any a priori knowledge of the stationary distribution just a precise representation of the initial distribution is required copyright 2013 john wiley sons ltd

gaussian particle filtering sequential bayesian estimation for nonlinear dynamic state space models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations this paper introduces a new filter called the gaussian particle filter it is based on the particle filtering concept and it approximates the posterior distributions by single gaussians similar to gaussian filters like the extended kalman filter and its variants it is shown that under the gaussianity assumption the gaussian particle filter is asymptotically optimal in the number of particles and hence has much improved performance and versatility over other gaussian filters especially when nontrivial nonlinearities are present simulation results are presented to demonstrate the versatility and improved performance of the gaussian particle filter over conventional gaussian filters and the lower complexity than known particle filters

the undecidability of type related problems in the type free style system f with finitely stratified polymorphic types we consider here a number of variations on system f that are predicative second order systems whose terms are intermediate between the curry style and the church style as in the church style the terms we deal with here contain the information on where universal quantifier elimination and introduction in the type inference process must take place however they omit the information on what types are involved in the rules which is similar to curry forms this can be viewed as a version of the partial type reconstruction problem considered by boehm and pfenning in which type erasure is done in a systematic way in this paper we prove the undecidability of the type checking type inference and typability problems for the system this demonstrates that the reason for undecidability is not the absence of the information where the second order rules should be applied but the actual shape of the polymorphic types to be used in the derivation moreover the proof works for the predicative version of the system with finitely stratified polymorphic types the result includes bounds on the leivant levels of types used in the instances leading to undecidability

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

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

belief condensation filtering inferring a sequence of variables from observations is prevalent in a multitude of applications traditional techniques such as kalman filters kfs and particle filters pfs are widely used for such inference problems however these techniques fail to provide satisfactory performance in many important nonlinear or non gaussian scenarios in addition there is a lack of a unified methodology for the design and analysis of different filtering techniques to address these problems in this paper we propose a new filtering methodology called belief condensation bc filtering first we establish a general framework for filtering techniques and propose an optimality criterion that leads to bc filtering we then propose efficient bc algorithms that can best represent the complex distributions arising in the filtering process the performance of the proposed techniques is evaluated for two representative nonlinear non gaussian problems showing that the bc filtering can provide accuracy approaching the theoretical bounds and outperform existing techniques in terms of the accuracy versus complexity tradeoff

a class of fast exact bayesian filters in dynamical models with jumps we address the statistical filtering problem in dynamical models with jumps when a particular application is adequately modeled by linear and gaussian probability density functions with jumps a usual method consists in approximating the optimal bayesian estimate in the sense of the minimum mean square error mmse in a linear and gaussian jump markov state space system jmss practical solutions include algorithms based on numerical approximations or on sequential monte carlo smc methods in this paper we propose a class of alternative methods which consists in building statistical models which locally similarly model the problem of interest but in which the computation of the mmse estimate can be be computed exactly without numerical nor smc approximations and at a computational cost which is linear in the number of observations

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

mixture densities maximum likelihood and the em algorithm the problem of estimating the parameters which determine a mixture density has been the subject of a large diverse body of literature spanning nearly ninety years during the last two decades the

the partition of unity finite element approach with hp refinement for the stationary fokker planck equation abstract in this paper the stationary fokker planck equation fpe is solved for nonlinear dynamical systems using a local numerical technique based on the meshless partition of unity finite element method pufem the method is applied to stationary fpe for 2 3 and 4 d systems and is argued to be an excellent candidate for higher dimensional problems and the transient problem local refinement is applied by introducing higher order polynomials in selected subdomains local p refinement to keep the problem size small while ensuring high approximation accuracy various local approximations are blended using novel pasting functions that provide any desired order of continuity results are compared with existing global and local techniques local p refinement is touted as an important step towards breaking the curse of dimensionality in numerical solution of fpe

adaptive approximation of higher order posterior statistics filtering is an approach for incorporating observed data into time evolving systems instead of a family of dirac delta masses that is widely used in monte carlo methods we here use the wiener chaos expansion for the parametrization of the conditioned probability distribution to solve the nonlinear filtering problem the wiener chaos expansion is not the best method for uncertainty propagation without observations nevertheless the projection of the system variables in a fixed polynomial basis spanning the probability space might be a competitive representation in the presence of relatively frequent observations because the wiener chaos approach not only leads to an accurate and efficient prediction for short time uncertainty quantification but it also allows to apply several data assimilation methods that can be used to yield a better approximate filtering solution the aim of the present paper is to investigate this hypothesis we answer in the affirmative for the stochastic lorenz 63 system based on numerical simulations in which the uncertainty quantification method and the data assimilation method are adaptively selected by whether the dynamics is driven by brownian motion and the near gaussianity of the measure to be updated respectively

on line inference for multiple changepoint problems we propose an on line algorithm for exact filtering of multiple changepoint problems this algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models the computational cost of this exact algorithm is quadratic in the number of observations we further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations at the expense of introducing small errors and propose two new optimum resampling algorithms for this problem one a version of rejection control allows the particle filter to automatically choose the number of particles required at each time step the new resampling algorithms substantially out perform standard resampling algorithms on examples we consider and we demonstrate how the resulting particle filter is practicable for segmentation of human gc content

dynamically orthogonal field equations for continuous stochastic dynamical systems abstract in this work we derive an exact closed set of evolution equations for general continuous stochastic fields described by a stochastic partial differential equation spde by hypothesizing a decomposition of the solution field into a mean and stochastic dynamical component we derive a system of field equations consisting of a partial differential equation pde for the mean field a family of pdes for the orthonormal basis that describe the stochastic subspace where the stochasticity lives as well as a system of stochastic differential equations that defines how the stochasticity evolves in the time varying stochastic subspace these new evolution equations are derived directly from the original spde using nothing more than a dynamically orthogonal condition on the representation of the solution if additional restrictions are assumed on the form of the representation we recover both the proper orthogonal decomposition equations and the generalized polynomial chaos equations we apply this novel methodology to two cases of two dimensional viscous fluid flows described by the navier stokes equations and we compare our results with monte carlo simulations

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

gaussian filters for nonlinear filtering problems we develop and analyze real time and accurate filters for nonlinear filtering problems based on the gaussian distributions we present the systematic formulation of gaussian filters and develop efficient and accurate numerical integration of the optimal filter we also discuss the mixed gaussian filters in which the conditional probability density is approximated by the sum of gaussian distributions a new update rule of weights for gaussian sum filters is proposed our numerical tests demonstrate that new filters significantly improve the extended kalman filter with no additional cost and the new gaussian sum filter has a nearly optimal performance

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

a nonlinear stochastic filter for continuous time state estimation nonlinear filters produce a nonparametric estimate of the probability density of state at each point in time currently known nonlinear filters include particle filters and the kushner equation and its un normalized version the zakai equation however these filters have limited measurement models particle filters require measurement at discrete times and the kushner and zakai equations only apply when the measurement can be represented as a function of the state we present a new nonlinear filter for continuous time measurements with a much more general stochastic measurement model it integrates to bayes rule over short time intervals and provides bayes optimal estimates from quantized intermittent or ambiguous sensor measurements the filter has a close link to information theory and we show that the rate of change of entropy of the density estimate is equal to the mutual information between the measurement and the state and thus the maximum achievable this is a fundamentally new class of filter that is widely applicable to nonlinear estimation for continuous time control

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

finitely stratified polymorphism abstract we consider predicative type abstraction disciplines based on type quantification with finitely stratified levels these lie in the vast middle ground between quantifier free parametric abstraction and full impredicative abstraction stratified polymorphism has an unproblematic set theoretic semantics and may lend itself to new approaches to type inference without sacrificing useful expressive power our main technical result is that the functions representable in the finitely stratified polymorphic calculus are precisely the super elementary functions i e the class e4 in grzegorczyk s subrecursive hierarchy this implies that there is no super elementary bound on the length of optimal normalization sequences and that the equality problem for finitely stratified polymorphic expressions is not super elementary we also observe that finitely stratified polymorphism augmented with type recursion admits functional algorithms that are not typable in the full second order calculus

square root receding horizon information filters for nonlinear dynamic system models new nonlinear filtering algorithms are designed based on a receding horizon strategy i e a finite impulse response fir structure and square root information filtering to achieve high accuracy and good performance in empirical error covariance tests the new nonlinear receding horizon filters reduce approximation errors in nonlinear filtering by considering a set of recent observations with non informative initial conditions by applying information filtering we are able to manage the non informative initial conditions and thus propose the square root version of the algorithm as a means of retaining the positive definiteness of the error covariance based on the proposed strategy we then implement known nonlinear filtering frameworks simulation results confirm that the new nonlinear receding horizon filters outperform existing nonlinear filters in well known nonlinear examples

non gaussian state space modeling of nonstationary time series abstract a non gaussian state space approach to the modeling of nonstationary time series is shown the model is expressed in state space form where the system noise and the observational noise are not necessarily gaussian recursive formulas of prediction filtering and smoothing for the state estimation and identification of the non gaussian state space model are given also given is a numerical method based on piecewise linear approximation to the density functions for realizing these formulas significant merits of non gaussian modeling and the wide range of applicability of the method are illustrated by some numerical examples a typical application of this non gaussian modeling is the smoothing of a time series that has mean value function with both abrupt and gradual changes simple gaussian state space modeling is not adequate for this situation here the model with small system noise variance cannot detect jump whereas the one with large system noise variance yields unfavorable wiggle to work

improper complex valued multiple model adaptive estimation motivated by the problem of estimating the discrete and continuous states of an improper complex valued stochastic hybrid system the paper proposes a class of widely linear augmented multiple model adaptive estimation algorithms referred to as the c mmae we show that for an improper complex valued signal pseudo covariance of the innovation sequence is not zero and therefore carries useful statistical information regarding the unknown behaviour mode of the hybrid system a new bayesian law is therefore derived as a function of the pseudo covariance of the innovation sequence and used to compute the probability that a hypothesized model is in effect at a certain time we show that the c mmae which uses the new bayesian law and utilizes the complete second order statistical characterization of the complex valued innovation sequence convergences faster than its counterpart which only uses the conventional covariance of the innovation sequence in order to simplify the computational complexity we develop two circularized versions of the c mmae using a preprocessing step referred to as the circularizing filter cf the cf is incorporated to convert the improper observations innovations into the proper ones in order to reduce the computational complexity of the hypothesis testing step finally an interacting version of the c mmae referred to as c imm is developed for improper complex valued systems with markovian switching coefficients simulation results indicate that the proposed hybrid estimators provide improved performance and convergence properties over their traditional counterparts

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

box gaussian mixture filter this note presents the box gaussian mixture filter bgmf which is an efficient filter for the systems with mainly linear measurements but enables utilizing highly nonlinear measurements bgmf contains a new way to approximate the prior distributions with a gaussian mixture whose components have small covariances in this note we present results on the weak convergence of bgmf in simulations we see that in our hybrid position example bgmf outperforms the conventional particle filter

effects of the smoothness of partitions of unity on the quality of representation of singular enrichments for gfem xfem stress approximations around brittle cracks abstract the convergence rates of the conventional generalized extended finite element method gfem xfem in crack modeling are similar to the convergence rates of the finite element method fem laborde et al 2005 and bechet et al 2005 unless the crack tip enrichment functions are applied in a subdomain with fixed dimension independently of the mesh parameter h and also demanding some special care for blending along the transition zone chahine et al 2006 and taracon et al 2009 thus to improve convergence rates more degrees of freedom dof are generated due to the larger quantity of enriched nodes this work seeks to identify and understand the advantages of better capturing the information provided by singular enrichments over mesh based smooth partitions of unity pou such pou with higher regularity can be built through the so called c k gfem framework following duarte et al 2006 based on a moving least square of degree zero and considering mesh based smooth weighting functions associated with arbitrary polygonal clouds the purpose herein is to investigate some possible advantages of mesh based smooth pou for modeling discontinuities and singularities in two dimensional problems of linear elastic fracture mechanics in such a fashion that the discretization error associated to stress discontinuities inherent in standard c 0 continuous gfem xfem approximations is eliminated the procedure shares features similar to the standard fem regarding domain partition and numerical integration but as neither the pou nor the enrichment functions are defined in natural domains the integrations are performed using only global coordinates the approximation capabilities of c k gfem discretizations with different patterns of singular enrichment distribution are investigated by analyzing the convergence rates of the h and p versions considering global measures in terms of strain energy and l 2 norm of displacements the effects on stability are also verified by analyzing the evolution of the condition number the effect of smoothness on conditioning is investigated and the eigenvalues distributions are used to identify the several aspects involved the smoothness of the pou the different types of enrichment functions and the pattern of enrichment the performance of the smooth approximations is compared to the c 0 counterparts built using conventional c 0 fem based pou it is shown that smoothness in the presence of extrinsically applied singular enrichments is important as the information provided by such enrichment is better captured in addition there are no stress jumps around singularities reducing error propagation beyond the neighborhood of the singularity

efficient sequential monte carlo with multiple proposals and control variates sequential monte carlo is a useful simulation based method for online filtering of state space models for certain complex state space models a single proposal distribution is usually not satisfactory and using multiple proposal distributions is a general approach to address various aspects of the filtering problem this article proposes an efficient method of using multiple proposals in combination with control variates the likelihood approach of tan 2004 is used in both resampling and estimation the new algorithm is shown to be asymptotically more efficient than the direct use of multiple proposals and control variates the guidance for selecting multiple proposals and control variates is also given numerical examples are used to demonstrate that the new algorithm can significantly improve over the bootstrap filter and auxiliary particle filter

marginalized particle filters for mixed linear nonlinear state space models the particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non gaussian filtering problems while the particle filter is fairly easy to implement and tune its main drawback is that it is quite computer intensive with the computational complexity increasing quickly with the state dimension one remedy to this problem is to marginalize out the states appearing linearly in the dynamics the result is that one kalman filter is associated with each particle the main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state space model several important special cases occurring in typical signal processing applications will also be discussed the marginalized particle filter is applied to an integrated navigation system for aircraft it is demonstrated that the complete high dimensional system can be based on a particle filter using marginalization for all but three states excellent performance on real flight data is reported

independent particle filters sequential monte carlo methods especially the particle filter pf and its various modifications have been used effectively in dealing with stochastic dynamic systems the standard pf samples the current state through the underlying state dynamics then uses the current observation to evaluate the sample s importance weight however there is a set of problems in which the current observation provides significant information about the current state but the state dynamics are weak and thus sampling using the current observation often produces more efficient samples than sampling using the state dynamics in this article we propose a new variant of the pf the independent particle filter ipf to deal with these problems the ipf generates exchangeable samples of the current state from a sampling distribution that is conditionally independent of the previous states a special case of which uses only the current observation each sample can then be matched with multiple samples of the previous states in

the augmented complex particle filter complex gaussian signals in engineering applications are typically noncircular that is they have rotation dependent distributions however current complex valued particle filters pfs have assumed implicitly or explicitly circular signal distributions which for noncircular signals leads to suboptimal performance in this correspondence we employ a recent development in the so called augmented complex statistics and propose the augmented complex pf acpf and the augmented complex gaussian pf acgpf for the sequential estimation of complex states in both circular and noncircular noise the analysis and simulations illuminate theoretical and practical advantages for the proposed solutions

a quaternion widely linear model for nonlinear gaussian estimation this paper deals with the nonlinear minimum mean squared error estimation problem by using a quaternion widely linear model on the basis of the information supplied by a gaussian signal and its square a quaternion observation process is defined and then by applying a widely linear processing an optimal estimator for the continuous time setting is provided the special structure of the estimator proves its superiority over the complex valued widely linear solution the continuous discrete version of the problem is also studied where the solution takes the form of a suboptimal estimator useful in practical applications in addition the particular case of signal plus noise is considered in which the suboptimal solution and its associated error can be implemented through an iterative algorithm two numerical simulation examples are presented showing the advantages of the proposed approach

saturated particle filter almost sure convergence and improved resampling nonlinear stochastic dynamical systems are widely used to model physical processes in many practical applications the state variables are defined on a compact set of the state space i e they are bounded or saturated to estimate the states of systems with saturated variables the saturated particle filter spf has recently been developed this filter exploits the structure of the saturated system using a specific importance sampling distribution in this paper we investigate the asymptotic properties of the filter in particular its almost sure convergence to the true posterior pdf furthermore an improved spf is developed that uses a novel resampling procedure to overcome the practical shortcomings of the original spf we prove that this new filter also converges almost surely to the true posterior pdf both versions of the spf are presented in easy to implement algorithmic forms

particle filtering for large dimensional state spaces with multimodal observation likelihoods we study efficient importance sampling techniques for particle filtering pf when either a the observation likelihood ol is frequently multimodal or heavy tailed or b the state space dimension is large or both when the ol is multimodal but the state transition pdf stp is narrow enough the optimal importance density is usually unimodal under this assumption many techniques have been proposed but when the stp is broad this assumption does not hold we study how existing techniques can be generalized to situations where the optimal importance density is multimodal but is unimodal conditioned on a part of the state vector sufficient conditions to test for the unimodality of this conditional posterior are derived our result is directly extendable to testing for unimodality of any posterior the number of particles n to accurately track using a pf increases with state space dimension thus making any regular pf impractical for large dimensional tracking problems but in most such problems most of the state change occurs in only a few dimensions while the change in the rest of the dimensions is small using this property we propose to replace importance sampling from a large part of the state space whose conditional posterior is narrow enough by just tracking the mode of the conditional posterior this introduces some extra error but it also greatly reduces the importance sampling dimension the net effect is much smaller error for a given n especially when the available n is small an important class of large dimensional problems with multimodal ol is tracking spatially varying physical quantities such as temperature or pressure in a large area using a network of sensors which may be nonlinear and or may have nonnegligible failure probabilities improved performance of our proposed algorithms over existing pfs is demonstrated for this problem

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

gaussian smoothers for nonlinear systems with one step randomly delayed measurements this technical note is concerned with the nonlinear state smoothing problem in the case that the measurements are randomly delayed by one sampling time under gaussian domain two general gaussian approximation ga and gaussian mixture approximation gma smoothers are proposed in minimum mean square error mmse sense the smoothing implementation is transformed into computing some special posterior covariances which triggers the development of the new unscented kalman smoother uks by applying unscented transformation ut simulation results demonstrate the superior performance of the proposed ga uks and gma uks algorithms

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

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

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

local dissipativity and attractors for the kuramoto sivashinsky equation in thin 2d domains here 0 e 5 1 is assumed to be sufficiently small so that the basic periodicity cell sz 0 2n x 0 2ne is a thin domain we shall also mention other types of boundary conditions for which the same methods are applicable the dissipativity of the general two and higher dimensional problem has been open for some time the essential difficulty being the lack of a proof of the existence of an absorbing set in fact if such a set exists then there exists a global attractor and one can prove very precise regularity results excellent references for these as well as many refined results on the geometry of the attractor are the paper by nicolaenko et af l il yashenko 2 and the books by ttmam 3 and constantin et al 4 the approach we shall adopt is based on the intuitive idea that l 1 3 should be close to one dimensional and is close to the methods introduced by hale and raugel 5 61 and raugel and sell 7 there are many nontrivial results available for the periodic one dimensional problem the odd periodic case was studied by l 81 the same authors g treat a neumann type of problem without symmetry and the rigid dirichlet problem is studied by 9 again without any symmetry assumptions the general periodic one dimensional problem has only recently been proved to be dissipative 2 our main result is the following theorem

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

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

adaptive joint detection and estimation in mimo systems a hybrid systems approach an adaptive receiver based on hybrid system theory is developed for a multiuser multiple input multiple output mimo fading code division multiple access cdma system the basic idea is to treat the transmitted symbols and channel gains as unknown states discrete and continuous within a hybrid systems framework the bayesian inference based state estimation is derived using multiple model theory resulting in an optimal joint sequence estimator which is shown to be intractable in its computational complexity a suboptimal receiver imm sic is then derived based on the well known interacting multiple model imm algorithm and successive interference cancellation sic scheme this paper shows the specific approximations made to the probability densities of the optimal receiver in deriving the imm sic receiver with complexity linear in number of users this receiver design is well suited for online recursive processing of space time coded cdma system where the decoding stage is incorporated within the multiple model framework

gaussian mixture nonlinear filtering with resampling for mixand narrowing a new gaussian mixture filter has been developed one that uses a resampling step in order to limit the covariances of its individual gaussian components the new filter has been designed to produce accurate solutions of difficult nonlinear non gaussian estimation problems it uses static multiple model filter calculations and extended kalman filter ekf approximations for each gaussian mixand in order to perform dynamic propagation and measurement update the resampling step uses a newly designed algorithm that employs matrix inequalities in order to bound each mixand s covariance resampling occurs between the dynamic propagation and the measurement update in order to ensure bounded covariance in both of these operations the resampling algorithm also attempts to economize on the number of new mixands the resulting filter has been tested on a difficult seven state nonlinear filtering problem it achieves significantly better accuracy than a simple ekf an unscented kalman filter a moving horizon estimator backwards smoothing ekf and a regularized particle filter

trivial stationary solutions to the kuramoto sivashinsky and certain nonlinear elliptic equations abstract we show that the only locally integrable stationary solutions to the integrated kuramoto sivashinsky equation in r and r 2 are the trivial constant solutions we extend our technique and prove similar results to other nonlinear elliptic problems in r n

on mmse estimation a linear model under gaussian mixture statistics in a bayesian linear model suppose observation y hx n stems from independent inputs x and n which are gaussian mixture gm distributed with known matrix h the minimum mean square error mmse estimator for x has analytical form however its performance measure the mmse itself has no such closed form because existing bayesian mmse bounds prove to have limited practical value under these settings we instead seek analytical bounds for the mmse both upper and lower this paper provides such bounds and relates them to the signal to noise ratio snr

likelihood consensus and its application to distributed particle filtering we consider distributed state estimation in a wireless sensor network without a fusion center each sensor performs a global estimation task based on the past and current measurements of all sensors using only local processing and local communications with its neighbors in this estimation task the joint all sensors likelihood function jlf plays a central role as it epitomizes the measurements of all sensors we propose a distributed method for computing at each sensor an approximation of the jlf by means of consensus algorithms this likelihood consensus method is applicable if the local likelihood functions of the various sensors viewed as conditional probability density functions of the local measurements belong to the exponential family of distributions we then use the likelihood consensus method to implement a distributed particle filter and a distributed gaussian particle filter each sensor runs a local particle filter or a local gaussian particle filter that computes a global state estimate the weight update in each local gaussian particle filter employs the jlf which is obtained through the likelihood consensus scheme for the distributed gaussian particle filter the number of particles can be significantly reduced by means of an additional consensus scheme simulation results are presented to assess the performance of the proposed distributed particle filters for a multiple target tracking problem

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

bayesian conditional monte carlo algorithms for nonlinear time series state estimation bayesian filtering aims at estimating sequentially a hidden process from an observed one in particular sequential monte carlo smc techniques propagate in time weighted trajectories which represent the posterior probability density function pdf of the hidden process given the available observations on the other hand conditional monte carlo cmc is a variance reduction technique which replaces the estimator of a moment of interest by its conditional expectation given another variable in this paper we show that up to some adaptations one can make use of the time recursive nature of smc algorithms in order to propose natural temporal cmc estimators of some point estimates of the hidden process which outperform the associated crude monte carlo mc estimator whatever the number of samples we next show that our bayesian cmc estimators can be computed exactly or approximated efficiently in some hidden markov chain hmc models in some jump markov state space systems jmss as well as in multitarget filtering finally our algorithms are validated via simulations

brief paper a quadrature based method of moments for nonlinear filtering according to the nonlinear filtering theory optimal estimates of a general continuous discrete nonlinear filtering problem can be obtained by solving the fokker planck equation coupled with a bayesian update rule this procedure does not rely on linearizations of the dynamical and or measurement models however the lack of fast and efficient methods for solving the fokker planck equation presents challenges in real time nonlinear filtering problems in this paper a direct quadrature method of moments is introduced to solve the fokker planck equation efficiently and accurately this approach involves representation of the state conditional probability density function in terms of a finite collection of dirac delta functions the weights and locations abscissas in this representation are determined by moment constraints and modified using the bayes rule according to measurement updates as demonstrated by numerical examples this approach appears to be promising in the field of nonlinear filtering

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

existential type systems between church and curry style type free style abstract we study type checking typability and type inference problems for second order existential systems in type free style the type free style is an intermediate representation of terms between the curry style and the church style terms in the type free style contain information on where the existential quantifier elimination and introduction take place but omit the information on which types are involved we show that all the problems are undecidable employing reduction of second order unification for considerably restricted special instances in flat form these results hold even in a fragment of the existential system where are only used and in case of predicative fragments of the existential systems

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

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

detection of random signals in gaussian mixture noise a locally optimal detection algorithm for random signals in dependent noise is derived and applied to independent identically distributed complex valued gaussian mixture noise the resulting detector is essentially a weighted sum of power detectors the power detector is the locally optimal detector for random signals in gaussian noise the weighting functions are modified to enhance the detection performance for small sample sizes an implementation of the mixture detector using the expectation maximization algorithm is described moments of these detectors are calculated from piecewise polynomial approximations of the weighting functions the sum of sufficiently many independent identically distributed detector outputs is then approximated by a normal distribution probability distributions are also derived for the power detector in gaussian mixture noise for a particular set of noise parameters the theoretical distributions are compared with those obtained from monte carlo simulation and seen to be quite close the theoretical distributions are then used to compare the performance of the mixture and power detectors in gaussian mixture noise over a range of parameters and to assess the impact of parameter error on detection performance in this study the signal gain of the mixture detectors varies from 15 to 38 db and the degradation of the probability of detection due to parameter estimation error is relatively minor

string submodular functions with curvature constraints consider the problem of choosing a string of actions to optimize an objective function that is string submodular it was shown in previous papers that the greedy strategy consisting of a string of actions that only locally maximizes the step wise gain in the objective function achieves at least a 1 e 1 approximation to the optimal strategy this paper improves this approximation by introducing additional constraints on curvature namely total backward curvature total forward curvature and elemental forward curvature we show that if the objective function has total backward curvature sigma then the greedy strategy achieves at least a 1 sigma 1 e sigma approximation of the optimal strategy if the objective function has total forward curvature epsilon then the greedy strategy achieves at least a 1 epsilon approximation of the optimal strategy moreover we consider a generalization of the diminishing return property by defining the elemental forward curvature we also introduce the notion of string matroid and consider the problem of maximizing the objective function subject to a string matroid constraint we investigate two applications of string submodular functions with curvature constraints 1 choosing a string of actions to maximize the expected fraction of accomplished tasks and 2 designing a string of measurement matrices such that the information gain is maximized

a numerical solver for high dimensional transient fokker planck equation in modeling polymeric fluids in this paper a tensor decomposition approach combined with chebyshev spectral differentiation is presented to solve the high dimensional transient fokker planck equations fpe arising in the simulation of polymeric fluids via multi bead spring mbs model generalizing the authors previous work on the stationary fpe the transient solution is obtained in a single candecomp parafac decomposition cpd form for all times via the alternating least squares algorithm this is accomplished by treating the temporal dimension in the same manner as all other spatial dimensions thereby decoupling it from them as a result the transient solution is obtained without resorting to expensive time stepping schemes a new relaxed approach for imposing the vanishing boundary conditions is proposed improving the quality of the approximation the asymptotic behavior of the temporal basis functions is studied the proposed solver scales very well with the dimensionality of the mbs model numerical results for systems up to 14 dimensional state space are successfully obtained on a regular personal computer and compared with the corresponding matrix riccati differential equation for linear models or monte carlo simulations for nonlinear models

steady solutions of the kuramoto sivashinsky equation abstract steady solutions of the kuramoto sivashinsky equation are studied these solutions are defined on the whole x line and propagate with a constant speed c 2 in time for large c 2 it is shown that the solution is unique and has a conical form for small c 2 there is a periodic solution and an infinite set of quasi periodic solutions as asserted by moser s twist map theorem numerical computations for intermediate values of c 2 suggest that below c 1 6 of every speed there is a continuum of odd quasi periodic solutions or a cantor set of chaotic solutions wrapped by infinite sequences of conic solutions

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

quasi monte carlo filtering in nonlinear dynamic systems we develop a new framework for bayesian filtering in general nonlinear dynamic systems based on the quasi monte carlo qmc numerical techniques we first propose a general approach to deterministic filtering called the quasi monte carlo kalman filter qmc kf which unifies several existing advanced filtering methods in the literature such as the unscented kalman filter ukf and the quadrature kalman filter qkf the computationally expensive step of calculating the jacobian matrix involved in the extended kalman filter ekf is avoided in the proposed qmc kf approach we also propose sequential quasi monte carlo sqmc filtering techniques which is analogous to the sequential monte carlo smc or particle filtering methods in the literature we show in particular how to effectively combine deterministic filtering and adaptive importance sampling schemes which lead to powerful sqmc filtering strategies the properties of the proposed sqmc and sqmc is methods in terms of almost sure convergence and numerical error propagation behavior are analyzed finally numerical examples are provided to demonstrate the effectiveness of the proposed new qmc based filtering algorithms

application of multi scale finite element methods to the solution of the fokker planck equation abstract this paper presents an application of multi scale finite element methods to the solution of the multi dimensional fokker planck equation the fokker planck or forward kolmogorov equation is a degenerate convective diffusion equation arising in markov process theory it governs the evolution of the transition probability density function of the response of a broad class of dynamical systems driven by gaussian noise and completely describes the response process analytical solutions for the fokker planck equation have been developed for only a limited number of low dimensional systems leading to a large body of approximation theory one such approach successfully applied to the solution of these problems in the past is the finite element method though for systems of dimension three or less in this paper a multi scale finite element method is applied to the fokker planck equation in an effort to develop a formulation that can yield higher accuracy on cruder spatial discretizations thus reducing the computational overhead associated with large scale problems that arise in higher dimensions

visual tracking by continuous density propagation in sequential bayesian filtering framework particle filtering is frequently used for visual tracking problems since it provides a general framework for estimating and propagating probability density functions for nonlinear and non gaussian dynamic systems however this algorithm is based on a monte carlo approach and the cost of sampling and measurement is a problematic issue especially for high dimensional problems we describe an alternative to the classical particle filter in which the underlying density function has an analytic representation for better approximation and effective propagation the techniques of density interpolation and density approximation are introduced to represent the likelihood and the posterior densities with gaussian mixtures where all relevant parameters are automatically determined the proposed analytic approach is shown to perform more efficiently in sampling in high dimensional space we apply the algorithm to real time tracking problems and demonstrate its performance on real video sequences as well as synthetic examples

numerical solution of high dimensional stationary fokker planck equations via tensor decomposition and chebyshev spectral differentiation abstract this paper focuses on the curse of dimensionality in the numerical solution of the stationary fokker planck equation for systems with state independent excitation a tensor decomposition approach is combined with chebyshev spectral differentiation to drastically reduce the number of degrees of freedom required to maintain accuracy as dimensionality increases following the enforcement of the normality condition via a penalty method the discretized system is solved using alternating least squares algorithm numerical results for a variety of systems including separable non separable systems linear nonlinear systems and systems with without closed form stationary solutions up to ten dimensional state space are presented to illustrate the effectiveness of the proposed method

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

elementary particles as solutions of the sivashinsky equation abstract stationary spherically symmetric solutions of the sivashinsky equation 1 c 2 s 2 t s 2 m 2 c 2 s 3 m 2 c 2 2 s are looked for the problem is reduced to finding all admissible solutions y y r of the ode d 2 dr 2 2 r d dr 1 d dr 2 r y y 2 i e solutions which are defined on the half line 0 r and satisfy y 0 y 0 it is proved that for each y 0 0 34 0 33 the solution of the initial value problem with y 0 y 0 0 is admissible in terms of the action function s these solutions are interpreted as free relativistic particles the proof of the result employs analytic asymptotic expansion near r 0 and r and a new technique of rigorous estimates by a computer the proved interval of existence y 0 0 34 0 33 nearly coincides with the one obtained by numerical experiments

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

fuzzy particle filtering for uncertain systems in this paper we propose a novel fuzzy particle filtering method for online estimation of nonlinear dynamic systems with fuzzy uncertainties this approach uses a sequential fuzzy simulation to approximate the possibilities of the state intervals in the state space and estimates the state by fuzzy expected value operator to solve the degeneracy problem of the fuzzy particle filter one corresponding resampling technique is introduced in addition we compare the fuzzy particle filter with ordinary particle filter in both aspects of the theoretical basis and algorithm design and demonstrate that the proposed filter outperforms standard particle filters especially when the number of the particles is small the numerical simulations of two continuous state nonlinear systems and a jump markov system are employed to show the effectiveness and robustness of the proposed fuzzy particle filter

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

radial asymptotically periodic solutions of the kuramoto sivashinsky equation abstract radial steady solutions of the kuramoto sivashinsky equation are studied it is shown that there exist solutions that approach at infinity the one dimensional periodic solutions both hyperbolic and elliptic periodic solutions are considered

a finite element method for the statistics of non linear random vibration the transitional probability density function for the random response of a certain class of non linear system satisfies the fokker planck kolmogorov equation this paper concerns the numerical solution of the stationary form of this equation yielding the stationary probability density function of response the weighted residual statement for the problem is integrated by parts to yield the weak form of the equations which are then solved by the finite element method the method is applied to a duffing oscillator and good agreement is found with the exact result and the method is compared favourably with a galerkin solution method given by bhandari and sherrer 1 also the method is applied to the ship rolling problem and good agreement is found with an approximate analytical result due to roberts 2

asymptotic optimality of the maximum likelihood kalman filter for bayesian tracking with multiple nonlinear sensors bayesian tracking is a general technique for state estimation of nonlinear dynamic systems but it suffers from the drawback of computational complexity this paper is concerned with a class of wiener systems with multiple nonlinear sensors such a system consists of a linear dynamic system followed by a set of static nonlinear measurements we study a maximum likelihood kalman filtering mlkf technique which involves maximum likelihood estimation of the nonlinear measurements followed by classical kalman filtering this technique permits a distributed implementation of the bayesian tracker and guarantees the boundedness of the estimation error the focus of this paper is to study the extent to which the mlkf technique approximates the theoretically optimal bayesian tracker we provide conditions to guarantee that this approximation becomes asymptotically exact as the number of sensors becomes large two case studies are analyzed in detail