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

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

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

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 scaling mean and a law of large permanents abstract in this paper we study two types of means of the entries of a nonnegative matrix the permanental mean which is defined using permanents and the scaling mean which is defined in terms of an optimization problem we explore relations between these two means making use of important results by egorychev and falikman the van der waerden conjecture friedland sinkhorn and others we also define a scaling mean for functions in a much more general context our main result is a law of large permanents a pointwise ergodic theorem for permanental means of dynamically defined matrices that expresses the limit as a functional scaling mean the concepts introduced in this paper are general enough so to include as particular cases certain classical types of means as for example symmetric means and muirhead means as a corollary we reobtain a formula of halasz and szekely for the limit of the symmetric means of a stationary random process

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

positive diagonal scaling of a nonnegative tensor to one with prescribed slice sums abstract in this paper we give necessary and sufficient conditions on a nonnegative tensor to be diagonally equivalent to a tensor with prescribed slice sums these conditions are variations of bapat raghavan and franklin lorenz conditions

discrete maximum principles for finite element solutions of nonlinear elliptic problems with mixed boundary conditions one of the most important problems in numerical simulations is the preservation of qualitative properties of solutions of the mathematical models by computed approximations for problems of elliptic type one of the basic properties is the continuous maximum principle in our work we present several variants of the maximum principles and their discrete counterparts for scalar second order nonlinear elliptic problems with mixed boundary conditions the problems considered are numerically solved by the continuous piecewise linear finite element approximations built on simplicial meshes sufficient conditions providing the validity of the corresponding discrete maximum principles are presented geometrically they mean that the employed meshes have to be of acute or nonobtuse type depending of the type of the problem finally some examples of real life problems where the preservation of maximum principles plays an important role are presented

sobolev gradient preconditioning for elliptic reaction diffusion problems with some nonsmooth nonlinearities abstract the sobolev gradient approach is an efficient way to construct preconditioned iterations for solving nonlinear problems we extend this technique to be applicable for elliptic equations describing stationary states of reaction diffusion problems if the nonlinearities have certain lack of differentiability we derive convergence results of the sobolev gradient method on an abstract level and then for our elliptic problem under different assumptions numerical tests show convergence as expected

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

sequential estimation of hidden arma processes by particle filtering part ii this is part ii of a series of two papers where we address sequential estimation of wide sense stationary autoregressive moving average arma state processes by particle filtering in part i we considered a state space model where the state was an arma process of known order and where the parameters of the process could be known or unknown in this paper we extend our work from part i by considering the same type of models with the added complexity that the arma processes are now of unknown order instead of working on a scheme that first tracks the state by operating with different assumed models and then selects the best model by using a predefined criterion we present a method that directly estimates the state without the need of knowing the model order we derive the transition density of the state for unknown arma model order and propose a particle filter based on that density and the empirical bayesian methodology we demonstrate the performance of the proposed method with computer simulations and compare it with the methods from part i

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

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

preconditioning operators and sobolevgradients for nonlinear elliptic problems a preconditioning framework is presented for the iterative solution of nonlinear elliptic problems based on the preconditioning operator approach various fixed preconditioning operators are used in the iteration which can be interpreted as a weighted sobolev gradient method

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

numerical solution of burgers equation by the sobolev gradient method abstract burgers equation is solved numerically with sobolev gradient methods a comparison is shown with other numerical schemes presented in this journal such as modified adomian method mam 1 and by a variational method vm which is based on the method of discretization in time 2 it is shown that the sobolev gradient methods are highly efficient while at the same time retaining the simplicity of steepest descent algorithms

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

an extension of a theorem of darroch and ratcliff in loglinear models and its application to scaling multidimensional matrices abstract let c c ij be an m n matrix with real entries let b be any nonzero m vector let k c b 0 be bounded let x x 1 x 2 x n y y 1 y 2 y n be two nonnegative vectors with y k and x j 0 y j 0 for any coordinate j then it is shown that there exists a k and positive numbers z 1 z 2 z m such that j x j m i 1 z c ij i for all j th theorem slightly generalizes a theorem of darroch and ratcliff in loglinear models with a completely different proof technique the proof relies on an extension of a topological theorem of kronecker to set valued maps and the duality theorem of linear programming many theorems in scaling of matrices and multidimensional matrices are direct consequences of this theorem the main idea is to associate a suitable zero one matrix of transportation with any multidimensional matrix some motivations for scaling applications are also discussed

d1ad2 theorems for multidimensional matrices abstract a new technique for proving d 1 ad 2 theorems is given also a generalization of d 1 ad 2 theorems to multidimensional matrices is indicated

numerical approximation of time evolution related to ginzburg landau functionals using weighted sobolev gradients sobolev gradients have been discussed in sial et al 2003 as a method for energy minimization related to ginzburg landau functionals in this article a weighted sobolev gradient approach for the time evolution of a ginzburg landau functional is presented for different values of k a comparison is given between the weighted and unweighted sobolev gradients in a finite element setting it is seen that for small values of k the weighted sobolev gradient method becomes more and more efficient compared to using the unweighted sobolev gradient a comparison with newton s method is given where the failure of newton s method is demonstrated for a test problem

on the scaling of multidimensional matrices abstract elementary proofs are given for theorems of bapat and raghavan on the scaling of nonnegative multidimensional matrices theorems of sinkhorn and of brualdi parter and schneider are derived as corollaries for positive two dimensional matrices hilbert s projective metric and a theorem of g birkhoff are used to prove that sinkhorn s original iterative procedure converges geometrically the ratio of convergence is estimated from the given data

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

on pairs of multidimensional matrices abstract recently bapat applied a topological theorem of kronecker and generalized a theorem of sinkhorn on positive matrices here we give an alternative proof of a slightly stronger version of his generalization this proof combines kakutani s fixed point theorem and the duality theorem of linear programming and gives yet another proof of a theorem of bacharach and menon on pairs of nonnegative matrices

rao blackwellisation of sampling schemes summary this paper proposes a post simulation improvement for two common monte carlo methods the accept reject and metropolis algorithms the improvement is based on a rao blackwellisation method that integrates over the uniform random variables involved in the algorithms and thus post processes the standard estimators we show how the rao blackwellised versions of these algorithms can be implemented and through examples illustrate the improvement in variance brought by these new procedures we also compare the improved version of the metropolis algorithm with ordinary and rao blackwellised importance sampling procedures for independent and general metropolis set ups

approximations of the optimal importance density using gaussian particle flow importance sampling abstractrecently developed particle flow algorithms provide an alternative to importance sampling for drawing particles from a posterior distribution and a number of particle filters based on this principle have been proposed samples are drawn from the prior and then moved according to some dynamics over an interval of pseudo time such that their final values are distributed according to the desired posterior in practice implementing a particle flow sampler requires multiple layers of approximation with the result that the final samples do not in general have the correct posterior distribution in this article we consider using an approximate gaussian flow for sampling with a class of nonlinear gaussian models we use the particle flow within an importance sampler correcting for the discrepancy between the target and actual densities with importance weights we present a suitable numerical integration procedure for use with this flow and an accompanying step size control algorithm in a filtering co

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