truncated unscented kalman filtering we devise a filtering algorithm to approximate the first two moments of the posterior probability density function pdf the novelties of the algorithm are in the update step if the likelihood has a bounded support we can use a modified prior distribution that meets bayes rule exactly applying a kalman filter kf to the modified prior distribution referred to as truncated kalman filter tkf can vastly improve the performance of the conventional kalman filter particularly when the measurements are informative relative to the prior the application of the tkf to practical problems in which the measurement noise pdf has unbounded support is achieved by imposing several approximating assumptions which are valid only when the measurements are informative this implies that we adaptively choose between an approximation to the kf or the tkf according to the information provided by the measurement the resulting algorithm based on the unscented transformation is referred to as truncated unscented kf

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

on the derivative nonlinear schro dinger equation abstract in this paper we discuss the cauchy problem for the derivative nonlinear schrodinger equation i t 2i x 2 0 0 x x where 0 under an explicit smallness condition of the initial data we prove the unique global existence of solutions to this problem in the usual sobolev spaces in the weighted sobolev spaces and in the schwartz class we describe the smoothing effect in detail furthermore for the data decaying exponentially at infinity we prove that the above equation has unique local solutions which are analytic in the space direction

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

different approaches for state filtering in nonlinear systems with uncertain observations this paper addresses the least squares filtering problem for nonlinear systems with uncertain observations when random interruptions in the observation process are modelled by a sequence of independent bernoulli random variables we propose four filtering algorithms which are based on different approximations of the first and second order statistics of a nonlinear transformation of random vectors perturbed by additive and multiplicative noises these algorithms generalize the extended and unscented kalman filters to the case in which there is a positive probability that the observation in each time consists of noise alone and hence does not contain the signal to be estimated the accuracy of the different approximations is also analyzed and the performance of the proposed algorithms is compared in a numerical simulation example

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

ukf based nonlinear filtering using minimum entropy criterion a novel filter for nonlinear and non gaussian systems is proposed in this paper the unscented kalman filter is designed to give a preliminary estimation of the state an additional rbf network is added to the ukf innovation term to compensate for the non gaussianity of the whole system the renyi s entropy of the innovation is introduced and parameters of the rbf network are updated using minimum entropy criterion at each time step it has been shown that the proposed algorithm has a high accuracy in estimation because entropy can characterize all the randomness of the residual while ukf only cares for the mean and the covariance it has been proved that with properly chosen bandwidth the minimum entropy problem of the innovation is convex therefore the proposed adaptive nonlinear filter will be globally convergent and the misadjustment will be proportional to the step size the effectiveness of the proposed method is shown by simulation

well posedness and smoothing effect of schrodinger poisson equation in this work we take under consideration the cauchy problem for the schrodinger poisson type equation i tu x2u v u u f u 2 u where f represents a local nonlinear interaction we take into account both attractive and repulsive models and v is taken as a suitable solution of the poisson equation v 1 2 x c u 2 c cc is the doping profile or impurities we show that this problem is locally well posed in the weighted sobolev spaces hs hs r 1 x2 1 2 2 with s 1 which means the local existence uniqueness and continuity of the solution with respect to the initial data moreover under suitable assumptions on the local interaction we show the existence of global solutions finally we establish that for s 1 local in time and space smoothing effects are present in the solution more precisely in this problem there is locally a gain of half a derivative

conditional posterior cramer rao lower bounds for nonlinear sequential bayesian estimation the posterior cramerrao lower bound pcrlb for sequential bayesian estimators which was derived by tichavsky in 1998 provides a performance bound for a general nonlinear filtering problem however it is an offline bound whose corresponding fisher information matrix fim is obtained by taking the expectation with respect to all the random variables namely the measurements and the system states as a result this unconditional pcrlb is not well suited for adaptive resource management for dynamic systems the new concept of conditional pcrlb is proposed and derived in this paper which is dependent on the actual observation data up to the current time and is implicitly dependent on the underlying system state therefore it is adaptive to the particular realization of the underlying system state and provides a more accurate and effective online indication of the estimation performance than the unconditional pcrlb both the exact conditional pcrlb and its recursive evaluation approach including an approximation are derived further a general sequential monte carlo solution is proposed to compute the conditional pcrlb recursively for nonlinear non gaussian sequential bayesian estimation problems the differences between this new bound and existing measurement dependent pcrlbs are investigated and discussed illustrative examples are also provided to show the performance of the proposed conditional pcrlb

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

analyticity and global existence of small solutions to some nonlinear schrodinger equations in this paper we will study the nonlinear schrodinger equations begin gathered i partial t u tfrac 1 2 delta u left u right 2 u t x in mathbb r times mathbb r x n hfill u 0 x phi x x in mathbb r x n hfill end gathered it is shown that the solutions of exist and are analytic in space variables fort 0 if x h2n 1 2 xn decay exponentially as x andn 2

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

recursive bayesian estimation using piece wise constant approximations abstract in bayesian estimation the objective is to calculate the complete density function for an unknown quantity conditioned on noisy observations of that quantity this work considers recursive estimation of a nonlinear discrete time system state using successive observations the formal recursion for the density function is easily written but generally there is no closed form solution the numerical solution proposed here is obtained by modifying the recursion and using a simple piece wise constant approximation to the density functions the approach also allows detailed analysis of error propagation through the algorithm yielding a bound on the maximum error growth and a characterization of the situations with potential for large errors the stability of the algorithm is demonstrated by comparing its long term performance to a kalman filter for a linear system with gaussian noises comparison to the point mass algorithm shows improved estimation accuracy and for moderately dense grids faster computation as an example the algorithm is applied to a system identification problem and the results compared to a popular second order minimum variance estimator the optimal estimate derived from the approximate density is seen to be far superior

data driven power control for state estimation we consider sensor transmission power control for state estimation using a bayesian inference approach a sensor node sends its local state estimate to a remote estimator over an unreliable wireless communication channel with random data packet drops as related to packet dropout rate transmission power is chosen by the sensor based on the relative importance of the local state estimate the proposed power controller is proved to preserve gaussianity of local estimate innovation which enables us to obtain a closed form solution of the expected state estimation error covariance comparisons with alternative non data driven controllers demonstrate performance improvement using our approach

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

dynamic generalized linear models and bayesian forecasting abstract dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and posterior distributions for the exponential family parameters this leads to the calculation of closed standard form predictive distributions for forecasting and model criticism the structure of the models depends on the time evolution of underlying state variables and the feedback of observational information to these variables is achieved using linear bayesian prediction methods data analytic aspects of the models concerning scale parameters and outliers are discussed and some applications are provided dynamic bayesian models are developed for application in nonlinear non normal time series and regression problems providing dynamic extensions of standard generalized linear models a key feature of the analysis is the use of conjugate prior and

analytic solutions to nonelliptic nonlinear schrodinger equations abstract we prove local existence of analytic solutions for nonlinear schrodinger type equations the class we consider includes a number of equations derived from the physical context of water waves

derivation of the phd and cphd filters based on direct kullback leibler divergence minimization in this paper we provide novel derivations of the probability hypothesis density phd and cardinalised phd cphd filters without using probability generating functionals or functional derivatives we show that both the phd and cphd filters fit in the context of assumed density filtering and implicitly perform kullback leibler divergence kld minimizations after the prediction and update steps we perform the kld minimizations directly on the multitarget prediction and posterior densities

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

brief paper distribution function tracking filter design using hybrid characteristic functions a new tracking filtering algorithm for a class of multivariate dynamic stochastic systems is presented the system is expressed by a set of time varying discrete systems with non gaussian stochastic input and nonlinear output a new concept such as hybrid characteristic function is introduced to describe the stochastic nature of the dynamic conditional estimation errors where the key idea is to ensure the distribution of the conditional estimation error to follow a target distribution for this purpose the relationships between the hybrid characteristic functions of the multivariate stochastic input and the outputs and the properties of the hybrid characteristic function are established a new performance index of the tracking filter is then constructed based on the form of the hybrid characteristic function of the conditional estimation error an analytical solution which guarantees the filter gain matrix to be an optimal one is then obtained a simulation case study is included to show the effectiveness of the proposed algorithm and encouraging results have been obtained

nonlinear estimation applying an unscented transformation in systems with correlated uncertain observations an approximation to the least squares filter is proposed for discrete signals whose evolution is governed by nonlinear functions when the estimation is based on nonlinear observations with additive noise which can consist only of random noise this uncertainty in the observation process is modelled by bernoulli random variables which are correlated at consecutive time instants and are otherwise independent the proposed recursive approximation is based on the unscented principle successive applications of the unscented transformation to a suitable augmented state vector enable us to approximate the one stage state and observation predictors from the state filter at the previous time instant the performance of the proposed algorithm is compared with that of an extended algorithm in a numerical simulation example

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

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

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

design and implementation of gaussian filter for nonlinear system with randomly delayed measurements and correlated noises abstract in this paper we focus on the nonlinear state estimation problem with both one step randomly delayed measurements and correlated noises firstly a general framework of gaussian filter is designed under gaussian assumption on the conditional density furthermore the implementation of gaussian filter is transformed into the computation of the nonlinear numerical integrals in the proposed framework secondly a new cubature kalman filtering ckf algorithm is developed on the basis of the spherical radial cubature rule for approximating such nonlinear integrals finally the performance of the modified ckf is verified by a numerical simulation example

new conditional posterior cramer rao lower bounds for nonlinear sequential bayesian estimation the recursive procedure to compute the posterior cramer rao lower bound pcrlb for sequential bayesian estimators derived by tichavsky provides an off line performance bound for a general nonlinear filtering problem since the corresponding fisher information matrix fim is obtained by taking the expectation with respect to all the random variables this pcrlb is not well suited for online adaptive resource management for dynamic systems for online estimation performance evaluation in a nonlinear system the concept of conditional pcrlb was proposed by zuo in 2011 in this paper two other online conditional pcrlbs are proposed which are alternatives to the one proposed by zuo numerical examples are provided to show that the three online bounds namely the conditional pcrlb proposed by zuo and the two conditional pcrlbs proposed in this paper are very close to one another

comments on gaussian particle filtering with the gaussian assumption the above paper proposed an optimal gaussian filer under the particle filtering framework this comment presents a different perspective from the standpoint of the conventional gaussian filters in this respect the gaussian particle filter actually extends the conventional gaussian filter using monte carlo integration and the bayesian update rule hopefully the use of quasi monte carlo integration in place of monte carlo integration will improve the particle filtering

well posedness of the initial value problem for the korteweg de vries equation 1 1 itu axu u1xu o x t e r u x 0 uo x the kdv equation which was first derived as a model for unidirectional propagation of nonlinear dispersive long waves 21 has been considered in different contexts namely in its relation with the inverse scattering method in plasma physics and in algebraic geometry see 24 and references therein our purpose is to study local and global well posedness of the ivp 1 1 in classical sobolev spaces hs r we shall say that the ivp 1 1 is locally resp globally well posed in the function space x if it induces a dynamical system on x by generating a continuous local resp global flow it was established in the works of bona and smith 3 bona and scott 2 saut and temam 30 and kato 1 5 that the ivp 1 1 is locally resp globally well posed in hs with s 3 2 resp s 2 roughly speaking global well posedness in hs depends on the available local theory and on the conservation laws satisfied by solutions of 1 1 namely

dark solitons for a combined potential kdv and schwarzian kdv equations with t dependent coefficients and forcing term in this work we formally derive the dark soliton solutions for the combined potential kdv and schwarzian kdv equations the combined kdv and schwarzian kdv equations with time dependent coefficients and forcing term are then investigated to obtain dark soliton solutions the solitary wave ansatz is used to carry out the analysis for both models