spontaneous symmetry breaking in a two lane system with parallel update this paper studies a two lane totally asymmetric simple exclusion processes tasep with narrow entrances under parallel update particles move on two parallel lanes in the opposite directions without lane changing the narrow entrances are modelled in this way the entry of a particle is not allowed if the exit site of the other lane is occupied see also pronina and kolomeisky 2007 j phys a math theor 40 2275 we mainly focus on the case where particles hop deterministically in the bulk the phase diagram bulk density and particle currents are analysed using mean field approximation it is shown that there are two symmetry breaking phases and one of them i e asymmetric low density low density phase occupies only a line in the phase diagram a multi stable phenomenon is also observed monte carlo simulations are carried out and the simulation results deviate from the mean field prediction because correlations are not considered in mean field calculation a seesaw phase is reproduced when 1 the results are also compared with that obtained from the two lane system with random update finally preliminary simulation results where particles hop with the rate q 1 in the bulk are reported and it is shown that the introduction of stochastic hopping changes the phase diagram structure

truncation nonlinear filters for state estimation with nonlinear inequality constraints the paper focuses on the state estimation problem of nonlinear non gaussian systems with state subject to a nonlinear inequality constraint taking into account the available additional information about the state given by the constraint increases the estimate quality compared to classical state estimation methods which cannot utilize the information considering the constraint in the form of an inequality involving a nonlinear function of the state makes the state estimation problem difficult and hence treated only marginally in this paper a generic local filter for the inequality constrained estimation problem is proposed it covers the extended kalman filter unscented kalman filter and divided difference filter as special cases and enforces the constraint by truncating the conditional density of the state the truncation is computationally cheap yet it provides high estimate quality of the constrained estimate the same idea is then utilized in a truncation gaussian mixture filter which is also proposed in the paper to increase the estimate quality further by providing a global constrained estimate superior estimate quality and computational efficiency of the proposed filters are illustrated in two numerical examples

multiple conversions of measurements for nonlinear estimation a multiple conversion approach mca to nonlinear estimation is proposed in this paper it jointly considers multiple hypotheses on the joint distribution of the quantity to be estimated and its measurement the overall mca estimate is a probabilistically weighted sum of the hypothesis conditional estimates to describe the hypothesized joint distributions used to match the truth a general distribution form characterized by a linear or nonlinear measurement conversion is found this form is more general than gaussian and includes gaussian as a special case moreover the minimum mean square error mmse optimal estimate given a hypothesized distribution in this form is simply the linear mmse lmmse estimate using the converted measurement lmmse based estimators including the original lmmse estimator and its generalization the recently proposed uncorrelated conversion based filter can all be incorporated into the mca framework given a nonlinear problem a specific form of the hypothesized distribution can be optimally obtained by quadratic programming using the information in the nonlinear measurement function and the measurement conversion then the mca estimate can be obtained easily for dynamic problems an interacting multiple conversion algorithm is proposed for recursive estimation the mca approach has a simple and flexible structure and takes advantage of multiple lmmse based nonlinear estimators the overall estimates are obtained adaptively depending on the performance of the candidate estimators simulation results demonstrate the effectiveness of the proposed approach compared with other nonlinear filters

nonlinear estimation based on conversion sample optimization abstract for nonlinear estimation the linear minimum mean square error lmmse estimator using the original measurement is the best of all estimators linear in the measurement recently it has been proven that an lmmse estimator using a stacked measurement vector composed of the original measurement and its nonlinear conversion transformation or function outperforms the original lmmse estimator however to find an optimal conversion for various nonlinear problems is very difficult because it involves functional optimization recognizing that the conversion affects estimation performance only through conversion dependent quantities needed by the augmented lmmse based estimator this paper proposes an optimized conversion sample filter ocf which optimizes all these quantities to optimize estimation performance these quantities are much easier to obtain than the optimal conversion itself using deterministic sampling obtaining these quantities amounts to determining the converted values at both the deterministic sample points and the measurement value in the ocf these values are obtained optimally and analytically by solving a constrained rayleigh quotient problem the proposed ocf has a simple and analytical form and can be generally applied to nonlinear estimation simulation results demonstrate the effectiveness of the proposed ocf compared with some popular nonlinear estimators including several lmmse based filters a recently proposed uncorrelated conversion based filter and a particle filter

possibilistic decisions and fuzzy statistical tests the paper deals with the problem of the interpretation of the results of statistical tests in terms of the theory of possibility the well known concept in statistics of the observed test size p also known as p value and significance has been given a new possibilistic interpretation and generalised for the case of imprecisely defined statistical hypotheses and vague statistical data the proposed approach allows a practitioner to evaluate the test results using intuitive concepts of possibility necessity or indifference

the sr approach a new estimation procedure for non linear and non gaussian dynamic term structure models abstract this paper suggests a new approach for estimating linear and non linear dynamic term structure models with latent factors we impose no distributional assumptions on the factors which therefore may be non gaussian the novelty of our approach is to use many observables yields or bond prices in the cross section dimension this implies that the latent factors can be determined quite accurately by a sequence of cross section regressions we also show how output from these regressions can be used to obtain model parameters by a two or three step moment based estimation procedure

adaptive ode solvers in extended kalman filtering algorithms this paper studies numerical methods that are used to treat ordinary differential equations arising in extended kalman filtering algorithms such problems are called the moment equations and constitute an important subclass of differential equations they all possess a number of specific properties that make the standard available software ineffective for some mathematical models in this area for instance we show that built in matlab ode solvers are not able to cope with a number of tests considered here in contrast the hybrid method developed by mazzoni 2007 exhibits much better performance on the same examples the latter means that specially designed numerical schemes are needed for efficient solution of the moment equations instead of the standard software designed for general systems of ordinary differential equations

sparse grid quadrature nonlinear filtering in this paper a novel nonlinear filter named sparse grid quadrature filter sgqf is proposed the filter utilizes weighted sparse grid quadrature points to approximate the multi dimensional integrals in the nonlinear bayesian estimation algorithm the locations and weights of the univariate quadrature points with a range of accuracy levels are determined by the moment matching method then the univariate quadrature point sets are extended to form a multi dimensional grid using the sparse grid theory compared with the conventional point based methods the estimation accuracy level of the sgqf can be flexibly controlled and the number of sparse grid quadrature points for the sgqf is a polynomial of the dimension of the system which alleviates the curse of dimensionality for high dimensional problems the unscented kalman filter ukf is proven to be a subset of the sgqf at the level 2 accuracy the performance of this filter is demonstrated by an orbit estimation problem the simulation results show that the sgqf achieves higher accuracy than the extended kalman filter ekf the ukf and the cubature kalman filter ckf in addition the sgqf is computationally much more efficient than the multi dimensional gauss hermite quadrature filter ghqf with the same performance

a gaussian approximation recursive filter for nonlinear systems with correlated noises this paper proposes a gaussian approximation recursive filter gasf for a class of nonlinear stochastic systems in the case that the process and measurement noises are correlated with each other through presenting the gaussian approximations about the two step state posterior predictive probability density function pdf and the one step measurement posterior predictive pdf a general gasf framework in the minimum mean square error mmse sense is derived based on the framework the gasf implementation is transformed into computing the multi dimensional integrals which is solved by developing a new divided difference filter ddf with correlated noises simulation results demonstrate the superior performance of the proposed ddf as compared to the standard ddf the existing ukf and ekf with correlated noises

recursive estimators of signals from measurements with stochastic delays using covariance information least squares linear one stage prediction filtering and fixed point smoothing algorithms for signal estimation using measurements with stochastic delays contaminated by additive white noise are derived the delay is considered to be random and modelled by a binary white noise with values zero or one these values indicate that the measurements arrive in time or they are delayed by one sampling time recursive estimation algorithms are obtained without requiring the state space model generating the signal but just using covariance information about the signal and the additive noise in the observations as well as the delay probabilities

development of fuzzy and control charts using α cuts statistical process control spc is an approach that uses statistical techniques to monitor the process shewhart introduced the control charts that are one of the most important techniques of quality control to detect if assignable causes exist the widely used control charts are and these are called traditional variable control charts in the traditional variable control charts center line upper control limit and lower control limit are represented by numeric values a process is either in control or out of control depending on numeric observation values for many problems control limits could not be so precise uncertainty comes from the measurement system including operators and gauges and environmental conditions in this context fuzzy set theory is a useful tool to handle this uncertainty numeric control limits can be transformed to fuzzy control limits by using membership functions if a sample mean is too close to the control limits and the used measurement system is not so sensitive the decision may be faulty fuzzy control limits provide a more accurate and flexible evaluation this study constructs the fuzzy and control charts with a cuts an application is presented for fuzzy control charts by using fuzzy and control charts the flexibility of traditional control limits is increased

theoretical investigation of synchronous totally asymmetric exclusion processes on lattices with multiple input single output junctions in this paper we investigate the dynamics of synchronous totally asymmetric exclusion processes on lattices with a multiple input single output miso junction which consists of m subchains for the input and one main chain for the output a miso junction is a type of complex geometry that is relevant to many biological processes as well as vehicular and pedestrian traffic flow a mean field approach is developed to deal with the junction that connects the subchains and the main chain theoretical results for stationary particle currents density profiles and a phase diagram have been obtained it is found that the phase boundary moves toward the left in the phase diagram with an increase of the number of subchains the nonequilibrium stationary states stationary state phases and phase boundaries are determined by the boundary conditions of the system as well as by the number of subchains the density profiles obtained from computer simulations show very good agreement with our theoretical analysis

optimal h filtering for singular markovian jump systems abstract this paper considers h filtering for continuous time singular markovian jump systems smjss while the existing researches in the literature suggested only sufficient conditions in terms of strict or non strict linear matrix inequalities lmis for sub optimal h filtering this paper successfully derives a necessary and sufficient condition in terms of strict lmis for optimal h filtering first the necessary and sufficient condition that guarantees the stochastic admissibility of the filtering error system is obtained in terms of matrix inequalities to reformulate it into strict lmis the congruence transformation by specially designed matrices is used two numerical examples show the validity of proposed h filtering

general equivalence between two kinds of noise correlation filters a recent comment chang 2014 theoretically demonstrated that for the linear system with the correlated process and measurement noises the gasf framework proposed in the paper wang et al 2012 was equivalent to the conventional de coupling filtering framework in this note we would further show that such equivalence between the two frameworks can be justified in a more general way even for the nonlinear system

brief paper h filtering for nonlinear discrete time stochastic systems with randomly varying sensor delays this paper is concerned with the h filtering problem for a general class of nonlinear discrete time stochastic systems with randomly varying sensor delays where the delayed sensor measurement is governed by a stochastic variable satisfying the bernoulli random binary distribution law in terms of the hamilton jacobi isaacs inequalities preliminary results are first obtained that ensure the addressed system to possess an l 2 gain less than a given positive scalar c next a sufficient condition is established under which the filtering process is asymptotically stable in the mean square and the filtering error satisfies the h performance constraint for all nonzero exogenous disturbances under the zero initial condition such a sufficient condition is then decoupled into four inequalities for the purpose of easy implementation furthermore it is shown that our main results can be readily specialized to the case of linear stochastic systems finally a numerical simulation example is used to demonstrate the effectiveness of the results derived

unscented kalman filter aspects and adaptive setting of scaling parameter this technical note deals with the unscented kalman filter for state estimation of nonlinear stochastic dynamic systems with a special focus on the scaling parameter of the filter its standard choice is analyzed and its impact on the estimation quality is discussed on the basis of the analysis a novel method for adaptive setting of the parameter in the unscented kalman filter is proposed the results are illustrated in a numerical example

a numerical integration perspective on gaussian filters this paper proposes a numerical integration perspective on the gaussian filters a gaussian filter is approximation of the bayesian inference with the gaussian posterior probability density assumption being valid there exists a variation of gaussian filters in the literature that derived themselves from very different backgrounds from the numerical integration viewpoint various versions of gaussian filters are only distinctive from each other in their specific treatments of approximating the multiple statistical integrations a common base is provided for the first time to analyze and compare gaussian filters with respect to accuracy efficiency and stability factor this study is expected to facilitate the selection of appropriate gaussian filters in practice and to help design more efficient filters by employing better numerical integration methods

spontaneous symmetry breaking in two channel asymmetric exclusion processes with narrow entrances multi particle non equilibrium dynamics in two channel asymmetric exclusion processes with narrow entrances is investigated theoretically particles move on two parallel lattices in opposite directions without changing them while the channels are coupled only at the boundaries a particle cannot enter the corresponding lane if the exit site of the other lane is occupied stationary phase diagrams particle currents and densities are calculated in a mean field approximation it is shown that there are four stationary phases in the system with two of them exhibiting spontaneous symmetry breaking phenomena extensive monte carlo computer simulations confirm qualitatively our predictions although the phase boundaries and stationary properties deviate from the mean field results computer simulations indicate that several dynamic and phase properties of the system have a strong size dependence and one of the stationary phases predicted by the mean field theory probably disappears in the thermodynamic limit

unscented kalman filter with advanced adaptation of scaling parameter the paper deals with state estimation of the nonlinear stochastic systems by means of the unscented kalman filter with a focus on specification of the points their position is influenced by two design parameters the scaling parameter determining the spread of the points and a covariance matrix decomposition determining rotation of the points in this paper a choice of the scaling parameter is analyzed it is shown that considering other values than the standard choice may lead to increased quality of the estimate especially if the scaling parameter is adapted several different criteria for the adaptation are proposed and techniques to reduce computational costs of the adaptation are developed the proposed algorithm of the unscented kalman filter with advanced adaptation of the scaling parameter is illustrated in a numerical example

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

multiline queues with spectral parameters using the description of multiline queues as functions on words we introduce the notion of a spectral weight of a word by defining a new weighting on multiline queues we show that the spectral weight of a word is invariant under a natural action of the symmetric group giving a proof of the commutativity conjecture of arita ayyer mallick and prolhac we give a determinant formula for the spectral weight of a word which gives a proof of a conjecture of the first author and linusson

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

sonar based robot navigation using non linear robust discrete time observers in this paper we address the sonar based nagivation of mobile robots the extended kalman filtering ekf technique is considered but from a deterministic not a stochastic point of view for this problem we present results on the robustness of the non linear discrete time observation scheme this work is strongly based on our previous paper on continuous time ekf here we provide the discrete time counterpart of these results the original feature of our approach is that the region of convergence question is posed in its complete non linear framework that is considering the dynamics not only of the estimation error but also of the covariance matrix p in this way the approach followed makes the treatment less conservative and improves the convergence analysis in discrete time new problems and difficulties appeared for proving convergence the jacobians of f and h a k and c k respectively are evaluated at different trajectories and the exponential weighting factor has a multiplicative effec

synchronization of kinks in the two lane totally asymmetric simple exclusion process with open boundary conditions we study the motion of kinks in a two lane model of the totally asymmetric simple exclusion process with open boundaries we analytically study the motion of the kinks by a decoupling approximation in terms of the decoupling approximation we find that the positions of the kinks become synchronized though the difference in the number of particles between lanes remains non zero when the rate of lane change is asymmetric the validity of this result is confirmed for small asymmetric cases through the monte carlo simulation

brief paper derivative free estimation methods new results and performance analysis the derivative free nonlinear estimation methods exploiting the stirling s interpolation and the unscented transformation for discrete time nonlinear stochastic systems are treated the divided difference and unscented filters smoothers and predictors based on the methods are introduced in the unified framework the new relations among the first order stirling s interpolation the second order stirling s interpolation and the unscented transformation are derived and their impact on the covariance matrices of the state estimates of the corresponding filters is analysed the theoretical results are illustrated and used for the explanation of the unexpected behaviour of the sigma point gaussian sum filters given as a mixture of the derivative free filters

local inhomogeneity in asymmetric simple exclusion processes with extended objects totally asymmetric simple exclusion processes tasep with particles which occupy more than one lattice site and with a local inhomogeneity far away from the boundaries are investigated these non equilibrium processes are relevant for the understanding of many biological and chemical phenomena the steady state phase diagrams currents and bulk densities are calculated using a simple approximate theory and extensive monte carlo computer simulations it is found that the phase diagram for tasep with a local inhomogeneity is qualitatively similar to homogeneous models although the phase boundaries are significantly shifted the complex dynamics is discussed in terms of domain wall theory for driven lattice systems

accurate numerical implementation of the continuous discrete extended kalman filter this paper addresses an accurate and effective implementation of the continuous discrete extended kalman filtering method the technique under discussion is grounded in numerical solution of the moment differential equations to predict the state mean of the stochastic dynamical system and the corresponding error covariance matrix here we apply an efficient embedded runge kutta pair possessing superior stability and many other attractive features including automatic global error control in order to improve performance of the complex computational procedure consisting of the extended kalman filter and the underlying adaptive ode solver thus we introduce a new continuous discrete adaptive extended kalman filter and show its advantage over the standard variant on two test examples in practice this technique allows for much longer sampling intervals without any loss of accuracy and that improves the applied potential of the extended kalman filtering method significantly

on a nonlinear kalman filter with simplified divided difference approximation abstract we present a new ensemble based approach that handles nonlinearity based on a simplified divided difference approximation through stirling s interpolation formula which is hence called the simplified divided difference filter sddf the sddf uses stirling s interpolation formula to evaluate the statistics of the background ensemble during the prediction step while at the filtering step the sddf employs the formulae in an ensemble square root filter ensrf to update the background to the analysis in this sense the sddf is a hybrid of stirling s interpolation formula and the ensrf method while the computational cost of the sddf is less than that of the ensrf numerical comparison between the sddf and the ensrf with the ensemble transform kalman filter etkf as the representative is conducted the experiment results suggest that the sddf outperforms the etkf with a relatively large ensemble size and thus is a good candidate for data assimilation in systems with moderate dimensions

nonlinear estimation using correlation information the approximate karhunen loegraveve kl expansions are used as a tool for systems identification providing an approximate state model for the signal of interest the identified model can then be used to derive sequential algorithms for the nonlinear estimation problem by using standard estimation techniques the proposed solution is specially indicated in those situations where a state equation is not at hand and the only information available is the correlation matrix of the signal

performance analysis of the kalman filter with mismatched noise covariances the kalman filter is a powerful state estimator and has been successfully applied in many fields to guarantee the optimality of the kalman filter the noise covariances need to be exactly known however this is not necessarily true in many practical applications usually they are either completely unknown or at most partially known in this technical note we study performance of the kalman filter with mismatched process and measurement noise covariances for this purpose three mean squared errors mses are used namely the ideal mse imse the filter calculated mse fmse and the true mse tmse the main contribution of this work is that the relationships between the three mses are disclosed from two points of views the first view is about their ordering and the second view is about the relative closeness from the fmse and tmse to the imse using the first view it is found that for the case with positive definite deviation from the truth the fmse is the worst and the imse is the best and for the case with negative definite deviation the tmse is the worst and the best is the fmse using the second view it is found that the tmse is relatively closer to the imse than the fmse if the deviation is larger than certain threshold and the tmse will be farther away otherwise numerical examples further verify these conclusions

various ways to compute the continuous discrete extended kalman filter the extended kalman filter ekf is a very popular tool dealing with state estimation its continuous discrete version cd ekf estimates the state trajectory of continuous time nonlinear models whose internal state is described by a stochastic differential equation and which is observed through a noisy nonlinear form of the sampled state the prediction step of the cd ekf leads to solve a differential equation that cannot be generally solved in a closed form this technical note presents an overview of the numerical methods including recent works usually implemented to approximate this filter comparisons of theses methods on two different nonlinear models are finally presented the first one is the van der pol oscillator which is widely used as a benchmark the second one is a neuronal population model this more original model is used to simulate eeg activity of the cortex experiments showed better stability properties of implementations for which the positivity of the prediction matrix is guaranteed

nonlinear estimation by lmmse based estimation with optimized uncorrelated augmentation for nonlinear estimation the linear minimum mean square error lmmse estimator using the measurement augmented by its nonlinear conversion can achieve better performance than using the original measurement the main reason is that the original measurement cannot be fully utilized by the lmmse estimator in a linear way to effectively extract additional measurement information which can be further utilized by a linear estimator a nonlinear approach named uncorrelated conversion uc is proposed the uncorrelated conversions of the measurement are uncorrelated with the measurement itself two specific approaches to generating ucs are proposed based on a gaussian assumption and a reference distribution respectively then a uc based filter ucf is proposed based on lmmse estimation using the measurement augmented by its uncorrelated conversions to minimize the mean square error of the overall estimate an optimized ucf oucf with an analytical form is proposed by optimizing the reference distribution based ucs in the ucf measurement augmentation can be continued using the proposed nonlinear uc approach and all augmenting terms are uncorrelated under certain conditions thus the performance of the ucf and the oucf may be continually improved simulation results demonstrate the effectiveness of the proposed estimator compared with some popular nonlinear estimators

fuzzy hypotheses testing in the framework of fuzzy logic abstract testing hypotheses about the probability distribution underlying the available empirical data is one of the fundamental data analytic tasks in any application domain basically it consists in checking the null hypothesis that the probability distribution a priori assumed to belong to a certain set of distributions actually belongs to some its narrow subset which must be precisely delimited in advance however sometimes there are not enough clues for such a precise delimitation especially if the purpose of the data analysis is explorative a situation encountered increasingly often due to the growing amount of routinely collected data and the increasing importance of data mining that is why generalizations of statistical hypotheses testing to vague hypotheses have been investigated for more than a decade so far based on the most straightforward approach to replace the set defining the null hypothesis by a fuzzy set in this paper a principally different approach is presented motivated by the observational logic and its success in automated knowledge discovery its key idea is to view statistical testing of a fuzzy hypothesis as the application of an appropriate generalized quantifier of a fuzzy predicate calculus to predicates describing the data the theoretical principles of the approach are explained and its first implementations are briefly sketched

sliding mode estimators for a class of non linear systems affected by bounded disturbances the problem of state estimation for a class of non linear systems with lipschitz non linearities is addressed using sliding mode estimators stability conditions have been found to guarantee asymptotic convergence to zero of the estimation error in the absence of noise and non divergence if the state perturbations and measurement noise are bounded a method is proposed to find a suitable solution to the algebraic riccati equation on which the design of the estimator is based the performance of the resulting sliding mode filter minimizes an upper bound on the asymptotic estimation error based on such an approach a sliding mode estimator may be designed so as to outperform the extended kalman filter in practical applications with models affected by uncertainty and strong possibly unknown non linearities as shown by means of simulations

a finite difference method for linearization in nonlinear estimation algorithms abstract linearizations of nonlinear functions that are based on jacobian matrices often cannot be applied in practical applications of nonlinear estimation techniques an alternative linearization method is presented in this paper the method assumes that covariance matrices are determined on a square root factored form a factorization of the output covariance from a nonlinear vector function is directly determined by perturbing the nonlinear function with the columns of the factored input covariance without explicitly calculating the linearization and with no differentiations involved the output covariance is more accurate than that obtained with the ordinary jacobian linearization method it also has an advantage that jacobian matrices do not have to be derived symbolically

nonlinear estimation with state dependent gaussian observation noise we consider the problem of estimating the state of a system when measurement noise is a function of the system s state we propose generalizations of the extended kalman filter and the iterated extended kalman filter that can be utilized when the state estimate distribution is approximately gaussian the state estimate is computed by an iterative root searching method that maximizes a maximum likelihood function the new filter allows for the consistent treatment of a class of control problem involving nonlinear estimation from measurements with state dependent noise the effectiveness of the estimation algorithm is illustrated for a control problem with a mobile bearing only sensor

algorithmic survey of parametric value function approximation reinforcement learning rl is a machine learning answer to the optimal control problem it consists of learning an optimal control policy through interactions with the system to be controlled the quality of this policy being quantified by the so called value function a recurrent subtopic of rl concerns computing an approximation of this value function when the system is too large for an exact representation this survey reviews state of the art methods for parametric value function approximation by grouping them into three main categories bootstrapping residual and projected fixed point approaches related algorithms are derived by considering one of the associated cost functions and a specific minimization method generally a stochastic gradient descent or a recursive least squares 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

the robustness of spontaneous symmetry breaking in a bridge model a simple two species asymmetric exclusion model in one dimension with bulk and boundary exchanges of particles is investigated for the existence of spontaneous symmetry breaking the model is a generalization of the bridge model for which earlier studies have confirmed the existence of symmetry broken phases and the motivation here is to check the robustness of the observed symmetry breaking with respect to additional dynamical moves in particular the boundary exchange of the two species of particle our analysis based on general considerations mean field approximation and numerical simulations shows that the symmetry breaking in the bridge model is sustained for a range of values of the boundary exchange rate moreover the mechanism through which symmetry is broken is similar to that in the bridge model our analysis allows us to plot the complete phase diagram of the model demarcating regions of symmetric and symmetry broken phases

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

dynamic modeling of neuronal responses in fmri using cubature kalman filtering this paper presents a new approach to inverting fitting models of coupled dynamical systems based on state of the art cubature kalman filtering crucially this inversion furnishes posterior estimates of both the hidden states and parameters of a system including any unknown exogenous input because the underlying generative model is formulated in continuous time with a discrete observation process it can be applied to a wide variety of models specified with either ordinary or stochastic differential equations these are an important class of models that are particularly appropriate for biological time series where the underlying system is specified in terms of kinetics or dynamics i e dynamic causal models we provide comparative evaluations with generalized bayesian filtering dynamic expectation maximization and demonstrate marked improvements in accuracy and computational efficiency we compare the schemes using a series of difficult nonlinear toy examples and conclude with a special focus on hemodynamic models of evoked brain responses in fmri our scheme promises to provide a significant advance in characterizing the functional architectures of distributed neuronal systems even in the absence of known exogenous experimental input e g resting state fmri studies and spontaneous fluctuations in electrophysiological studies importantly unlike current bayesian filters e g dem our scheme provides estimates of time varying parameters which we will exploit in future work on the adaptation and enabling of connections in the brain

statistical tests for fuzzy data abstract in this paper we investigate the impacts of vague and imprecise data on the statistical task of hypotheses testing test results are evaluated with respect to this ambiguity the issue of how to aggregate fuzzy data to a fuzzy sample vector is discussed and different eventualities are considered their consequences on the test results are compared the domain of the used test statistics is extended to fuzzy sample vectors by the means provided in the first part of this paper different methods for the defuzzification of the obtained fuzzy test results are discussed and the fuzzy nature of the classical verification task for statistical hypotheses is studied in this context a way of how to overcome the general insufficiency of statistical tests of being conclusive only in one direction is proposed by admitting fuzzy results

relations between sparse grid quadrature rule and spherical radial cubature rule in nonlinear gaussian estimation the recently emerging cubature kalman filter and the sparse grid quadrature filter approximate the numerical integrations for the mean and covariance in gaussian filters using the spherical radial cubature rule and the sparse grid quadrature rule respectively this technical note reveals that 1 spherical rules can be obtained by the projection of sparse grid quadrature rules 2 the third and some of the fifth degree spherical radial cubature rules can be directly constructed from sparse grid quadrature rules

nonlinear gaussian smoothers with colored measurement noise this paper is concerned with the gaussian approximation ga smoothing estimation for the nonlinear system with the colored measurement noise modeled as an autoregressive process firstly based on measurement differencing scheme designing the ga smoothers with the colored measurement noise is transformed into deriving the ga ones with delayed state secondly the novel fixed interval fixed point and fixed lag ga smoothers are proposed via the recursive operation of analytical computation and nonlinear integrals as the general and unifying frameworks they are applicable for both linear and nonlinear systems by setting the noise correlation parameter as zero they can automatically reduce to the standard ga smoothers with uncorrelated white noises many implementations of the ga frameworks can be developed through utilizing different numerical technologies for computing such nonlinear integrals e g the cubature rule based cubature kalman smoothers ckss with the colored measurement noise finally the superior performance in estimation accuracy and computation efficiency of the proposed smoothing methods is demonstrated with a multi sensor target tracking example

a novel a priori state computation strategy for the unscented kalman filter to improve computational efficiency a priori state vector and error covariance computation for the unscented kalman filter ukf is described the original ukf propagates multiple sigma points to compute the a priori mean state vector and the error covariance resulting in a higher computational time compared to the extended kalman filter ekf in the proposed method the posterior mean state vector is propagated and then the sigma points at the current time step are calculated using the first order taylor series approximation this reduces the computation time significantly as demonstrated using two example applications which show improvements of 90 5 and 92 6 this method shows the estimated state vector and the error covariance are accurate to the first order taylor series terms a second method using richardson extrapolation improves prediction accuracy to the second order taylor series terms this is implemented on the two examples improving efficiency by 85 5 and 86 8

moment estimation using a marginalized transform we present a method for estimating mean and covariance of a transformed gaussian random variable the method is based on evaluations of the transforming function and resembles the unscented transform and gauss hermite integration in that respect the information provided by the evaluations is used in a bayesian framework to form a posterior description of the parameters in a model of the transforming function estimates are then derived by marginalizing these parameters from the analytical expression of the mean and covariance an estimation algorithm based on the assumption that the transforming function can be described using hermite polynomials is presented and applied to the non linear filtering problem the resulting marginalized transform mt estimator is compared to the cubature rule the unscented transform and the divided difference estimator the evaluations show that the presented method performs better than these methods more specifically in estimating the covariance matrix contrary to the unscented transform the resulting approximation of the covariance matrix is guaranteed to be positive semidefinite

advanced point mass method for nonlinear state estimation state estimation of discrete time nonlinear non gaussian stochastic systems by point mass approach which is based on discretization of state space by a regular grid and numerical solution of bayesian recursive relations is treated the stress is laid to grid design which is crucial for estimator quality and significantly affects the computational demands of the estimator boundary based grid design thrifty convolution and multigrid design with grid splitting and merging are proposed the main advantages of these techniques are nonnegligible support delimitation time saving computation of convolution and effective processing of multimodal probability density functions respectively the techniques are involved into the basic point mass approach and a new general purpose more sophisticated point mass algorithm is designed computational demands and estimation quality of the designed algorithm are presented and compared with the particle filter in a numerical example

comment on a new method for the nonlinear transformation of means and covariances in filters and estimators with authors reply the above paper julier et al ieee trans automat contr vol 45 pp 477 82 2000 generalizes the kalman filter to nonlinear systems by transforming approximations of the probability distributions through the nonlinear process and measurement functions this comment derives exactly the same estimator by linearizing the process and measurement functions by a statistical linear regression through some regression points in contrast with the extended kalman filter which uses an analytic linearization in one point this insight allows one 1 to understand predict the performance of the estimator for specific applications and 2 to make adaptations to the estimator i e the choice of the regression points and their weights in those cases where the original formulation does not assure good results in reply the authors state that the commenters conclusion is unnecessarily narrow interpretation of results

h filtering for singular markovian jump systems with partly unknown transition rates abstract this paper suggests h filtering for singular markovian jump systems smjss with partly unknown transition rates while the existing researches in the literature have derived only the sufficient conditions this paper successfully demonstrates the necessary and sufficient condition for the existence of h filtering for smjss with partly unknown transition rates first a new bounded real lemma for smjs is derived in terms next the matrix inequalities which come from the bounded real lemma for the filtering error system with partly unknown transition rates are reformulated into the strict lmis two numerical examples are presented to show the effectiveness of the proposed result

asymmetric exclusion processes on m input n output junctions with parallel update abstract in this paper we investigate totally asymmetric exclusion processes taseps on lattices with an m input n output junction in parallel update a general theoretical solution for traffic dynamics of taseps with a junction is developed more interestingly m input n output junctions can be classified by a parameter m n the junctions with the same exhibit the same dynamic properties e g phase diagrams stationary currents and density profiles when the number of m and or n changes the low density and high density regions can be measured qualitatively and quantitatively the phase diagram is obtained from a simple mean field approximation and supported by computer simulations stationary current and density profiles are calculated which show good agreement with computer simulations

measurement random latency probability identification this technical note focuses on efficiently identifying the unknown or time varying random latency probability rlp of the measurements in the networked multi sensor system by resorting to expectation maximization em framework firstly a novel scheme is proposed for equivalently decomposing the complete data log likelihood function into a summation form parameterized by rlp secondly the rapid computation of the expectation in e step is achieved by skillfully introducing jessen s inequality to avoid the state augmentation of the traditional method thirdly the analytical identification result of rlp is obtained in m step by constructing lagrange operator to maximize the expectation with the parameter constraint naturally such analytical result is so simple that it can be quickly carried out which is demonstrated by quantitative computation complexity analysis finally an example motivated by the maneuvering target tracking application is presented to show the superiority of the new method

unscented rauch tung striebel smoother this note considers the application of the unscented transform to optimal smoothing of nonlinear state space models in this note a new rauch tung striebel type form of the fixed interval unscented kalman smoother is derived the new smoother differs from the previously proposed two filter formulation based unscented kalman smoother in the sense that it is not based on running two independent filters forward and backward in time instead a separate backward smoothing pass is used which recursively computes corrections to the forward filtering result the smoother equations are derived as approximations to the formal bayesian optimal smoothing equations the performance of the new smoother is demonstrated with a simulation

approximating sample state vectors using the espt for computationally efficient particle filtering the extrapolated single propagation technique espt based particle filter is proposed instead of propagating all the sample state vectors using multiple numerical integrations only one sample state vector is propagated in the espt other sample states are computed at the next epoch with an accuracy of the second order taylor series expansion terms it is theoretically shown that the particle filter algorithm which uses the espt for state propagation requires up to text 90 reduced processing time than the conventional particle filter using a benchmark non linear estimation problem the performance of the modified algorithm is compared with the particle filter the experimental results confirm the theoretical analysis and demonstrate the effectiveness of the proposed method for non linear state estimation the proposed algorithm significantly reduces the processing time of the particle filter with a minor degradation in the estimation accuracy

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

nonparametric rank based statistics and significance tests for fuzzy data nonparametric rank based statistics depending only on linear orderings of the observations are extended to fuzzy data the approach relies on the definition of a fuzzy partial order based on the necessity index of strict dominance between fuzzy numbers which is shown to contain in a well defined sense all the ordinal information present in the original data a concept of fuzzy set of linear extensions of a fuzzy partial order is introduced allowing the approximate computation of fuzzy statistics alpha cutwise using a markov chain monte carlo simulation approach the usual notions underlying significance tests are also extended leading to the concepts of fuzzy p value and graded rejection of the null hypothesis quantified by a degree of possibility and a degree of necessity at a given significance level this general approach is demonstrated in two special cases kendall s rank correlation coefficient and wilcoxon s two sample rank sum statistic

new developments in state estimation for nonlinear systems based on an interpolation formula accurate state estimators for nonlinear systems can be derived the estimators do not require derivative information which makes them simple to implement

a derivative free implementation of the extended kalman filter a nonlinear estimation paradigm is developed to estimate the mean and covariance of a time evolving state distribution the approach represents uncertainty by an ensemble set of state vectors rather than by the traditional mean and covariance measures avoiding the need for the calculation of matrix partial derivatives jacobian matrices the paradigm is shown to be equivalent to the extended kalman filter in a limiting case implementation of the new filtering approach is illustrated with a simple example and a step by step description the paradigm is not significantly more computationally intensive than traditional filters and proves ideal for the rapid implementation of complex nonlinear system and observation models

cubature kalman filters in this paper we present a new nonlinear filter for high dimensional state estimation which we have named the cubature kalman filter ckf the heart of the ckf is a spherical radial cubature rule which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear bayesian filter specifically we derive a third degree spherical radial cubature rule that provides a set of cubature points scaling linearly with the state vector dimension the ckf may therefore provide a systematic solution for high dimensional nonlinear filtering problems the paper also includes the derivation of a square root version of the ckf for improved numerical stability the ckf is tested experimentally in two nonlinear state estimation problems in the first problem the proposed cubature rule is used to compute the second order statistics of a nonlinearly transformed gaussian random variable the second problem addresses the use of the ckf for tracking a maneuvering aircraft the results of both experiments demonstrate the improved performance of the ckf over conventional nonlinear filters

totally asymmetric exclusion process with extended objects a model for protein synthesis the process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent covering more than one lattice site we expand the well studied totally asymmetric exclusion process in which particles typically cover a single lattice site to include cases with extended objects exact solutions can be determined for a uniform closed system we analyze the uniform open system through two approaches first a continuum limit produces a modified diffusion equation for particle density profiles second an extremal principle based on domain wall theory accurately predicts the phase diagram and currents in each phase finally we briefly consider approximate approaches to a nonuniform open system with quenched disorder in the particle hopping rates and compare these approaches with monte carlo simulations

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

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

particle filters for partially observed boolean dynamical systems abstract partially observed boolean dynamical systems pobds are a general class of nonlinear models with application in estimation and control of boolean processes based on noisy and incomplete measurements the optimal minimum mean square error mmse algorithms for pobds state estimation namely the boolean kalman filter bkf and boolean kalman smoother bks are intractable in the case of large systems due to computational and memory requirements to address this we introduce approximate mmse filtering and smoothing algorithms based on the auxiliary particle filter apf method which are called apf bkf and apf bks respectively for joint state and parameter estimation the apf bkf is used jointly with maximum likelihood ml methods for simultaneous state and parameter estimation in pobds models in the case the unknown parameters are discrete the proposed ml adaptive filter consists of multiple apf bkfs running in parallel in a manner reminiscent of the multiple model adaptive estimation mmae method in classical linear filtering theory in the presence of continuous parameters the proposed ml adaptive filter is based on an efficient particle based expectation maximization em algorithm for the pobds model which is based on a modified forward filter backward simulation ffbsi in combination with the apf bks the performance of the proposed particle based adaptive filters is assessed through numerical experiments using a pobds model of the well known cell cycle gene regulatory network observed through noisy rna seq time series data

a strong tracking extended kalman observer for nonlinear discrete time systems the authors show how the extended kalman filter used as an observer for nonlinear discrete time systems or extended kalman observer eko becomes a useful state estimator when the arbitrary matrices namely r sub k and q sub k are adequately chosen as a first step we use the linearization technique given by boutayed et al 1997 which consists of introducing unknown diagonal matrices to take the approximation errors into account it is shown that the decreasing lyapunov function condition leads to a linear matrix inequality lmi problem which points out the connection between a good convergence behavior of the eko and the instrumental matrices r sub k and q sub k in order to satisfy the obtained lmi a particular design of q sub k is given high performances of the proposed technique are shown through numerical examples under the worst conditions

weakly coupled antiparallel totally asymmetric simple exclusion processes we study a system composed of two parallel totally asymmetric simple exclusion processes with open boundaries where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely proportional to the length of the system stationary density profiles are determined and the phase diagram of the model is constructed in the hydrodynamic limit by solving the differential equations describing the steady state of the system analytically for vanishing total current and numerically for nonzero total current the system possesses phases with a localized shock in the density profile in one of the lanes similarly to exclusion processes endowed with nonconserving kinetics in the bulk besides the system undergoes a discontinuous phase transition where coherently moving delocalized shocks emerge in both lanes and the fluctuation of the global density is described by an unbiased random walk this phenomenon is analogous to the phase coexistence observed at the coexistence line of the totally asymmetric simple exclusion process however as a consequence of the interaction between lanes the density profiles are deformed and in the case of asymmetric lane change the motion of the shocks is confined to a limited domain

a systematization of the unscented kalman filter theory in this paper we propose a systematization of the discrete time unscented kalman filter ukf theory we gather all available ukf variants in the literature present corrections to theoretical inconsistencies and provide a tool for the construction of new ukf s in a consistent way this systematization is done mainly by revisiting the concepts of sigma representation unscented transformation ut scaled unscented transformation sut ukf and square root unscented kalman filter srukf inconsistencies are related to 1 matching the order of the transformed covariance and cross covariance matrices of both the ut and the sut 2 multiple ukf definitions 3 issue with some reduced sets of sigma points described in the literature 4 the conservativeness of the sut 5 the scaling effect of the sut on both its transformed covariance and cross covariance matrices and 6 possibly ill conditioned results in srukf s with the proposed systematization the symmetric sets of sigma points in the literature are formally justified and we are able to provide new consistent variations for ukf s such as the scaled srukf s and the ukf s composed by the minimum number of sigma points furthermore our proposed srukf has improved computational properties when compared to state of the art methods

stochastic integration filter the technical note deals with state estimation of nonlinear stochastic dynamic systems traditional filters providing local estimates of the state such as the extended kalman filter unscented kalman filter or the cubature kalman filter are based on computationally efficient but approximate integral evaluations on the other hand the monte carlo based kalman filter takes an advantage of asymptotically exact integral evaluations but at the expense of substantial computational demands the aim of the technical note is to propose a new local filter that utilises stochastic integration methods providing the asymptotically exact integral evaluation with computational complexity similar to the traditional filters the technical note will demonstrate that the unscented and cubature kalman filters are special cases of the proposed stochastic integration filter the proposed filter is illustrated by a numerical example

brief paper adaptive divided difference filtering for simultaneous state and parameter estimation a novel adaptive version of the divided difference filter ddf applicable to non linear systems with a linear output equation is presented in this work in order to make the filter robust to modeling errors upper bounds on the state covariance matrix are derived the parameters of this upper bound are then estimated using a combination of offline tuning and online optimization with a linear matrix inequality lmi constraint which ensures that the predicted output error covariance is larger than the observed output error covariance the resulting sub optimal high gain filter is applied to the problem of joint state and parameter estimation simulation results demonstrate the superior performance of the proposed filter as compared to the standard ddf

the linearization method based on the equivalence of dissipated energies for nonlinearly damped structural systems even though the nonlinear damping characteristics inherently pertain to most structural systems many useful dynamic models are still linear as a consequence a method that is able to equivalently linearize eql the nonlinear damping so that it can be directly applied in these existing linear models is essential in the present paper a novel eql method for nonlinearly damped and single degree of freedom systems is developed the method is theoretically derived by modulating the steady state responses of the original nonlinear system during the linearization the new eql method requires the dissipated energy of the target linear system to equal that of the original nonlinear one in effect this criterion is equivalent to forcing both the phase angles and amplitudes of the two systems to be equal or at least to within a small allowable error furthermore the present paper proves that it is possible for the dissipative energy to be expressed in terms of the fourier coefficients of the modulated signal thus the equivalent viscous damping ratio can be computed from these fourier coefficients this new eql method is numerically tested using examples of bi linear damping models and subjected to experimental measurements both the simulation results and the experimental data verify the validity of the method they also prove that the current method gives the equivalent viscous damping with good accuracy in addition a quality index that signifies how well the eql system reaches is appropriately added

correspondence comments on performance evaluation of ukf based nonlinear filtering this note points out that the main result of the paper xiong k zhang h y chan c w 2006 performance evaluation of ukf based nonlinear filtering automatica 42 2 261 270 can be extended to a class of so called gaussian filters it justifies a practical countermeasure of the divergence i e adding small quantities to the noise covariance matrix to stabilize the filter

two channel totally asymmetric simple exclusion processes totally asymmetric simple exclusion processes consisting of two coupled parallel lattice chains with particles interacting with hard core exclusion and moving along the channels and between them are considered in the limit of strong coupling between the channels the particle currents density profiles and a phase diagram are calculated exactly by mapping the system into an effective one channel totally asymmetric exclusion model for intermediate couplings a simple approximate theory that describes the particle dynamics in vertical clusters of two corresponding parallel sites exactly and neglects the correlations between different vertical clusters is developed it is found that similarly to the case of one channel totally asymmetric simple exclusion processes there are three stationary state phases although the phase boundaries and stationary properties strongly depend on inter channel coupling extensive computer monte carlo simulations fully support the theoretical predictions

spontaneous symmetry breaking in totally asymmetric simple exclusion processes on two intersected lattices this paper studies totally asymmetric simple exclusion processes taseps on two intersected lattices three different models are introduced model a for molecular motor motion and models b and c for vehicle traffic extensive monte carlo simulations are carried out phase diagrams and density profiles of the three models are investigated it is shown that phase diagrams of all the three models are divided into three regions the phase boundaries are calculated by an approximate mean field approach it is found that the analytic solutions are in good agreement with the results of monte carlo simulations for models b and c spontaneous symmetry breaking is identified the particle density histograms and qualitative domain wall explanation are presented to describe the spontaneous symmetry breaking phenomenon finally in model c the effect of lane changing probability p on spontaneous symmetry breaking is investigated a threshold of p for the occurrence of symmetry breaking is obtained