constants and label equivalence a decision procedure for reflexive regular splicing languages abstract a structural characterization of reflexive splicing languages has been recently given in p bonizzoni c de felice r zizza the structure of reflexive regular splicing languages via schutzenberger constants theoretical computer science 334 2005 71 98 and p bonizzoni g mauri regular splicing languages and subclasses theoretical computer science 340 2005 349 363 showing surprising connections between long standing notions in formal language theory the syntactic monoid and schutzenberger constant and the splicing operation in this paper we provide a procedure to decide whether a regular language is a reflexive splicing language based on the above mentioned characterization that is given in terms of a finite set of constants for the language the procedure relies on the notion of label equivalence that induces a finite refinement of the syntactic monoid of a regular language l a finite set of representatives for label equivalent classes of constant words in l is defined and it is proved that such a finite set provides the splice sites of splicing rules generating language l

non linear observer based on the euler discretization in this paper we present an estimator based on the euler discretization first we show that the proposed estimator is an exponential observer in the case when the error between trajectories of continuous time and its associated euler discretized system can be neglected otherwise we show that the error of estimation is exponentially attracted by some neighbourhood of the origin which depends only on the sampling time finally numerical simulations using a bioreactor model are given in order to highlight the performance of the proposed estimator

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

remarks on linearization of discrete time autonomous systems and nonlinear observer design abstract this paper presents necessary and sufficient conditions under which a discrete time autonomous system with outputs is locally state equivalent to an observable linear system or a system in the nonlinear observer form krener and isidori 1983 in particular an open problem raised in lee and nam 1991 namely the observer linearization problem is solved for a nonlinear system which may not be invertible i e the mapping f may not be a local diffeomorphism as a consequence the nonlinear observer design problem is solved by means of exact linearization techniques

on two weakers forms of continuous order homomorphisms the aim of this paper is to find further connections between two different current researches on fuzzy topology the one based on the concepts of neighborhood filter and zadeh function and the other based on the concepts of remote neighborhood ideal and order homomorphism on fuzzy lattices to approach this the paper studies two weaker forms of continuous order homomorphisms the semi continuous order homomorphism and the weakly semi continuous order homomorphism between l fuzzy topological spaces these order homomorphisms can be characterized in each of the notions remote neighborhood neighborhood ideal filter and molecular net in addition some relations connecting weakly semi continuous order homomorphisms semi hausdorff l fts and urysohn l fts have also been established

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

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

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

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 new procedure for time varying linearization up to output injection new necessary and sufficient conditions for time varying linearization up to output injection tvloi are presented they yield a straightforward tvloi procedure

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

linearization of discrete time nonlinear systems and a canonical structure linearizable nonlinear discrete time systems are described as a composition of diffeomorphisms linearizability of a general nonlinear system is obtained as an extension of linearizability of the system expressed in terms of the diffeomorphisms

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

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

global time varying linearization up to output injection this paper following the purpose of synthesis of observers for nonlinear systems investigates the question of equivalence of a nonlinear system with a bilinear system or more generally a linear time dependent system plus an output injection in a previous work by the same authors such questions have already been dealt with from the local point of view the goal herein is to examine the global situation using basic facts from algebraic topology it is shown that in the single output case whenever the possibility to bilinearize up to output injection holds locally everywhere it also holds globally

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

convergence analysis of the extended kalman filter used as an observer for nonlinear deterministic discrete time systems in this paper convergence analysis of the extended kalman filter ekf when used as an observer for nonlinear deterministic discrete time systems is presented based on a new formulation of the first order linearization technique sufficient conditions to ensure local asymptotic convergence are established furthermore it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified ekf significantly the efficiency of this approach compared to the classical version of the ekf is shown through a nonlinear identification problem as well as a state and parameter estimation of nonlinear discrete time systems

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

simple nonlinear observers for on line estimation of kinetic rates in bioreactors abstract in this paper we propose a global theoretical framework for the analysis of bioreactor dynamics we concentrate on the problem of kinetic rates estimation inside the reactor we show how efficient estimators of these kinetics can be designed in a systematic and rigorous way from a minimal knowledge of their structures the proposed approach does not require any model for the kinetic rates and is very successful in accurately estimating these variables it uses technical tools issued from the non linear systems theory which allow the design of observer based estimators these estimators are designed to work with continuous and discrete data measurements the continuous and discrete versions of the corresponding observers are presented and their convergences are established an important point lies in the facility of implementing and calibrating the proposed estimators indeed due to the particular structure of their gain their tuning is reduced to the calibration of a single parameter whatever the number of considered components and reactions the performances of the proposed estimators are illustrated in simulation through a typical example dealing with microbial growth and biosynthesis reactions

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

sampled data observer error linearization the effects of time sampling on the solvability conditions for the observer linearization design methodology are investigated it is shown that the class of systems for which this design method can be applied for an open set of sampling times is quite small in particular when the dimension of the state space is two it consists only of those systems that are state equivalent to a linear system the practical implication is that digital implementations of this methodology will have to be approximate

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

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

t convergence of nets of l fuzzy sets and its applications abstract in this paper the theory of convergence on nets of l fuzzy sets which is a generalization of the convergence theory of fuzzy nets introduced by sarma and ajmal is established some important and interesting results in l fuzzy topology are obtained by means of the theory

state equivalence of discrete time nonlinear control systems to state affine form up to input output injection in this paper the problem of transformation of a discrete time nonlinear control system into a state affine form up to input output injection is addressed a set of coordinate free necessary and sufficient conditions for such a transformation to be possible is first proposed and a more constructive procedure is then presented no restriction of invertibility of the state transition map is required

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

sr convergence theory in fuzzy lattices abstract convergence theory and order homomorphisms theory are two important objects of study in fuzzy lattices in this paper sr convergence theory for molecular nets and ideals is established and the concepts of r irresolute sr continuous and almost irresolute order homomorphisms in topological molecular lattices are introduced and systematically characterized some mutual relations between these concepts and others are obtained

new applications of l nets in l fuzzy multifunctions in this paper we will give new applications of l net in l fuzzy multifunctions using l net we will further study l fuzzy continuous almost continuous and r continuous multifunctions some interesting characterizations are obtained

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

decentralized sampled data fuzzy observer design for nonlinear interconnected systems this paper presents the decentralized sampled data fuzzy observer design techniques for nonlinear interconnected systems which are assumed to be composed of fuzzy subsystems and unknown interconnections to design the decentralized fuzzy observer the estimation error dynamics is obtained and the performance function is defined based on the estimation error dynamics and the performance function the continuous time decentralized fuzzy observer is first proposed to minimize the interconnection bound to attenuation degree ratio in addition the decentralized sampled data fuzzy observers are designed by using the approximate discretization and the exact discrete time design approaches respectively each proposed observer design technique is formulated into the optimal problems with the linear matrix inequalities finally several simulation examples show the validity and superiority of the proposed observer design techniques by comparing with the conventional techniques

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

brief on robustness and precision of mobile robots missions this paper proposes solutions for the robust achievement of displacement missions by a wheeled mobile robot the considered disturbances are generated by the use of inaccurate configuration estimates as feedback information those errors are characterized in a bounded error context we introduce a trajectory tracking controller whose stability is analysed by a lyapunov function the time derivative of which is negative definite inside a large domain around the zero error this property makes it possible to define a bounded attractive domain around the nominal trajectory quantifying thus the guaranteed precision of the mission the method is extended to a parking non stationary controller and illustrated by a real experiment

further remarks on dna overlap assembly abstract the operation of overlap assembly was defined by csuhaj varju petre and vaszil as a formal model of the linear self assembly of dna strands the overlap assembly of two strings xy and yz which share an overlap y results in the string xyz this paper continues the exploration of the properties of the overlap assembly operation by investigating closure of various language classes under iterated overlap assembly and the decidability of the completeness of a language it also investigates the problem of deciding whether a given string is terminal with respect to a language and the problem of deciding if a given language can be generated by an overlap assembly operation of two given others

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

σ convergence theory and its applications in fuzzy lattices moore smith convergence theory is enriched in a fuzzy lattice the limit point and cluster point of a molecular net and a filter in a fuzzy lattice are defined and their various properties are discussed and the closure the interior operators and topological molecular lattices are introduced by the concept of ordered pair of r neighborhoods mutual relationships between convergence moore smith convergence convergence and urysohn convergence of a molecular net and a filter are studied moreover several applications based on the convergence theory of a molecular net and a filter are provided for continuous order homomorphisms

brief paper an ekf based nonlinear observer with a prescribed degree of stability the topic of this article is a nonlinear observer based on a slight modification of the extended kalman filter the purpose of this modification is twofold first the degree of stability can be assigned in advance and secondly this modification allows an effective treatment of the nonlinearities using the second method of lyapunov it is proved that the proposed observer is an exponential observer to examine the practical usefulness the proposed observer is applied to the highly nonlinear flux and angular velocity estimation problem for induction machines

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

regular splicing languages and subclasses recent developments in the theory of finite splicing systems have revealed surprising connections between long standing notions in the formal language theory and splicing operation more precisely the syntactic monoid and schutzenberger constant have strong interaction with the investigation of regular splicing languages this paper surveys results of structural characterization of classes of regular splicing languages based on the above two notions and discusses basic questions that motivate further investigations in this field in particular we improve the result in 6 that provides a structural characterization of reflexive symmetric splicing languages by showing that it can be extended to the class of all reflexive splicing languages this is the larger class for which a characterization is known

complexity of a problem concerning reset words for eulerian binary automata abstract a word is called a reset word for a deterministic finite automaton if it maps all the states of the automaton to a unique state deciding about the existence of a reset word of a given length for a given automaton is known to be an np complete problem we prove that it remains np complete even if restricted to eulerian automata with binary alphabets as it has been conjectured by martyugin 2011

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

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

existence of constants in regular splicing languages in spite of wide investigations of finite splicing systems in formal language theory basic questions such as their characterization remain unsolved it has been conjectured that a necessary condition for a regular language l to be a splicing language is that l must have a constant in the schutzenberger sense we prove this longstanding conjecture to be true the result is based on properties of strongly connected components of the minimal deterministic finite state automaton for a regular splicing language using constants of the corresponding languages we also provide properties of transitive automata and path automata

theory of topological molecular lattices abstract the aim of this paper is to bring the theories of point set topology fuzzy topology and l fuzzy topology into a unified theory the theory of topological molecular lattices for this purpose we first introduce the concepts of molecule for completely distributive complete lattice molecular lattice for short the cotopology on it and the concept of remote neighborhoods of molecules therefrom we develop the theory of pointwise topology on molecular lattices

observers for discrete time nonlinear systems abstract the problem of observers for discrete time nonlinear systems has been considered and a simple easy to implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems some numerical examples show the effectiveness of the proposed observer

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

nonlinear observer design by observer error linearization this paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs necessary and sufficient conditions for the existence of the linearization transformation are derived for nonlinear systems without inputs the conditions are shown to be corrections to an existing result a computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented

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

sofic shifts with synchronizing presentations abstract a sofic shift s is a symbolic dynamical system that can be viewed as a set of all bi infinite sequences obtained by reading the labels of all bi infinite paths in a finite directed labeled graph g the presentation g is synchronizing if for every vertex v there is a word x v such that every path in g labeled with x v has v as a terminal vertex we present an example of a subshift of finite type that has no unique minimal deterministic presentation and we show that if a sofic shift has a synchronizing deterministic presentation sdp then it has a unique minimal one irreducible sofic shifts subshifts of finite type and nonwandering systems have synchronizing deterministic presentations we give an intrinsic characterization of a sofic shift s that has an sdp in terms of the syntactic monoid m s of the factor language f s of s another characterization of sofic shifts with sdp s is given in terms of the predecessor sets we show that a sofic shift can have at most one bi synchronizing presentation

parameter estimation in stochastic grey box models an efficient and flexible parameter estimation scheme for grey box models in the sense of discretely partially observed ito stochastic differential equations with measurement noise is presented along with a corresponding software implementation the estimation scheme is based on the extended kalman filter and features maximum likelihood as well as maximum a posteriori estimation on multiple independent data sets including irregularly sampled data sets and data sets with occasional outliers and missing observations the software implementation is compared to an existing software tool and proves to have better performance both in terms of quality of estimates for nonlinear systems with significant diffusion and in terms of reproducibility in particular the new tool provides more accurate and more consistent estimates of the parameters of the diffusion term

on the observer problem for discrete time control systems this paper studies the construction of observers for nonlinear time varying discrete time systems in a general context where a certain function of the states must be estimated appropriate notions of robust complete observability are proposed under which a constructive proof of existence of an observer is developed moreover a transitive observer property is proven according to which a state observer can be generated as the series connection of two observers the analysis and the results are developed in general normed linear spaces to cover both finite dimensional and infinite dimensional systems

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

brief applying the ekf to stochastic differential equations with level effects a transformation is introduced to effectively remove level effects i e the state dependency of the diffusion function in a restricted class of multivariate stochastic differential equations such that the general continuous discrete time nonlinear filtering problem may be solved using new or existing implementations of the extended kalman filter ekf an implementation of a quasi maximum likelihood qml method for direct estimation of embedded parameters in nonlinear multivariate stochastic differential equations using discrete time input output data encumbered with additive measurement noise is discussed and its properties are compared with those provided by another software package

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

the characterizations of semi continuous and irresolute order homomorphisms on fuzzes abstract the concepts of semi continuous and irresolute order homomorphisms on fuzzes were introduced in j jianghan petroleum institute 2 1988 96 97 in this paper we first present the theory with respect to s convergence s convergence of molecular nets and ideals on fuzzes secondly we introduce the notions of strong semicontinuity strong irresoluteness and s irresoluteness on fuzzes then we systematically study the characterizations of these notions with the aid of the s convergence s convergence of molecular nets and ideals and give the relations of them

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

order homomorphisms on fuzzes abstract in this paper basic properties of the concept of order homomorphisms on fuzzes 4 which is a proper generalization of the concept of fuzz functions 1 are studied conditions for fuzz functions to be functions of zadeh s type are obtained moreover the concepts of continuous closed and open order homomorphisms are introduced and studied

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

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

the structure of reflexive regular splicing languages via schutzenberger constants the splicing operation was introduced in 1987 by head as a mathematical model of the recombination of dna molecules under the influence of restriction and ligases enzymes this operation allows us to define a computing language generating device called a splicing system other variants of this original definition were also proposed by paun and pixton respectively the computational power of splicing systems has been thoroughly investigated nevertheless an interesting problem is still open namely the characterization of the class of regular languages generated by finite splicing systems in this paper we will solve the problem for a special class of finite splicing systems termed reflexive splicing systems according to each of the definitions of splicing given by paun and pixton this special class of systems contains in perticular finite head splicing systems the notion of a constant given by schutzenberger once again intervenes

estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors linear families of models and estimators the problem of parameter estimation and of the evaluation of related uncertainty intervals is considered in the case that a probabilistic description of noise and errors is not available of suitable but only a bound on them is known in the present paper only linear parametrizations and estimators are considered very simple and computationally feasible algorithms are derived for evaluating two different types of uncertainty intervals estimates uncertainty intervals parameter uncertainty intervals the relationships between the eui s and the pui s are established and the solution to the problem of the minimum uncertainty intervals estimator is given the latter can be obtained by means of a simple linear programming algorithm

from continuous time design to sampled data design of observers in this work a sampled data nonlinear observer is designed using a continuous time design coupled with an inter sample output predictor the proposed sampled data observer is a hybrid system it is shown that under certain conditions the robustness properties of the continuous time design are inherited by the sampled data design as long as the sampling period is not too large the approach is applied to linear systems and to triangular globally lipschitz systems

brief paper robust h observer design for sampled data lipschitz nonlinear systems with exact and euler approximate models an lmi approach is proposed for the design of robust h observers for a class of lipschitz nonlinear systems two type of systems are considered lipschitz nonlinear discrete time systems and lipschitz nonlinear sampled data systems with euler approximate discrete time models observer convergence when the exact discrete time model of the system is available is shown then practical convergence of the proposed observer is proved using the euler approximate discrete time model as an additional feature maximizing the admissible lipschitz constant the solution of the proposed lmi optimization problem guaranties robustness against some nonlinear uncertainties the robust h observer synthesis problem is solved for both cases the maximum disturbance attenuation level is achieved through lmi optimization

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