approximate finite dimensional filtering for polynomial states over polynomial observations in this article the mean square filtering problem for polynomial system states over polynomial observations is studied proceeding from the general expression for the stochastic ito differentials o

reduced order generalized h_ infty filtering for linear discrete time systems with application to channel equalization this paper investigates the problem of reduced order generalized h infty filtering for linear discrete time systems generalized h infty filtering covers standard h infty filtering as a special case and can make use of the frequency domain characteristics of practical signals moreover reduced order filters are more attractive than full order ones regarding implementability by virtue of the generalized bounded real lemma a new necessary and sufficient condition is proposed for analyzing the generalized h infty performance of the filtering error system to compute reduced order generalized h infty filters a necessary and sufficient condition is then derived in terms of matrix inequalities to solve which iterative linear matrix inequality algorithms are further developed in addition the proposed filter design method is applied to cope with the channel equalization problem examples are finally presented for illustrating the proposed method

network based robust h_infty filtering for uncertain linear systems the problem of network based robust hinfin filtering for uncertain linear systems is investigated different from the design of the traditional filter the effects of the network induced delay and data dropout on the performance of a filtering error system are considered the derived criteria for hinfin performance analysis of the filtering error system and filter design are expressed as a set of linear matrix inequalities which can be solved by using convex optimization method numerical examples show the effectiveness of the design method

a balanced finite element method for singularly perturbed reaction diffusion problems consider the singularly perturbed linear reaction diffusion problem varepsilon 2 delta u bu f in omega subset mathbb r d u 0 on partial omega where d ge 1 the domain ome

h fixed lag smoothing for linear discrete time varying systems with uncertain observations this paper deals with the problem of h fixed lag smoothing for linear discrete time varying systems with uncertain observations and l 2 norm bounded noise first the design of h smoother is equivalent to the problem that a certain indefinite quadratic form with respect to a new state space constraints has a minimum and the smoother is such that the minimum is positive then by introducing a krein space stochastic system and applying re organized innovation analysis approach the minimum of indefinite quadratic form and its existence condition are derived finally through analyzing the existence condition of the minimum and guaranteeing the positivity of the minimum a sufficient and necessary condition for the existence of an h smoother is proposed and the smoother is obtained in terms of two standard riccati difference equations a numerical example is given to show the effectiveness of the proposed method

quantised polynomial filtering for nonlinear systems with missing measurements abstractthis paper is concerned with the polynomial filtering problem for a class of nonlinear systems with quantisations and missing measurements the nonlinear functions are approximated with polynomials of a chosen degree and the approximation errors are described as low order polynomial terms with norm bounded coefficients the transmitted outputs are quantised by a logarithmic quantiser and are also subject to randomly missing measurements governed by a bernoulli distributed sequence taking values on 0 or 1 dedicated efforts are made to derive an upper bound of the filtering error covariance in the simultaneous presence of the polynomial approximation errors the quantisations as well as the missing measurements at each time instant such an upper bound is then minimised through designing a suitable filter gain by solving a set of matrix equations the filter design algorithm is recursive and therefore applicable for online computation an illustrative example is exploited to show the effectiveness

stochastic stability of the extended kalman filter with intermittent observations in this technical note we analyze the error behavior of the discrete time extended kalman filter for nonlinear systems with intermittent observations modelling the arrival of the observations as a random process we show that given a certain regularity of the system the estimation error remains bounded if the noise covariance and the initial estimation error are small enough we also study the effect of different measurement models on the bounds for the error covariance matrices

h_ infty positive filtering for positive linear discrete time systems an augmentation approach in this note we address the reduced order positive filtering problem of positive discrete time systems under the h performance commonly employed approaches such as linear transformation and elimination technique may not be applicable in general due to the positivity constraint of the filter to cope with the difficulty we first represent the filtering error system as a singular system by means of the system augmentation approach which will facilitate the consideration of the positivity constraint two necessary and sufficient conditions are obtained in terms of matrix inequalities under which the filtering error system has a prescribed h performance then a necessary and sufficient condition is proposed for the existence of the desired positive filters and an iterative linear matrix inequality lmi algorithm is presented to compute the filtering matrices which can be easily checked by standard software finally a numerical example to illustrate the effectiveness of the proposed design procedures is presented

improved robust h2 and h filtering for uncertain discrete time systems this paper is concerned with the robust h 2 and h filtering problems for linear discrete time systems with polytopic parameter uncertainty we aim to derive a less conservative design than existing linear matrix inequality lmi based sufficient conditions it is shown that a more efficient evaluation of robust h 2 or h performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations when applying this new matrix inequality condition to the robust filter design these parameters provide extra degrees of freedom in optimizing the guaranteed h 2 or h performance and lead to a less conservative design

brief paper robust filtering with stochastic nonlinearities and multiple missing measurements this paper is concerned with the filtering problem for a class of discrete time uncertain stochastic nonlinear time delay systems with both the probabilistic missing measurements and external stochastic disturbances the measurement missing phenomenon is assumed to occur in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval 01 such a probabilistic distribution could be any commonly used discrete distribution over the interval 01 the multiplicative stochastic disturbances are in the form of a scalar gaussian white noise with unit variance the purpose of the addressed filtering problem is to design a filter such that for the admissible random measurement missing stochastic disturbances norm bounded uncertainties as well as stochastic nonlinearities the error dynamics of the filtering process is exponentially mean square stable by using the linear matrix inequality lmi method sufficient conditions are established that ensure the exponential mean square stability of the filtering error and then the filter parameters are characterized by the solution to a set of lmis illustrative examples are exploited to show the effectiveness of the proposed design procedures

fixed order robust h sub spl infin filter design for markovian jump systems with uncertain switching probabilities this paper discusses the fixed order robust h sub spl infin filtering problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertainties under consideration are assumed to be norm bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix respectively first a criterion based on linear matrix inequalities is provided for testing the h sub spl infin filtering level of a filter over all the admissible uncertainties then a sufficient condition for the existence of the fixed order robust h sub spl infin filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints to determine the filter a globally convergent algorithm involving convex optimization is suggested finally a numerical example is used to illustrate that the developed theory is more effective than the existing results

a discrete time robust extended kalman filter for uncertain systems with sum quadratic constraints this technical note outlines the formulation of a novel discrete time robust extended kalman filter for uncertain systems with uncertainties described in terms of sum quadratic constraints the robust filter is an approximate set valued state estimator which is robust in the sense that it can handle modeling uncertainties in addition to exogenous noise riccati and filter difference equations are obtained as an approximate solution to a reverse time optimal control problem defining the set valued state estimator in order to obtain a solution to the set valued state estimation problem the discrete time system dynamics are modeled backwards in time

nonlinear state estimation for uncertain systems with an integral constraint this paper considers a problem of robust filtering for a class of uncertain nonlinear systems the solution involves a set valued state estimate that is obtained by solving a hamilton jacobi bellman equation in addition a less computationally intensive approximate solution to the problem is obtained for filtering problems defined over a large time interval the paper also presents an approximate solution to the robust filtering problem which leads to a robust version of the extended kalman filter

filtering and fault detection for nonlinear systems with polynomial approximation this paper is concerned with polynomial filtering and fault detection problems for a class of nonlinear systems subject to additive noises and faults the nonlinear functions are approximated with polynomials of a chosen degree different from the traditional methods the approximation errors are not discarded but formulated as low order polynomial terms with norm bounded coefficients the aim of the filtering problem is to design a least squares filter for the formulated nonlinear system with uncertain polynomials and an upper bound of the filtering error covariance is found and subsequently minimized at each time step the desired filter gain is obtained by recursively solving a set of riccati like matrix equations and the filter design algorithm is therefore applicable for online computation based on the established filter design scheme the fault detection problem is further investigated where the main focus is on the determination of the threshold on the residual due to the nonlinear and time varying nature of the system under consideration a novel threshold is determined that accounts for the noise intensity and the approximation errors and sufficient conditions are established to guarantee the fault detectability for the proposed fault detection scheme comparative simulations are exploited to illustrate that the proposed filtering strategy achieves better estimation accuracy than the conventional polynomial extended kalman filtering approach the effectiveness of the associated fault detection scheme is also demonstrated

robust kalman filtering for uncertain discrete time systems this paper is concerned with the problem of a kalman filter design for uncertain discrete time systems the system under consideration is subjected to time varying norm bounded parameter uncertainty in both the state and output matrices the problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties furthermore the guaranteed cost can be optimized by appropriately searching a scaling design parameter

robust discrete time minimum variance filtering the bounded variance filtered estimation of the state of an uncertain linear discrete time system with an unknown norm bounded parameter matrix is considered an upper bound on the variance of the estimation error is found for all admissible systems and estimators are derived that minimize the latter bound we treat the finite horizon time varying case and the infinite time case where the nominal system model is time invariant in the special stationary case where it is known that the uncertain system is time invariant we provide a robust filter for all uncertainties that still keep the system asymptotically stable

optimal filtering with random sensor delay multiple packet dropout and uncertain observations this paper studies the problem of optimal filtering of discrete time systems with random sensor delay multiple packet dropout and uncertain observation the random sensor delay multiple packet dropout or uncertainty in observation is transformed to a stochastic parameter in the system representation a new formulation enables us to design an optimal filter for a system with multiple packet dropout in sensor data based on a stochastic definition of the norm of a system with a stochastic parameter new relations for stochastic norm are derived the stochastic norm of the estimation error is used as a criterion for the filter design the relations derived for the new norm definition are used to obtain a set of linear matrix inequalities lmis to solve the filter design problems simulation examples show the effectiveness of the proposed method

state estimation for stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels abstract this paper deals with robust state estimation problem for a class of stochastic discrete time systems with multiplicative noises and unknown inputs over fading channels an unbiased unknown input insensitive filter is designed such that the variance of the estimation error is minimized in the sense of the so called p estimation the filter gain matrix is derived through solving a recursive riccati equation and a generalized lyapunov equation a necessary and sufficient condition that guarantees the existence of the filter is given which establishes a fundamental limit on the mean square capacity of each fading channel unknown input estimation and finite horizon stability of the proposed filter are also discussed to illustrate the effectiveness of the proposed approach the proposed algorithm is applied to a faulty remote controlled uninterruptible power system where both the state and the fault are estimated

extended kalman filtering with stochastic nonlinearities and multiple missing measurements in this paper the extended kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon both deterministic and stochastic nonlinearities are included in the system model where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances the phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval 0 1 such a probability distribution is allowed to be any commonly used distribution over the interval 0 1 with known conditional probability the aim of the addressed filtering problem is to design a filter such that in the presence of both the stochastic nonlinearities and multiple missing measurements there exists an upper bound for the filtering error covariance subsequently such an upper bound is minimized by properly designing the filter gain at each sampling instant it is shown that the desired filter can be obtained in terms of the solutions to two riccati like difference equations that are of a form suitable for recursive computation in online applications an illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme

stability conditions for multi sensor state estimation over a lossy network this paper studies a networked state estimation problem for a spatially large linear system with a distributed array of sensors each of which offers partial state measurements a lossy communication network is used to transmit the sensor measurements to a central estimator where the minimum mean square error mmse state estimate is computed under a markovian packet loss model we provide necessary and sufficient conditions for the stability of the estimator for any diagonalizable system in the sense that the mean of the state estimation error covariance matrix is uniformly bounded in particular the stability conditions for the second order systems with an i i d packet loss model are explicitly expressed as simple inequalities in terms of the largest open loop pole and the packet loss rate

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

improved cubature kalman filter for gnss ins based on transformation of posterior sigma points error tightly coupled gnss ins has been widely approved as a promising substitute for standalone gnss in urban areas navigation however due to the frequent gnss signal outages the filter used in gnss ins should be insensitive to the less informative observations in this paper a novel sigma points update method is proposed to enhance the robustness of cubature kalman filter ckf under the circumstance of unavailable observations first the problems of existing sampling based filters are analyzed then by transforming the posterior sigma points error matrix from prediction phase of filtering to the posterior domain of update the updated sigma points are expected to capture the covariance more precisely than traditional sigma points finally an improved ckf ickf is developed by embedding these points into the bayesian estimation framework and the upper bounds of error covariance matrices are analyzed theoretically signal outages with different durations are simulated and results demonstrate that ickf outperforms state of the art methods

brief paper optimal linear estimation for systems with multiple packet dropouts this paper is concerned with the optimal linear estimation problem for linear discrete time stochastic systems with multiple packet dropouts based on a packet dropout model the optimal linear estimators including filter predictor and smoother are developed via an innovation analysis approach the estimators are computed recursively in terms of the solution of a riccati difference equation of dimension equal to the order of the system state plus that of the measurement output the steady state estimators are also investigated a sufficient condition for the convergence of the optimal linear estimators is given simulation results show the effectiveness of the proposed optimal linear estimators

brief paper exponential stability of nonlinear time delay systems with delayed impulse effects the problem of exponential stability for nonlinear time delay systems with delayed impulses is addressed in this paper lyapunov based sufficient conditions for exponential stability are derived respectively for two kinds of delayed impulses i e destabilizing delayed impulses and stabilizing delayed impulses it is shown that if a nonlinear impulsive time delay system without impulse input delays is exponentially stable then under some conditions its stability is robust with respect to small impulse input delays moreover it is also shown that for a stable nonlinear impulsive time delay system if the magnitude of the delayed impulses is sufficiently small then under some conditions the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays the efficiency of the proposed results is illustrated by three numerical examples

variance constrained filtering for uncertain stochastic systems with missing measurements in this note we consider a new filtering problem for linear uncertain discrete time stochastic systems with missing measurements the parameter uncertainties are allowed to be norm bounded and enter into the state matrix the system measurements may be unavailable i e missing data at any sample time and the probability of the occurrence of missing data is assumed to be known the purpose of this problem is to design a linear filter such that for all admissible parameter uncertainties and all possible incomplete observations the error state of the filtering process is mean square bounded and the steady state variance of the estimation error of each state is not more than the individual prescribed upper bound it is shown that the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like inequalities or linear matrix inequalities the explicit expression of the desired robust filters is parameterized and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach

brief paper weighted h model reduction for linear switched systems with time varying delay this paper is concerned with model reduction for continuous time linear switched systems with time varying delay for a given stable switched system our attention is focused on construction of a reduced order model such that the error system is exponentially stable with a prescribed weighted performance by applying the average dwell time approach and the piecewise lyapunov function technique delay dependent deley independent sufficient conditions are proposed in terms of linear matrix inequality lmi to guarantee the exponential stability and the weighted performance for the error system the model reduction problem is solved by using the projection approach which casts the model reduction problem into a sequential minimization problem subject to lmi constraints by employing the cone complementary linearization algorithm a numerical example is provided to illustrate the effectiveness of the proposed theory