metriques de carnot cartheodory et quasiisometries des espaces symetriques de rang un we exhibit a rigidity property of the simple groups sp n 1 and f7 20 which implies mostow rigidity this property does not extend to o n 1 and u n 1 the proof relies on quasiconformal theory applied in the cr setting extensions are given to a class of solvable lie groups as a byproduct a result on quasiisometries of infinite nilpotent groups is obtained dans cet article on etablit une propriete de rigidite des groupes simples de rang un sp n 1 n 2 2 et fqui entraine la rigidite de mostow 1 theoreme toute quasiisornwtrie de 1 espace hyperbolique quaternionien hhn n 2 resp du plan hyperbolique de cayley cah2 est d distance bornee d une isometrie i e differe d une isomnetrie par une application qui diplace les points d une distance bornee une application f entre espaces metriques est une quasiisometrie s il existe des constantes l et c telles que l image de f soit c dense et que pour tous x y c d x y d fx fy ld x y c l une quasiisometrie entre des g et g est une sorte d isomorphisme virtuel dans la categorie topologique en effet cela correspond a une action de g sur un fibre principal c de groupe g sur une base compacte cf ra un isomorphisme entre sous groupes cocompacts covolume fini suffit pour les groupes simples de rang un de groupes de lie s etend en une quasiisometrie des espaces symetriques ou des groupes de lie si celle ci est proche d une isometrie des espaces symetriques resp un isomorphisme des groupes de lie les sous groupes sont conjugues c est la rigidite de mostow m2 la propriete ci dessus ne s etend pas aux groupes o n 1 et u n 1 en effet paragraphe 11 7 ceux ci ont beaucoup de quasiisometries au moins this content downloaded from 207 46 13 92 on sun 20 nov 2016 04 26 46 utc all use subject to http about jstor org terms

state estimation with partially observed inputs a unified kalman filtering approach for linear stochastic time varying state space models with gaussian noises this paper investigates state estimation for the scenario where the input variables of the state equation are not fully observed but rather the input data are available only at an aggregate level unlike the existing filters for unknown inputs that are based on the approach of minimum variance unbiased estimation this paper does not impose the unbiasedness condition for state estimation instead it incorporates a bayesian approach to derive a modified kalman filter by pooling the prior knowledge about the state vector at the aggregate level with the measurements on the output variables at the original level of interest the estimated state vector is shown to be a minimum mean square error estimator the developed filter provides a unified approach to state estimation it includes the existing filters obtained under two extreme scenarios as its special cases i e the classical kalman filter where all the inputs are observed and the filter for unknown inputs

h_inf functional filtering for linear systems with unknown inputs a new method for the h1 functional filtering for systems with unknown inputs is presented first a functional filtering technique is presented then we show that the dynamic of the estimation error can be modeled in the descriptor system form this formulation makes it possible to describe the dynamic estimation error free of the derivative of the disturbances the filter parameters are obtained from the bounded real lemma of descriptor systems the developed approach unifies the design of functional reduced order and full order filters necessary and sufficient conditions for the solvability of the problem are obtained in terms of a set of bilinear matrix inequalities bmi under certain conditions these inequalities can be transformed to a set of linear matrix inequalities lmi two numerical examples are presented to illustrate the approach described in the paper the first example concerns the estimation of the state of charge soc of the the lithium ion battery and the second example highlights the reduced nature of the proposed functional filter

parity equations based unknown input reconstruction for mimo stochastic systems with an application in this paper an approach for reconstructing an unknown input for multiple input multiple output systems is presented it is assumed that the system is affected by process noise whereas the available system inputs are contaminated by measurement noise the novel approach is based on a parity equations concept and forms an extension of the idea developed previously by the authors a modification of the algorithm is also provided which allows the approach to deal with systems whose zero is close to unity the order of the parity space can be treated as a tuning parameter allowing for a trade off between the smoothness of the reconstructed unknown input and a phase lag an analytical solution of the overall problem is obtained by making use of a lagrange multiplier method the utility of the scheme is demonstrated when applied to a practical hydrological system

linear filtering for bilinear stochastic differential systems with unknown inputs investigates the problem of state estimation for bilinear stochastic multivariable differential systems in the presence of an additional disturbance whose statistics are completely unknown a linear filter is proposed based on a suitable decomposition of the state of the bilinear system into two components the first one is a computable function of the observations while the second component is estimated via a suitable linear filtering algorithm no a priori information on the disturbance is required for the filter implementation the proposed filter is robust with respect to the unknown input in that the covariance of the estimation error is not affected by such input numerical simulations show the effectiveness of the proposed filter

brief extension of minimum variance estimation for systems with unknown inputs in this paper we address the problem of minimum variance estimation for discrete time time varying stochastic systems with unknown inputs the objective is to construct an optimal filter in the general case where the unknown inputs affect both the stochastic model and the outputs it extends the results of darouach and zasadzinski automatica 33 1997 717 where the unknown inputs are only present in the model the main difficulty in treating this problem lies in the fact that the estimation error is correlated with the systems noises this fact leads generally to suboptimal filters necessary and sufficient conditions for the unbiasedness of this filter are established then conditions under which the estimation error and the system noises are uncorrelated are presented and an optimal estimator and a predictor filters are derived sufficient conditions for the existence of these filters are given and sufficient conditions for their stability are obtained for the time invariant case a numerical example is given in order to illustrate the proposed method

event based state estimation of linear dynamic systems with unknown exogenous inputs in this work an event based optimal state estimation problem for linear time varying systems with unknown inputs is investigated by treating the unknown input as a process with a non informative prior the event based minimum mean square error mmse estimator is obtained in a recursive form it is shown that for the general time varying case the closed loop matrix of the optimal event based estimator is exponentially stable and the estimation error covariance matrix is asymptotically bounded for each sample path of the event triggering process the results are also extended to the multiple sensor scenario where each sensor is allowed to have its own event triggering condition the efficiency of the proposed results is illustrated by a numerical example and comparative simulation with the mmse estimators obtained based on time triggered measurements the results are potentially applicable to event based secure state estimation of cyber physical systems

the gauss green theorem in stratified groups abstract we lay the foundations for a theory of divergence measure fields in noncommutative stratified nilpotent lie groups such vector fields form a new family of function spaces which generalize in a sense the bv fields they provide the most general setting to establish gauss green formulas for vector fields of low regularity on sets of finite perimeter we show several properties of divergence measure fields in stratified groups ultimately achieving the related gauss green theorem

riccati equations in optimal filtering of nonstabilizable systems having singular state transition matrices until recently it was believed that a necessary and sufficient condition for convergence of the riccati difference equation of optimal filtering was that the system be both delectable and stabilizable recently it has been shown that the stabilizability condition can be removed but convergence has only established under restrictive assumptions including the requirement that the state transition matrix be nonsingular the present paper generalizes these results in several directions first properties of the algebraic riccati equation are established for the case of singular state transition matrix second several assumptions previously imposed in establishing convergence of the riccati difference equation for systems with unreachable modes on the unit circle are relaxed including replacing observability by detectability weakening the conditions on the initial covariance and allowing the state transition matrix to be singular third results on the convergence and properties of the riccati equations are expressed as both necessary and sufficient conditions whereas previous results were only sufficient these extensions mean that the results have wider applicability including fixed lag smoothing problems and filtering for systems with time delays the implications of the results in the dual problem of optimal control are also studied

on existence optimality and asymptotic stability of the kalman filter with partially observed inputs for linear stochastic time varying systems we investigate the properties of the kalman filter with partially observed inputs we first establish the existence condition of a general linear filter when the unknown inputs are partially observed then we examine the optimality of the kalman filter with partially observed inputs finally on the basis of the established existence condition and optimality result we investigate asymptotic stability of the filter for the corresponding time invariant systems it is shown that the results on existence and asymptotic stability obtained in this paper provide a unified approach to accommodating a variety of filtering scenarios as its special cases including the classical kalman filter and state estimation with unknown inputs

estimation of systems with statistically constrained inputs abstract this paper discusses the estimation of a class of discrete time linear stochastic systems with statistically constrained unknown inputs ui which can represent an arbitrary combination of a class of un modeled dynamics random ui with unknown covariance matrix and deterministic ui in filter design an upper bound filter is explored to compute recursively and adaptively the upper bounds of covariance matrices of the state prediction error innovation and state estimate error furthermore the minimum upper bound filter mubf is obtained via online scalar parameter convex optimization in pursuit of the minimum upper bounds two examples a system with multiple piecewise uis and a continuous stirred tank reactor cstr are used to illustrate the proposed mubf scheme and verify its performance

isoperimetric and sobolev inequalities for carnot caratheodory spaces and the existence of minimal surfaces after hormander s fundamental paper on hypoellipticity 54 the study of partial differential equations arising from families of noncommuting vector fields has developed significantly in this paper we study some basic functional and geometric properties of general families of vector fields that include the hormander type as a special case similar to their classical counterparts such properties play an important role in the analysis of the relevant differential operators both linear and nonlinear to motivate our results we recall some classical inequalities let e c r be a caccioppoli set a measurable set having a locally finite perimeter then one has the isoperimetric inequality

brief paper unbiased minimum variance state estimation for linear systems with unknown input the problem of state estimation for a linear system with unknown input which affects both the system and the output is discussed in this paper a recursive optimal filter with global optimality in the sense of unbiased minimum variance over all linear unbiased estimators is provided the necessary and sufficient condition for the convergence and stability is also given which is milder than existing approaches

simultaneous input and state estimation for nonlinear systems with applications to flow field estimation this paper studies the problem of simultaneous input and state estimation sise for nonlinear dynamical systems with and without direct input output feedthrough we take a bayesian perspective to develop a sequential joint input and state estimation approach our scheme gives rise to a nonlinear maximum a posteriori optimization problem which we solve using the classical gauss newton method the proposed approach generalizes a number of sise methods presented in the literature we illustrate the effectiveness of the proposed scheme for nonlinear systems with direct feedthrough in an oceanographic flow field estimation problem involving submersible drogues that measure position intermittently and acceleration continuously

technical communique on the asymptotic stability of minimum variance unbiased input and state estimation in this note we investigate the asymptotic stability of the filter for minimum variance unbiased input and state estimation developed by gillijns and de moor sufficient conditions for the stability are proposed and proven with inspiration from the kalman filter stability analysis

on gradient bounds for the heat kernel on the heisenberg group it is known that the couple formed by the two dimensional brownian motion and its levy area leads to the heat kernel on the heisenberg group which is one of the simplest sub riemannian space the associated diffusion operator is hypoelliptic but not elliptic which makes difficult the derivation of functional inequalities for the heat kernel however driver and melcher and more recently h q li have obtained useful gradient bounds for the heat kernel on the heisenberg group we provide in this paper simple proofs of these bounds and explore their consequences in terms of functional inequalities including cheeger and bobkov type isoperimetric inequalities for the heat kernel

extension of friedland s separate bias estimation to randomly time varying bias of nonlinear systems by extending b friedland s 1969 separate bias estimation algorithm for linear systems to nonlinear systems and combining the result with the suboptimal fading extended kalman filter proposed by d h zhou 1990 and by d h zhou et al a pseudo separate bias estimation algorithm for randomly time varying bias of a class of nonlinear time varying stochastic systems is obtained a simulation example is presented to illustrate the effectiveness of the algorithm

state estimation for descriptor systems via the unknown input filtering method this paper addresses the optimal unbiased minimum variance state estimation of descriptor systems in the framework of unknown input filtering it is shown that any descriptor system can be equivalently transformed into a standard state space system with unknown inputs the existing globally optimal state estimators can then be readily used to facilitate the optimal filter design this research highlights the relationship between descriptor state estimation and unknown input filtering for standard state space systems with unknown inputs a direct application to the state estimation of descriptor systems with unknown inputs via the proposed results is also addressed an illustrative example is given to show the novelty of the proposed results

technical communique reduced order kalman filter with unknown inputs this paper presents an optimal reduced order kalman filter for discrete time dynamic stochastic linear systems with unknown inputs the problem is to estimate a part of the state vector in the case where none of the observations are assumed to be noise free the proposed filter is obtained by minimizing the trace of the estimation error covariance matrix with respect to the remaining degrees of freedom after noninteresting state and unknown inputs decoupling the necessary and sufficient conditions for stability and convergence of the filter are established

brief paper unbiased minimum variance input and state estimation for linear discrete time systems this paper addresses the problem of simultaneously estimating the state and the input of a linear discrete time system a recursive filter optimal in the minimum variance unbiased sense is developed where the estimation of the state and the input are interconnected the input estimate is obtained from the innovation by least squares estimation and the state estimation problem is transformed into a standard kalman filtering problem necessary and sufficient conditions for the existence of the filter are given and relations to earlier results are discussed

framework for state and unknown input estimation of linear time varying systems the design of unknown input decoupled observers and filters requires the assumption of an existence condition in the literature this paper addresses an unknown input filtering problem where the existence condition is not satisfied instead of designing a traditional unknown input decoupled filter a double model adaptive estimation approach is extended to solve the unknown input filtering problem it is proved that the state and the unknown inputs can be estimated and decoupled using the extended double model adaptive estimation approach without satisfying the existence condition numerical examples are presented in which the performance of the proposed approach is compared to methods from literature

deadbeat unknown input state estimation and input reconstruction for linear discrete time systems abstract this paper considers discrete time input reconstruction and state estimation assuming that the system has no invariant zeros without assuming that the initial condition is known and without assuming that at least one markov parameter has full column rank algorithms based on the generalized inverse of a block toeplitz matrix are given for unknown input state estimation and simultaneous input reconstruction and state estimation in both cases the unknown input is an arbitrary signal both algorithms are deadbeat which means that exact input reconstruction and state estimation are achieved in a finite number of steps

simultaneous input and state estimation for stochastic nonlinear systems with additive unknown inputs abstract this paper investigates simultaneous input and state estimation for a class of nonlinear stochastic systems we propose a recursive filter to concurrently estimate system states and unknown inputs we show that the estimation errors of the proposed filter are practically exponentially stable in probability and the estimation error covariance matrices are uniformly bounded

a robust estimator for stochastic systems under unknown persistent excitation a robust estimator for uncertain stochastic systems under unknown persistent disturbance is presented the given discrete time stochastic formulation neither requires a known bound on the magnitude of the unknown excitation nor assumes stability of the system however the proposed estimator assumes certain structural conditions on system uncertainties though the proposed estimator is developed based on stochastic lyapunov analysis its structure and performance are comparable to that of unbiased minimum variance filters based on the disturbance decoupling technique unlike unbiased minimum variance filters implementation of the developed estimator only requires adding an auxiliary term to the nominal steady state kalman filter and it does not involve any similarity transformation or propagation of matrix difference equations

rectifiability and perimeter in the heisenberg group in this paper we fully extend to the heisenberg group endowed with its intrinsic carnot caratheodory metric and perimeter the classical de giorgi s rectifiability divergence theorems

existence of isoperimetric regions in contact sub riemannian manifolds abstract we prove existence of regions minimizing perimeter under a volume constraint in contact sub riemannian manifolds whose quotient by the group of contact transformations preserving the sub riemannian metric is compact

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

a unified filter for simultaneous input and state estimation of linear discrete time stochastic systems in this paper we present a unified optimal and exponentially stable filter for linear discrete time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum variance sense without making any assumptions on the direct feedthrough matrix we also provide the connection between the stability of the estimator and a system property known as strong detectability and discuss the global optimality of the proposed filter finally an illustrative example is given to demonstrate the performance of the unified unbiased minimum variance filter

technical communique extension of unbiased minimum variance input and state estimation for systems with unknown inputs this paper extends the existing results on joint input and state estimation to systems with arbitrary unknown inputs the objective is to derive an optimal filter in the general case where not only unknown inputs affect both the system state and the output but also the direct feedthrough matrix has arbitrary rank the paper extends both the results of gillijns and de moor gillijns s de moor b 2007b unbiased minimum variance input and state estimation for linear discrete time systems with direct feedthrough automatica 43 934 937 and darouach zasadzinski and boutayeb darouach m zasadzinski m boutayeb m 2003 extension of minimum variance estimation for systems with unknown inputs automatica 39 867 876 the resulting filter is an extension of the recursive three step filter ertsf and serves as a unified solution to the addressed unknown input filtering problem the relationship between the ertsf and the existing literature results is also addressed

optimal filtering for systems with unknown inputs via the descriptor kalman filtering method this paper addresses globally optimal unbiased minimum variance state estimation for systems with unknown inputs that affect both the system and the output with the descriptor kalman filtering method it is shown that directly applying the conventional descriptor kalman filter dkf to the considered problem may not yield the globally optimal solution because the unknown input vector may not be estimable to remedy this problem three approaches are proposed to facilitate optimal filter design the transformed approach uses some input and output transformations the untrammeled approach does not require any transformations and the augmented approach reconstructs the unknown input dynamics then three 5 block forms of the extended dkf 5 block edkf are derived as globally optimal state estimators in the sense that the first two filters are equivalent to the recently developed extended recursive three step filter and the third is equivalent to the conventional augmented state kalman filter the relationship between the proposed edkfs and the existing results in the literature is addressed simulation results are given to illustrate the usefulness of the proposed filters

unbiased minimum variance linear state estimation abstract a method is developed for linear estimation in the presence of unknown or highly non gaussian system inputs the state update is determined so that it is unaffected by the unknown inputs the filter may not be globally optimum in the mean square error sense however it performs well when the unknown inputs take extreme or unexpected values in many geophysical and environmental applications it is performance during these periods which counts the most the application of the filter is illustrated in the real time estimation of mean areal precipitation

delayed unknown input observers for discrete time linear systems with guaranteed performance abstract in this paper we propose a state and unknown input observer for discrete time linear systems with bounded unknown inputs and measurement disturbances the design procedure is formulated using a set of linear matrix inequalities and leverages delayed or fixed lag estimates the observer error states and or user defined performance outputs are guaranteed to operate at certain performance bounds furthermore by employing sufficiently large delays the observer is guaranteed to provide exact asymptotic state and input estimates for minimum phase systems we demonstrate via numerical examples that the proposed observer can be used for a wider class of systems than those satisfying matching conditions

kalman filter for discrete time stochastic linear systems subject to intermittent unknown inputs state estimation of stochastic discrete time linear systems subject to persistent unknown inputs has been widely studied but only few works have been dedicated to the case where unknown inputs may be simultaneously or sequentially active or inactive in this technical note a kalman filter approach is proposed for state estimation of systems with unknown intermittent inputs the design is based on the minimisation of the trace of the state estimation error covariance matrix under the constraint that the state estimation error is decoupled from the unknown inputs corrupting the system at the current time the necessary and sufficient stability conditions are established considering the upper bound of the prediction error covariance matrix

perimeter as relaxed minkowski content in metric measure spaces abstract in this note we prove that on general metric measure spaces the perimeter is equal to the relaxation of the minkowski contents w r t convergence in measure

induced representations for sim d 1 1 and scaling of massless fields in even dimensional spaces using an invariant operator in the enveloping algebra of sim d 1 1 the similitude subgroup of the conformal group in d dimensions conformal invariance and the recent result for the eigenvalue of a generalized helicity operator the eigenvalue of massless fields under scale transformations is computed in higher even dimensions

the weighted isoperimetric type and sobolev type inequalities for hypersurfaces in carnot groups abstract this paper mainly studies hypersurfaces immersed in a sub riemannian step k carnot group g with a density e f where f is a smooth function on g we give the first variation formula about the weighted horizontal area of hypersurfaces furthermore on the base of some work we derive the weighted isoperimetric type and sobolev type inequalities for hypersurfaces

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

on the equivalence between the unbiased minimum variance estimation and the infinity augmented kalman filter in this paper the augment kalman filter akf approach is discussed under the infinity condition it is proved that the akf in infinity condition is equivalent to the minimum variance unbiased mv

unbiased minimum variance estimation for systems with unknown exogenous inputs a new method is developed for the state estimation of linear discrete time stochastic systems in the presence of an unknown disturbance the filter obtained is optimal in the unbiased minimum variance sense the necessary and sufficient conditions for the existence and the stability of the filter are given

quasiconformal maps in metric spaces with controlled geometry this paper develops the foundations of the theory of quasiconformal maps in metric spaces that satisfy certain bounds on their mass and geometry the principal message is that such a theory is both relevant and viable the first main issue is the problem of definition which we next describe quasiconformal maps are commonly understood as homeomorphisms that distort the shape of infinitesimal balls by a uniformly bounded amount this requirement makes sense in every metric space given a homeomorphism f from a metric space x to a metric space y then for x x and r 0 set

technical communique two stage kalman estimator with unknown exogenous inputs this paper presents a two stage estimator for bias and state filtering in discrete time stochastic linear systems affected by unknown inputs or disturbances we show that the state estimate can be expressed as x k k x k k b k kb k k where x k k is a bias free state estimate and b k k the optimal estimate of constant bias the proposed two stage estimator is based on an alternate derivation of the unbiased minimum variance estimator with unknown exogenous inputs developed by darouach and zasadzinski 1997 automatica 33 717 719

brief paper on the global optimality of unbiased minimum variance state estimation for systems with unknown inputs in this paper a globally optimal filtering framework is developed for unbiased minimum variance state estimation for systems with unknown inputs that affect both the system state and the output the resulting optimal filters are globally optimal within the unbiased minimum variance filtering over all linear unbiased estimators globally optimal state estimators with or without output and or input transformations are derived through the global optimality evaluation of this research the performance degradation of the filter proposed by darouach zasadzinski and boutayeb darouach m zasadzinski m boutayeb m 2003 extension of minimum variance estimation for systems with unknown inputs automatica 39 867 876 is clearly illustrated and the global optimality of the filter proposed by gillijns and de moor gillijns s de moor b 2007b unbiased minimum variance input and state estimation for linear discrete time systems with direct feedthrough automatica 43 934 937 is further verified the relationship with the existing literature results is addressed a unified approach to design a specific globally optimal state estimator that is based on the desired form of the distribution matrix from the unknown input to the output is also presented a simulation example is given to illustrate the proposed results

technical communique on the optimality of recursive unbiased state estimation with unknown inputs for system models with unknown inputs state estimates may be obtained using linear minimum variance unbiased estimation here a proof is presented showing that the optimal solution over the class of all linear unbiased estimates may be written in the form of a linear recursive filter thereby validating previous work in this area

unbiased minimum variance fault and state estimation for linear discrete time varying two dimensional systems the fault and state estimation problem is addressed for a class of linear discrete time varying two dimensional systems subject to state and measurement noises two estimators are proposed to compute the estimation of the system state and or fault recursively both of which are unbiased with minimum variance through formulating the estimation problem as the solvability problem of the corresponding matrix equations of estimator gains and system constraint the necessary and sufficient condition of the existence and the solution for the proposed estimators are given an example is used to demonstrate the effectiveness of the proposed estimators