robust kalman bucy filter development of a robust estimator for uncertain stochastic systems under persistent excitation is presented the given continuous time stochastic formulation assumes norm bounded parametric uncertainties and excitations when there are no system uncertainties the performance of the proposed robust estimator is similar to that of the kalman bucy filter and the proposed approach asymptotically recovers the desired optimal performance in the presence of uncertainties and or persistent excitation

kalman filtering with intermittent observations on the boundedness of the expected error covariance this paper addresses the stability of a kalman filter when measurements are intermittently available due to constraints in the communication channel between the sensor and the estimator we give a necessary condition and a sufficient condition with a trivial gap between them for the boundedness of the expected value of the estimation error covariance these conditions are more general than the existing ones in the sense that they only require the state matrix of the system to be diagonalizable and the sequence of packet losses to be a stationary finite order markov process hence we extend the class of systems for which these conditions are known in two directions namely by including degenerate systems and by considering network models more general than i i d and gilbert elliott we show that these conditions recover known results from the literature when evaluated for non degenerate systems under the assumption of i i d or gilbert elliott packet loss models

shift invariance and surface growth the invariance of equations for self affine surface growth to reparametrization under the abelian group of shift transformations h x t to h x t l is used to bound the form of nonlinear terms and related kinetic coefficients in relaxational surface growth equations for conserved growth small but relevant diffusive terms second order in the driving can always be expected it is also shown that the asymptotic growth distributions in d 2 can be expected to be skew and are not derivable from a hamiltonian description

birkhoff formula for conformal compressions of symmetric cones in this paper we derive the birkhoff formula for conformal compressions on symmetric cones let v be a euclidean jordan algebra and let be the associated symmetric cone then admits a natural finsler metric contracted by any conformal compressions of we show that the lipschitz constant of a conformal compression of is equal to the hyperbolic tangent of one fourth of the diameter of the image this is the same relation which was obtained by birkhoff on positive reals and by liverani and wojtkowski on the space of positive definite real matrices

new approaches to robust minimum variance filter design this paper is concerned with the design of robust filters that ensure minimum filtering error variance bounds for discrete time systems with parametric uncertainty residing in a polytope two efficient methods for robust kalman filter design are introduced the first utilizes a recently introduced relaxation of the quadratic stability requirement of the stationary filter design the second applies the new method of recursively solving a semidefinite program sdp subject to linear matrix inequalities lmis constraints to obtain a robust finite horizon time varying filter the proposed design techniques are compared with other existing methods it is shown via two examples that the results obtained by the new methods outperform all of the other designs

an alternative look at the constant gain kalman filter for state estimation over erasure channels this technical note studies state estimation problems subject to data loss we consider a class of switched estimators where missing data is replaced by optimal estimates the considered class of estimators encompasses a number of estimation schemes proposed in the literature we show that the estimator that minimizes the steady state estimation error covariance within that class is given by a constant gain kalman filter which was previously proposed as an alternative to the kalman filter with intermittent observations as a by product of our results we derive expressions that allow one to compare analytically popular suboptimal data dropout compensation mechanisms

stability of mmse state estimators over lossy networks using linear coding this paper studies the state estimation problem for a stochastic discrete time system over a lossy channel where the packet loss is modeled as an independent and identically distributed binary process to counter the effect of random packet loss we propose a linear coding method to preprocess the measured output and prove that the coded output is information preserving when packet loss is void and is information enhancing when packet loss is present an optimal state estimator under the minimum mean square error mmse criterion is derived for the coded output when subject to packet loss the maximum packet loss rate for ensuring a stable estimator is then derived and shown to be very close to a well known lower bound also considered is a compressed linear coding method where the measured output is first compressed onto a lower dimensional space before encoding and it is shown that the similar packet rate condition for stability holds

kalman filtering with intermittent observations tail distribution and critical value in this paper we analyze the performance of kalman filtering for discrete time linear gaussian systems where packets containing observations are dropped according to a markov process modeling a gilbert elliot channel to address the challenges incurred by the loss of packets we give a new definition of non degeneracy which is essentially stronger than the classical definition of observability but much weaker than one step observability which is usually used in the study of kalman filtering with intermittent observations we show that the trace of the kalman estimation error covariance under intermittent observations follows a power decay law moreover we are able to compute the exact decay rate for non degenerate systems finally we derive the critical value for non degenerate systems based on the decay rate improving upon the state of the art

compatible coarse nodal and edge elements through energy functionals we propose new algorithms for the setup phase of algebraic multigrid amg solvers for linear systems coming from edge element discretization the construction of coarse levels is performed by solving an optimization problem with a lagrange multiplier method we minimize the energy of coarse bases under a constraint linking coarse nodal and edge element bases on structured meshes the resulting amg method and the geometric multigrid method behave similarly as preconditioners on unstructured meshes the convergence rate of our method compares favorably with the amg method of reitzinger and schoberl

weighted maximum likelihood for dynamic factor analysis and forecasting with mixed frequency data for the purpose of forecasting key macroeconomic or financial variables from a panel of time series variables we adopt the dynamic factor model and propose a weighted likelihood based method for parameter estimation the loglikelihood function is split into two parts that are weighted differently the first part is associated with the key variables while the second part is associated with the related variables which may contribute to the forecasting of key variables we derive asymptotic properties including consistency and asymptotic normality of the weighted maximum likelihood estimator we show that this estimator outperforms the standard likelihood based estimator in approximating the true unknown distribution of the data as well as in out of sample forecasting accuracy we verify the new estimation method in a monte carlo study and investigate the role of different weights in different settings in the context of forecasting gross domestic product growth this key variable is typically observed at a low quarterly frequency while the supporting variables are observed at a high monthly frequency we adopt a low frequency representation of the mixed frequency dynamic factor model and discuss the computational efficiencies of this approach in our empirical study for the u s economy we present improvements in nowcasting and forecasting accuracy when the weighted likelihood based estimation procedure is adopted

kalman filtering with intermittent observations weak convergence to a stationary distribution the paper studies the asymptotic behavior of discrete time random riccati equations rre arising in kalman filtering when the arrival of the observations is described by a bernoulli independent and identically distributed i i d process we model the rre as an order preserving strongly sublinear random dynamical system rds under a sufficient condition stochastic boundedness and using a limit set dichotomy result for order preserving strongly sublinear rds we establish the asymptotic properties of the rre the sequence of random prediction error covariance matrices converges weakly to a unique invariant distribution whose support exhibits fractal behavior for stabilizable and detectable systems stochastic boundedness and hence weak convergence holds for any nonzero observation packet arrival probability and in particular we can establish weak convergence at operating arrival rates well below the critical probability for mean stability the resulting invariant measure in that situation does not possess a first moment we apply the weak feller property of the markov process governing the rre to characterize the support of the limiting invariant distribution as the topological closure of a countable set of points which in general is not dense in the set of positive semi definite matrices we use the explicit characterization of the support of the invariant distribution and the almost sure a s ergodicity of the sample paths to easily compute statistics of the invariant distribution a one dimensional example illustrates that the support is a fractured subset of the non negative reals with self similarity properties

the positive definite solution of the nonlinear matrix equation xp a m b x1 1m we consider the nonlinear matrix equation xp a m b x1 1m where p1 is a positive integer m is an arbitrary nn matrix and a and b are hermitian positive semidefinite matrices an elegant estimate of the hermitian positive definite hpd solution is derived a fixed point iteration and an inversion free variant iteration for obtaining the hpd solution are proposed some numerical examples are presented to show the efficiency of the proposed two iterative methods

asymptotics for parametric garch in mean models abstract in this paper we develop an asymptotic theory for the quasi maximum likelihood estimator qmle of the parametric garch in mean model the asymptotics is based on a study of the volatility as a process of the model parameters the proof makes use of stochastic recurrence equations for this random function and uses exponential inequalities to localize the problem our results show why the asymptotics for this specification is quite complex although it is a rather standard parametric model nevertheless our theory does not yet treat all standard specifications of the mean function

recursive state estimation for uncertain systems with an integral quadratic constraint this paper considers a robust state estimation problem for a class of uncertain systems where the noise and uncertainty are modeled deterministically via an integral quadratic constraint the robust state estimation problem involves constructing the set of all possible states at the current time consistent with given output measurements and the integral quadratic constraint

sensitivity penalization based robust state estimation for uncertain linear systems this technical note deals with robust state estimation when parametric uncertainties nonlinearly affect a plant state space model based on a simultaneous minimization of nominal estimation errors and their sensitivities an analytic solution is derived for the optimal estimator which can be recursively realized this estimator has a form similar to the robust estimator of and its computational complexity is comparable to the kalman filter under certain conditions this robust estimator is proved to converge to a stable system its estimation errors have a bounded covariance matrix and the estimate is asymptotically unbiased numerical simulations show that the obtained estimator has nice estimation performances

conditional central algorithms for worst case set membership identification and filtering this paper deals with conditional central estimators in a set membership setting the role and importance of these algorithms in identification and filtering is illustrated by showing that problems like worst case optimal identification and state filtering in contexts in which disturbances are described through norm bounds are reducible to the computation of conditional central algorithms the conditional chebyshev center problem is solved for the case when energy norm bounded disturbances are considered a closed form solution is obtained by finding the unique real root of a polynomial equation in a semi infinite interval

kalman filtering with random coefficients and contractions the riccati transformation of linear filtering control theory is shown to be a contraction on the space of positive symmetric matrices this is used to describe the asymptotic behavior of the filter for systems with stochastic stationary parameters

kalman filtering with intermittent observations convergence for semi markov chains and an intrinsic performance measure this technical note shows that the stationary distribution for the covariance of kalman filtering with intermittent observations exists under mild conditions for a very general class of packet dropping models semi markov chain these results are proved using the geometric properties of riccati recursions with respect to a particular riemannian distance moreover the riemannian mean induced by that distance is always bounded therefore it can be used for characterizing the performance of the system for regimes where the moments of the covariance do not exist other interesting properties of that mean include the symmetry between covariance and information matrices averaging covariances or their inverse gives the same result and its interpretation in information geometry as the natural mean for the manifold of gaussian distributions

quasi maximum likelihood estimation in conditionally heteroscedastic time series a stochastic recurrence equations approach this paper studies the quasi maximum likelihood estimator qmle in a general conditionally heteroscedastic time series model of multiplicative form xt t zt where the unobservable volatility t is a parametric function of xt 1 x t p t 1 t q for some p q 0 and zt is standardized i i d noise we assume that these models are solutions to stochastic recurrence equations which satisfy a contraction random lipschitz coefficient property these assumptions are satisfied for the popular garch asymmetric garch and exponential garch processes exploiting the contraction property we give conditions for the existence and uniqueness of a strictly stationary solution xt to the stochastic recurrence equation and establish consistency and asymptotic normality of the qmle we also discuss the problem of invertibility of such time series models 1 introduction gaussian quasi maximum likelihood estimation that is likelihood estimation under the hypothesis of gaussian innovations is a popular method which is widely used for inference in time series models however it is often a nontrivial task to establish the consistency and asymptotic normality of the quasi maximum likelihood estimator qmle applied to specific models and therefore an in depth analysis of the probabilistic structure generated by the model is called for a classical example of this kind is the seminal paper by hannan 18 on estimation in linear arma time series in this paper we study the qmle for a general class of conditionally heteroscedastic time series models which includes garch asymmetric garch and exponential garch recall that a garch p q generalized autoregressive conditionally heteroscedastic of order p q process 4 i s def ined by

technical communique robust state estimation for uncertain discrete time stochastic systems with missing measurements in this paper results of robust estimation of zhou 2010a are extended to state estimation with missing measurements a new procedure is derived which inherits the main properties of that of zhou 2010a in this extension a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult though introducing a monotonic function and using the so called squeeze rule this new robust estimator is proved to converge to a stable system numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of wang yang daniel and liu 2005

strict contractions of symmetric cones let v be a euclidean jordan algebra with an associative inner product hji and let be the corresponding symmetric cone then the linear automorphism group h of the symmetric cone acts transitively on it let t v i be the symmetric tube domain associated to the symmetric cone and let g t be the biholomorphic automorphism group of t there exists a conformal compactification m g t p of v with respect to a parabolic subgroup p a lie semigroup that is naturally related to the symmetric cone occurs as the semigroup of compressionsof in the lie group g t fg 2 g t j g g it turns out that admits an ol shanskii decomposition h expc for an ad h invariant convex cone c in the lie algebra g t of g t a triple decomposition h 8 9 and it determines a globally hyperbolic causal order on the homogeneous space g t h defined by ah bh if and only if a 1 b 2 the family of bilinear forms x u v hp x 1 ujvi defines a hinvariant riemannian metric on where the map p is the quadratic representation of the jordan algebra v in 8 koufany showed that the elements of are contractions of for the riemannian metric the main result of this paper is that the elements of the interior of called strict compressions are strict contractions of for the riemannian distance induced by

distortion outage analysis for joint space time coding and kalman filtering in this paper we consider the scenario of transmitting a first order gauss markov vector signal over a multi input multi output mimo rayleigh nonfrequency selective fading channel the signal is reconstructed at the receiver side with the help of a kalman filter in order to minimize the mean squared error orthogonal space time codes are utilized in order to increase the quality of estimation and mitigate the destructing effects of the fading channel as a criterion for estimation quality assessment we use the distortion outage probability we first obtain upper and lower bounds for the outage probability as a function of system parameters we then perform high snr analysis of the bounds through which we prove the achievability of the maximum diversity order for a n times k mimo fading channel in addition we obtain upper and lower bounds for the coding gain of the distortion outage probability in the high snr regime and outline the relation between system parameters and the coding gain

gaussian distributions on riemannian symmetric spaces statistical learning with structured covariance matrices the riemannian geometry of covariance matrices has been essential to several successful applications in computer vision biomedical signal and image processing and radar data processing for these applications an important ongoing challenge is to develop riemannian geometric tools which are adapted to structured covariance matrices this paper proposes to meet this challenge by introducing a new class of probability distributions gaussian distributions of structured covariance matrices these are riemannian analogs of gaussian distributions which only sample from covariance matrices having a preassigned structure such as complex toeplitz or block toeplitz the usefulness of these distributions stems from three features 1 they are completely tractable analytically or numerically when dealing with large covariance matrices 2 they provide a statistical foundation to the concept of structured riemannian barycentre i e frechet or geometric mean and 3 they lead to efficient statistical learning algorithms which realise among others density estimation and classification of structured covariance matrices this paper starts from the observation that several spaces of structured covariance matrices considered from a geometric point of view are riemannian symmetric spaces accordingly it develops an original theory of gaussian distributions on riemannian symmetric spaces of their statistical inference and of their relationship to the concept of riemannian barycentre then it uses this original theory to give a detailed description of gaussian distributions of three kinds of structured covariance matrices complex toeplitz and block toeplitz finally it describes algorithms for density estimation and classification of structured covariance matrices based on gaussian distribution mixture models

robust filtering for linear systems with convex bounded uncertain time varying parameters this note addresses the design of robust h2 filters for linear systems with a state space model subject to time varying uncertain parameters with limited variation the uncertain parameters and their rate of variation are assumed to belong to a given convex bounded polyhedral domain a method based on a parameter dependent lyapunov function is proposed for designing a linear stationary asymptotically stable filter with a guaranteed average error variance irrespective of the uncertain parameters the proposed design is formulated in terms of linear matrix inequalities

on the solution of the nonlinear matrix equation xn f x abstract we consider a class of nonlinear matrix equations x n f x 0 where f is a self map on the convex cone p k of k k positive definite real matrices it is shown that for n 2 the matrix equation has a unique positive definite solution depending continuously on the function f if f belongs to the semigroup of nonexpansive mappings with respect to the gl k r invariant riemannian metric distance on p k which contains congruence transformations translations the matrix inversion and in particular symplectic hamiltonians appearing in kalman filtering we show that the sequence of positive definite solutions varying over n 2 converges always to the identity matrix

beta negative binomial auto regressions for modelling integer valued time series with extreme observations the paper introduces a general class of heavy tailed auto regressions for modelling integer valued time series with outliers the specification proposed is based on a heavy tailed mixture of negative binomial distributions that features an observation driven dynamic equation for the conditional expectation the existence of a stationary and ergodic solution for the class of auto regressive processes is shown under general conditions the estimation of the model can be easily performed by maximum likelihood given the closed form of the likelihood function the strong consistency and the asymptotic normality of the estimator are formally derived two examples of specifications illustrate the flexibility of the approach and the relevance of the theoretical results in particular a linear dynamic equation and a score driven equation for the conditional expectation are studied the score driven specification is shown to be particularly appealing as it delivers a robust filtering method that attenuates the effect of outliers empirical applications to the series of narcotics trafficking reports in sydney and the euro pound sterling exchange rate illustrate the effectiveness of the method in handling extreme observations

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

asymptotic behavior of recursive state estimations with intermittent measurements convergence rate and stationary distribution approximation are investigated in this paper for both the covariance matrix of the kalman filter and the pseudo covariance matrix of a robust recursive state estimator developed by us when the measurement dropping process is described by a markov chain and an associated plant is both controllable and observable it is proved that if the dropping probability is less than 1 these two matrices converge exponentially to a stationary distribution independent of its initial values moreover when they are initialized with the stabilizing solution of an associated algebraic riccati equation both of them are shown to converge to an ergodic process based on these results two approximations are derived for their stationary probability distributions as well as a bound of approximation errors it has been made clear that rather than the delta function suggested by kar and moura a series of delta functions give a more accurate approximation and replacement of these estimators update gain by a constant matrix usually deteriorates their steady estimation accuracy a numerical example is provided to illustrate the obtained theoretical results

linear minimum mean square error estimation for discrete time markovian jump linear systems the linear minimum mean square error estimator lmmse for discrete time linear systems subject to abrupt changes in the parameters modeled by a markov chain spl theta k spl epsiv 1 n is considered the filter equations are derived from geometric arguments in a recursive form resulting in an on line algorithm suitable for computer implementation the author s approach is based on estimating x k 1 sub spl theta k i instead of estimating directly x k the uncertainty introduced by the markovian jumps increases the dimension of the filter to n n 1 where n is the dimension of the state variable an example where the dimension of the filter can be reduced to n is presented as well as a numerical comparison with the imm filter

diversity effects in kalman filtering over rayleigh fading channels a scalar first order gauss markov signal is sent over d parallel i i d rayleigh fading channels using uncoded transmission assuming perfect channel estimation at the receiver the optimal mmse estimator is the kalman filter with random instantaneous estimation error variance statistical characteristics of the instantaneous estimation error variance are studied to characterize the estimation quality one such characteristic is the estimation error outage which probabilistically depicts how often the value of the instantaneous estimation error variance exceeds a certain threshold in this paper we study the effect of channel diversity on the estimation error outage probability we show that for a certain range of outage thresholds the estimation error outage probability decreases with inverse of d th power of the average signal to noise ratio at the receiver side this means that analogous to the context of digital communication over fading channels our result implies a diversity order of d in estimating the input process

moderate deviations of a random riccati equation the paper characterizes the invariant filtering measures resulting from kalman filtering with intermittent observations in which the observation arrival is modeled as a bernoulli process with packet arrival probability our prior work showed that for 0 the sequence of random conditional error covariance matrices converges weakly to a unique invariant distribution this paper shows that as approaches one the family 0 satisfies a moderate deviations principle with good rate function i 1 as 1 the family converges weakly to the dirac measure p concentrated on the fixed point of the associated discrete time riccati operator 2 the probability of a rare event an event bounded away from p under decays to zero as a power law of 1 as 1 and 3 the best power law decay exponent is obtained by solving a deterministic variational problem involving the rate function i for specific scenarios the paper develops computationally tractable methods that lead to efficient estimates of rare event probabilities under

robust recursive state estimation with random measurement droppings a recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings this estimator has a similar form as that of kalman filter with intermittent observations but its parameters should be adjusted when a plant output measurement arrives a new recursive form is derived for the pseudo covariance matrix of estimation errors based on a riemannian metric for positive definite matrices some necessary and sufficient conditions have been obtained for the strict contractiveness of this recursion it has also been proved that under some controllability and observability conditions as well as some weak requirements on measurement arrival probability the update gain of this recursive robust state estimator and the mean of its squared estimation errors converge in probability one respectively to a corresponding stationary distribution numerical simulation results show that estimation accuracy of the suggested procedure is more robust against parametric modelling errors than kalman filter

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

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

asymptotic normality of the quasi maximum likelihood estimator for multidimensional causal processes strong consistency and asymptotic normality of the quasi maximum likelihood estimator qmle are given for a general class of multidimensional causal processes for particular cases already studied in the literature for instance univariate or multivariate garch arch arma garch processes the assumptions required for establishing these results are often weaker than existing conditions the qmle asymptotic behavior is also given for numerous new examples of univariate or multivariate processes for instance tarch or nlarch processes

convergence of nonlinear observers on bbr n with a riemannian metric part i we study how convergence of an observer whose state lives in a copy of the given system s space can be established using a riemannian metric we show that the existence of an observer guaranteeing the property that a riemannian distance between system and observer solutions is nonincreasing implies that the lie derivative of the riemannian metric along the system vector field is conditionally negative moreover we establish that the existence of this metric is related to the observability of the system s linearization along its solutions moreover if the observer has an infinite gain margin then the level sets of the output function are geodesically convex conversely we establish that if a complete riemannian metric has a lie derivative along the system vector field that is conditionally negative and is such that the output function has a monotonicity property then there exists an observer with an infinite gain margin

intrinsically bayesian robust kalman filter an innovation process approach in many contemporary engineering problems model uncertainty is inherent because accurate system identification is virtually impossible owing to system complexity or lack of data on account of availability time or cost the situation can be treated by assuming that the true model belongs to an uncertainty class of models in this context an intrinsically bayesian robust ibr filter is one that is optimal relative to the cost function in the classical sense and the prior distribution over the uncertainty class in the bayesian sense ibr filters have previously been found for both wiener and granulometric morphological filtering in this paper we derive the ibr kalman filter that performs optimally relative to an uncertainty class of state space models introducing the notion of bayesian innovation process and the bayesian orthogonality principle we show how the problem of designing an ibr kalman filter can be reduced to a recursive system similar to the classical kalman recursive equations except with effective counterparts such as the effective kalman gain matrix after deriving the recursive ibr kalman equations for discrete time we use the limiting method to obtain the ibr kalman bucy equations for continuous time finally we demonstrate the utility of the proposed framework for two real world problems sensor networks and gene regulatory network inference

h filtering for linear periodic systems with parameter uncertainty abstract this paper focuses on h filtering for a class of linear periodic systems with a certain type of norm bounded time varying parameter uncertainty which appears in both the state and output matrices the problem addressed is the design of a linear periodic estimator that guarantees both the quadratic stability and and prescribed h performance on infinite horizon for the estimation error for all admissible parameter uncertainties a solution to this problem is obtained via a riccati equation approach

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

mixed norm h 2 h regulation and estimation the discrete time case abstract a discrete time h2 static output feedback design problem involving a constraint on h disturbance attenuation is addressed and state space formulae are derived the dual problem of discrete time dynamic estimation with an h error bound is also addressed these results are analogous to results obtained previously for the continuous time problem

a framework for state space estimation with uncertain models develops a framework for state space estimation when the parameters of the underlying linear model are subject to uncertainties compared with existing robust filters the proposed filters perform regularization rather than deregularization it is shown that under certain stabilizability and detectability conditions the steady state filters are stable and that for quadratically stable models the filters guarantee a bounded error variance moreover the resulting filter structures are similar to various time and measurement update prediction and information forms of the kalman filter albeit ones that operate on corrected parameters rather than on the given nominal parameters simulation results and comparisons with spl hscr sub spl infin guaranteed cost and set valued state estimation filters are provided

set membership filtering for discrete time systems with nonlinear equality constraints in this technical note the problem of set membership filtering is considered for discrete time systems with nonlinear equality constraint between their state variables the nonlinear equality constraint is first linearized and transformed into a state linear equality constraint with two uncertain quantities related to linearizing truncation error and base point error s procedure method is then applied to merge all inequalities into one inequality and the solution to the unconstrained set membership filtering problem is provided the set membership filter with state constraint is finally derived from projecting the unconstrained set membership filter onto the constrained surface by using finsler s lemma a time varying linear matrix inequality optimization based approach is proposed to design the set membership filter with nonlinear equality constraint a recursive algorithm is developed for computing the state estimate ellipsoid that guarantees to contain the true state an illustrative example is provided to demonstrate the effectiveness of the proposed set membership filtering with nonlinear equality constraint

an energy minimizing interpolation for robust multigrid methods we propose a robust interpolation for multigrid based on the concepts of energy minimization and approximation it can handle pde coefficients of various types on structured or unstructured grids under one framework the formulation is general it can be applied to any dimension we demonstrate numerically the effectiveness of the multigrid method in two dimensions by applying it to a discontinuous coefficient problem an oscillatory coefficient problem and an anisotropic problem empirically the convergence rate is independent of the coefficients of the underlying pde in addition to being independent of the mesh size the proposed method is primarily designed for second order elliptic pdes with possible extensions to other classes of problems such as integral equations

mean square stability for kalman filtering with markovian packet losses this paper studies the stability of kalman filtering over a network subject to random packet losses which are modeled by a time homogeneous ergodic markov process for second order systems necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure while for certain classes of higher order systems necessary and sufficient conditions are also provided to ensure stability of the mean estimation error covariance matrices all stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the markov process their implications and relationships with related results in the literature are discussed

nonexpansiveness of the resolvent average abstract we show that the resolvent average for positive definite matrices which interpolates between the harmonic and the arithmetic means contracts the thompson metric on the convex cone of positive definite matrices classical results depending on the nonexpansive property of the arithmetic average are considered in the context of the resolvent average in particular resolvent power mean approximation to the karcher mean and ferrante and levy like matrix equations are investigated

brief paper optimal estimation of linear discrete time systems with stochastic parameters this paper considers optimal linear state estimation in the general case of linear discrete time systems with stochastic parameters which are statistically independent with respect to time the estimator is derived by transforming the system to one with deterministic parameters and state dependent additive system and observation noise it is shown that mean square stability of the system is a sufficient and almost necessary condition for the existence uniqueness and stability of the time invariant estimator

mutual information of wireless channels and block jacobi ergodic operators shannon s mutual information of a random multiple antenna and multipath time varying channel is studied in the general case where the process constructed from the channel coefficients is an ergodic and stationary process which is assumed to be available at the receiver from this viewpoint the channel can also be represented by an ergodic self adjoint block jacobi operator which is close in many aspects to a block version of a random schrodinger operator the mutual information is then related to the so called density of states of this operator in this paper it is shown that under the weakest assumptions on the channel the mutual information can be expressed in terms of a matrix valued stochastic process coupled with the channel process this allows numerical approximations of the mutual information in this general setting moreover assuming further that the channel coefficient process is a markov process a representation for the mutual information offset in the large signal to noise ratio regime is obtained in terms of another related markov process this generalizes previous results from levy et al it is also illustrated how the mutual information expressions that are closely related to those predicted by the random matrix theory can be recovered in the large dimensional regime

wulff construction and anisotropic surface properties of two dimensional eden clusters a relation between the shape of eden clusters and the number of perimeter sites per unit area of the surface is derived which is analogous to the wulff construction of equilibrium shapes in thermodynamic systems new data are presented for the surface width and the surface skewness of eden clusters grown on a square lattice the width depends on the average orientation of the surface with respect to the underlying lattice its corrections to scaling are discussed the skewness has unexpected changes of sign

regularized robust filters for time varying uncertain discrete time systems this note develops robust filters for time varying uncertain discrete time systems the developed filters are based on a data regularization solution and they enforce a minimum state error variance property simulation results confirm their superior performance over other robust filter designs

multiobjective filter design for uncertain stochastic time delay systems this note addresses the problem of robust multiobjective filtering for discrete time delay systems with mixed stochastic and deterministic uncertainties in addition to unmodeled nonlinearities a procedure is developed for the design of linear and exponentially stable filters with a bounded error variance exponential rate of decay and robust performance for the error system

performance of ensemble kalman filters in large dimensions contemporary data assimilation often involves more than a million prediction variables ensemble kalman filters enkf have been developed by geoscientists they are successful indispensable tools in science and engineering because they allow for computationally cheap low ensemble state approximation for extremely large dimensional turbulent dynamical systems the practical finite ensemble filters like enkf necessarily involve modifications such as covariance inflation and localization and it is a genuine mystery why they perform so well with small ensemble sizes in large dimensions this paper provides the first rigorous stochastic analysis of the accuracy and covariance fidelity of enkf in the practical regime where the ensemble size is much smaller than the large ambient dimension for enkfs with random coefficients a challenging issue overcome here is that enkf in huge dimensions introduces unavoidable bias and model errors that need to be controlled and estimated 2017 the authors communications on pure and applied mathematics is published by the courant institute of mathematics and wiley periodicals inc

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

multigrid in h div and h curl summary we consider the solution of systems of linear algebraic equations which arise from the finite element discretization of variational problems posed in the hilbert spaces bf h div and bf h curl in three dimensions we show that if appropriate finite element spaces and appropriate additive or multiplicative schwarz smoothers are used then the multigrid v cycle is an efficient solver and preconditioner for the discrete operator all results are uniform with respect to the mesh size the number of mesh levels and weights on the two terms in the inner products

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

toward an h independent algebraic multigrid method for maxwell s equations we propose a new algebraic multigrid amg method for solving the eddy current approximations to maxwell s equations this amg method has its roots in an algorithm proposed by reitzinger and schoberl the main focus in the reitzinger and schoberl method is to maintain null space properties of the weak nabla times nabla times operator on coarse grids while these null space properties are critical they are not enough to guarantee h independent convergence rates of the overall multigrid scheme we present a new strategy for choosing intergrid transfers that not only maintains the important null space properties on coarse grids but also yields significantly improved multigrid convergence rates this improvement is related to those we explored in a previous paper but is fundamentally simpler easier to compute and performs better with respect to both multigrid operator complexity and convergence rates the new strategy builds on ideas in smoothed aggregation to improve the approximation property of an existing interpolation operator by carefully choosing the smoothing operators we show how it is sometimes possible to achieve h independent convergence rates with a modest increase in multigrid operator complexity though this ideal case is not always possible the overall algorithm performs significantly better than the original scheme in both iterations and run time finally the reitzinger and schoberl method as well as our previous smoothed method are shown to be special cases of this new algorithm

on asymptotic behaviors of a sensitivity penalization based robust state estimator abstract asymptotic properties are investigated in this paper for the robust state estimator derived by zhou 2008 11 a new formula is derived for the update of the pseudo covariance matrix of estimation errors in the case where plant nominal parameters are time invariant it is shown that in order to guarantee that this pseudo covariance matrix converges to a constant positive definite matrix it is necessary and sufficient that some stabilizability and detectability conditions are satisfied it is also proved that when these conditions are satisfied the robust estimator converges to a stable time invariant system moreover when the system is exponentially stable this estimate is asymptotically unbiased and its estimation errors are upper bounded

optimal linear state estimation over a packet dropping network using linear temporal coding we consider the problem of linear minimum mean square error estimation for a discrete time system over a packet dropping network in order to improve the estimation performance different from the standard approach of sending the current measurement data we choose sending a linear combination of the current measurement and the measurement collected at the previous time a method called linear temporal coding we assume the packet arrival sequence is unknown and the noise contained in the packet may come from sensor or communication channel in an effort to cope with colored noise caused by measurement combination after comparing with the classic state augmentation approach and measurement differencing approach we derive a recursive estimation algorithm by means of orthogonal projection principle and innovation sequence approach our algorithm consists of two parts smooth and estimate for large measurement noise case numerical example shows the benefit of using linear temporal coding strategy compared with directly sending the current data on the contrary when communication noise plays the dominating role for scalar system we prove there is no benefit to choose this scheme

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

gossip and distributed kalman filtering weak consensus under weak detectability the paper presents the gossip interactive kalman filter gikf for distributed kalman filtering for networked systems and sensor networks where intersensor communication and observations occur at the same time scale the communication among sensors is random each sensor occasionally exchanges its filtering state information with a neighbor depending on the availability of the appropriate network link we show that under a weak distributed detectability condition 1 the gikf error process remains stochastically bounded irrespective of the instability of the random process dynamics and 2 the network achieves weak consensus i e the conditional estimation error covariance at a uniformly randomly selected sensor converges in distribution to a unique invariant measure on the space of positive semidefinite matrices independent of the initial state to prove these results we interpret the filtering states estimates and error covariances at each node in the gikf as stochastic particles with local interactions we analyze the asymptotic properties of the error process by studying as a random dynamical system the associated switched random riccati equation the switching being dictated by a nonstationary markov chain on the network graph

the contraction rate in thompson s part metric of order preserving flows on a cone application to generalized riccati equations abstract we give a formula for the lipschitz constant in thompson s part metric of any order preserving flow on the interior of a possibly infinite dimensional closed convex pointed cone this shows that in the special case of order preserving flows a general characterization of the contraction rate in thompson s part metric given by nussbaum leads to an explicit formula as an application we show that the flow of the generalized riccati equation arising in stochastic linear quadratic control is a local contraction on the cone of positive definite matrices and characterize its lipschitz constant by a matrix inequality we also show that the same flow is no longer a contraction in other invariant finsler metrics on this cone including the standard invariant riemannian metric this is motivated by a series of contraction properties concerning the standard riccati equation established by bougerol liverani wojtkowski lawson lee and lim we show that some of these properties do and that some other do not carry over to the generalized riccati equation

robust filtering for linear time invariant continuous systems the problem of robust filtering for linear time invariant lti continuous systems subject to parametric uncertainties is treated in this paper through transfer function and polynomial representations and then in the state space domain the basic idea consists of introducing the gradient of the estimation error with respect to the uncertain parameters in the optimization scheme via a epsiv contaminated model the general solution to the problem is given in the transfer function representation while in the polynomial framework the causal estimator is obtained by means of a spectral factorization and a diophantine equation the state space realization of the causal estimator is discussed examples show the ability of the proposed technique to provide a reliable estimation in presence of model uncertainty

an improved algebraic multigrid method for solving maxwell s equations we propose two improvements to the reitzinger and schoberl algebraic multigrid amg method for solving the eddy current approximations to maxwell s equations the main focus in the reitzinger schoberl method is to maintain null space properties of the weak nabla times nabla times operator on coarse grids while these null space properties are critical they are not enough to guarantee h independent convergence of the overall multigrid method we illustrate how the reitzinger schoberl amg method loses h independence due to the somewhat limited approximation property of the grid transfer operators we present two improvements to these operators that not only maintain the important null space properties on coarse grids but also yield significantly improved multigrid convergence rates the first improvement is based on smoothing the reitzinger schoberl grid transfer operators the second improvement is obtained by using higher order nodal interpolation to derive the corresponding amg interpolation operators while not completely h independent the resulting amg cg method demonstrates improved convergence behavior while maintaining low operator complexity

dynamic scaling and phase transitions in interface growth abstract the dynamic scaling approach is an effective tool for understanding the temporal evolution of fluctuating interfaces the surface width w obeys the scaling form w l t l t l where and are exponents which characterize how the surface width grows with the length scale l and the time t applications of dynamic scaling to a number of surface growth models are discussed the results of a large scale simulation of the ballistic deposition model in three dimensions are presented and compared with recent conjectures the question of universality in interface growth is addressed and a finite temperature generalization of the restricted solid on solid model is studied this model appears to undergo a phase transition from the usual rough phase at high temperatures to a new phase at low temperatures numerical solutions of the generalized langevin equation indicate that there is no phase transition in 2 1 dimensions thus the relation between the continuum equation and the discrete models is still an open question

exact de rham sequences of spaces defined on macro elements in two and three spatial dimensions this paper proposes new finite element spaces that can be constructed for agglomerates of standard elements that have certain regular structure the main requirement is that the agglomerates share faces that have closed boundaries composed of 1 d edges the spaces resulting from the agglomerated elements are subspaces of the original de rham sequence of h 1 conforming h mathbf curl conforming h mathbf div conforming and piecewise constant spaces associated with an unstructured fine mesh the procedure can be recursively applied so that a sequence of nested de rham complexes can be constructed as an illustration we generate coarser spaces from the sequence corresponding to the lowest order nedelec spaces lowest order raviart thomas spaces and for piecewise linear h 1 conforming spaces all in three dimensions the resulting v cycle multigrid methods used in preconditioned conjugate gradient iterations appear to perform similar to those of the geometrically refined case

finsler metrics on symmetric cones let v be a simple euclidean jordan algebra with an associative inner product langle cdot cdot rangle and let omega be the corresponding symmetric cone let mathcal j v be the compact symmetric space of all primitive idempotents of v we show that the function s a b defined by

optimal linear state estimator with multiple packet dropouts this technical note is concerned with the optimal linear estimation problem in the presence of multiple packet dropouts in both sensor to controller and controller to actuator channels the considered stochastic packet dropouts are independent and bernoulli distributed based on a linear packet dropout model with stochastic parameters a linear minimum variance lmv filter is proposed using the orthogonality principle a sufficient condition for convergence of the steady state lmv filter under a dc controller output is also given simulation results show the effectiveness of the proposed filter

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

robust h sub 2 h sub spl infin state estimation for systems with error variance constraints the continuous time case the paper is concerned with the state estimator design problem for perturbed linear continuous time systems with h sub spl infin norm and variance constraints the perturbation is assumed to be time invariant and norm bounded and enters into both the state and measurement matrices the problem we address is to design a linear state estimator such that for all admissible measurable perturbations the variance of the estimation error of each state is not more than the individual prespecified value and the transfer function from disturbances to error state outputs satisfies the prespecified h sub spl infin norm upper bound constraint simultaneously existence conditions of the desired estimators are derived in terms of riccati type matrix inequalities and the analytical expression of these estimators is also presented a numerical example is provided to show the directness and effectiveness of the proposed design approach

coordinated one step optimal distributed state prediction for a networked dynamical system a new recursive one step state prediction procedure is derived for a networked dynamic system under the coordination of a collaboration unit that provides optimal update gains for each individual subsystem utilizing merely system parameters this predictor estimates plant s local states based only on local system output measurements this estimator can be easily realized in a distributed way and can also be simply scaled to systems with a large amount of subsystems provided it has enough communication and storage capacities it is proved that when prediction error variances are adopted in performance comparisons the optimal gain matrix is usually unique recursive and explicit expressions are derived for both this optimal gain matrix and the covariance matrix of the corresponding prediction errors the optimal gain matrix for every subsystem in this distributed recursive predictor has been shown to be equal to that of the well known kalman filter utilizing only local system output measurements which makes it possible to robustify this state predictor using a sensitivity penalization approach numerical simulation results illustrate that prediction accuracy of the suggested procedure may sometimes be as good as that of the lumped kalman filter