strong detectability and observers conditions are given for the existence of observers that estimate unmeasured outputs on the basis of partial information on the input and the state the concepts of strong detectability and strong observability introduced before in the literature for discrete time systems only are defined and studied for continuous time systems it is shown that there are two different concepts of strong detectability which coincide for discrete time systems algebraic conditions for either concept are given it is shown that these concepts are intimately related to the existence of strong observers i e observers that only use the output of the plant

infinite horizon stochastic h2 h control for discrete time systems with state and disturbance dependent noise this paper studies the infinite horizon mixed h 2 h control for discrete time stochastic systems with state and disturbance dependent noise we shall first establish a version of stochastic bounded real lemma sbrl which by itself has theoretical importance based on the sbrl it is shown that under the condition of exact observability the existence of a static state feedback h 2 h controller is equivalent to the solvability of four coupled matrix valued equations a suboptimal h 2 h controller design is given based on a convex optimization approach and an iterative algorithm is proposed to solve the four coupled matrix valued equations

a minimaxity criterion in nonparametric regression based on large deviations probabilities a large deviations criterion is proposed for optimality of nonparametric regression estimators the criterion is one of minimaxity of the large deviations probabilities we study the case where the underlying class of regression functions is either lipschitz or holder and when the loss function involves estimation at a point or in supremum norm exact minimax asymptotics are found in the gaussian case

brief paper h filtering for uncertain stochastic time delay systems with sector bounded nonlinearities in this paper we deal with the robust h filtering problem for a class of uncertain nonlinear time delay stochastic systems the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delays as well as sector bounded nonlinearities we aim at designing a full order filter such that for all admissible uncertainties nonlinearities and time delays the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square while achieving the prescribed h disturbance rejection attenuation level by using the lyapunov stability theory and ito s differential rule sufficient conditions are first established to ensure the existence of the desired filters which are expressed in the form of a linear matrix inequality lmi then the explicit expression of the desired filter gains is also characterized finally a numerical example is exploited to show the usefulness of the results derived

quantum limits to information about states for finite dimensional hilbert space a refined bound for the correlation information of an n trial apparatus is developed via an heuristic argument for hilbert spaces of arbitrary finite dimensionality conditional upon the proof of an easily motivated in equality the author then finds the optimal apparatus for large ensemble quantum inference thereby solving the asymptotic optimal state determination problem in this way he identifies an alternative inferential uncertainty principle which is then contrasted with the usual heisenberg uncertainty principle

asymptotic estimation theory for a finite dimensional pure state model the optimization of measurement for n samples of pure states are studied the error of the optimal measurement for n samples is asymptotically compared with the one of the maximum likelihood estimators from n data given by the optimal measurement for one sample

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

recursive state estimation for two dimensional shift varying systems with random parameter perturbation and dynamical bias abstract in this paper the state estimation problem is investigated for a class of two dimensional 2 d stochastic systems with shift varying parameters the stochasticity with the underlying system comes from three sources namely random parameter perturbations dynamical biases and additive white noises the measurement output is subject to the uniform quantization as a result of communication constraints on the sensors the purpose of the addressed problem is to recursively estimate the system states with prescribed estimation performance in spite of the stochastic disturbances and the uniform quantizations an augmented model is first constructed to combine the information about the state and the bias and the dynamical evolution is subsequently discussed furthermore through stochastic analysis and mathematical induction the estimator design algorithm is developed to acquire certain upper bound on the estimation error variance and such an upper bound is then minimized in the matrix trace sense moreover the boundedness issue of the estimation errors is investigated via matrix inversion lemma and inductive analysis technique finally the effectiveness of the proposed state estimation algorithm is validated on a typical 2 d system modeled by the well known darboux equation with extensive application potentials in industrial processes

ergodicity of the 2d navier stokes equations with random forcing we consider the navier stokes equation on a two dimensional torus with a random force acting at discrete times and analytic in space for arbitrarily small viscosity coefficient we prove the existence and uniqueness of the invariant measure for this system as well as exponential mixing in time

stochastic dissipative pde s and gibbs measures we study a class of dissipative nonlinear pde s forced by a random force omega t x with the space variable x varying in a bounded domain the class contains the 2d navier stokes equations under periodic or dirichlet boundary conditions and the forces we consider are those common in statistical hydrodynamics they are random fields smooth in t and stationary short correlated in time t in this paper we confine ourselves to kick forces of the form where the k s are smooth bounded identically distributed random fields the equation in question defines a markov chain in an appropriately chosen phase space a subset of a function space that contains the zero function and is invariant for the random flow of the equation concerning this markov chain we prove the following main result see theorem 2 2 the markov chain has a unique invariant measure to prove this theorem we present a construction assigning to any invariant measure a gibbs measure for a 1d system with compact phase space and apply a version of ruelle perron frobenius uniqueness theorem to the corresponding gibbs system we also discuss ergodic properties of the invariant measure and corresponding properties of the original randomly forced pde

attaining the ultimate precision limit in quantum state estimation we derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non degenerate our results hold under an assumption called local asymptotic covariance which is weaker than unbiasedness or local unbiasedness the derivation is based on an analysis of the limiting distribution of the estimator s deviation from the true value of the parameter and takes advantage of quantum local asymptotic normality a useful asymptotic characterization of identically prepared states in terms of gaussian states we first prove our results for the mean square error of a special class of models called d invariant and then extend the results to arbitrary models generic cost functions and global state estimation where the unknown parameter is not restricted to a local neighbourhood of the true value the extension includes a treatment of nuisance parameters i e parameters that are not of interest to the experimenter but nevertheless affect the precision of the estimation as an illustration of the general approach we provide the optimal estimation strategies for the joint measurement of two qubit observables for the estimation of qubit states in the presence of amplitude damping noise and for noisy multiphase estimation

finite horizon h_ infty filtering with missing measurements and quantization effects in this paper a new h filtering approach is developed for a class of discrete time varying systems subject to missing measurements and quantization effects the missing measurements are modeled via a diagonal matrix consisting of a series of mutually independent random variables satisfying certain probabilistic distributions on the interval 0 1 the measured output is quantized by a logarithmic quantizer attention is focused on the design of a stochastic h filter such that the h estimation performance is guaranteed over a given finite horizon in the simultaneous presence of probabilistic missing measurements quantization effects as well as external non gaussian disturbances a necessary and sufficient condition is first established for the existence of the desired time varying filters in virtue of the solvability of certain coupled recursive riccati difference equations rdes owing to its recursive nature the proposed rde approach is shown to be suitable for online application without the need of increasing the problem size the simulation experiment is carried out for the mobile robot localization problem with non gaussian disturbances missing measurements and quantization effects the effectiveness of the proposed method is demonstrated in the numerical example

existence of densities for the 3d navier stokes equations driven by gaussian noise we prove three results on the existence of densities for the laws of finite dimensional functionals of the solutions of the stochastic navier stokes equations in dimension 3 in particular under very mild assumptions on the noise we prove that finite dimensional projections of the solutions have densities with respect to the lebesgue measure which have some smoothness when measured in a besov space this is proved thanks to a new argument inspired by an idea introduced in fournier and printems 2010

a kalman filtering derivation of simultaneous input and state estimation abstract simultaneous input and state estimation algorithms are studied as particular limits of kalman filtering problems this admits interpretation of the algorithm properties and critical analysis of their claims to being partly model free and to providing unbiased estimates a disturbance model white noise of unbounded variance is provided and the bias feature is shown to be a geometric projection property rather than probabilistic in nature as a consequence of this analysis the algorithm is connected in the stationary case to algebraic riccati equation computations for the gains estimate covariances and filter frequency response

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

optimal filtering for systems with unknown inputs an optimal filtering formula is derived for linear time varying discrete systems with unknown inputs by making use of the well known innovations filtering technique the derivation is an extension of a new observer design method for time invariant deterministic systems with unknown inputs the systems under consideration have the most general form the derived optimal filter has a similar form to the standard kalman filter with some modified covariance and gain matrices

quantum hypothesis testing for gaussian states quantum analogues of χ 2 t and f tests we consider quantum counterparts of testing problems for which the optimal tests are the 2 t and f tests these quantum counterparts are formulated as quantum hypothesis testing problems concerning gaussian state families and they contain nuisance parameters which have group symmetry the quantum hunt stein theorem removes some of these nuisance parameters but other difficulties remain in order to remove them we combine the quantum hunt stein theorem and other reduction methods to establish a general reduction theorem that reduces a complicated quantum hypothesis testing problem to a fundamental quantum hypothesis testing problem using these methods we derive quantum counterparts of the 2 t and f tests as optimal tests in the respective settings

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

nonparametric input estimation in physiological systems problems methods and case studies input estimation from output data is an important problem in the analysis of physiological systems because many signals of interest are not directly accessible to measurement when the system is time invariant this problem is often referred to as deconvolution three representative physiological problems regarding hormone secretion insulin dynamics and hepatic glucose production are used to illustrate the major challenges ill conditioning confidence intervals assessment infrequent and nonuniform sampling nonnegativity constraints and computational efficiency the paper provides a critical overview of the existing techniques focusing on regularization theory and bayesian estimation in order to overcome some inadequacies of the existing methods some new results are derived in particular the connection between the maximum likelihood estimate of the regularization parameter and the notion of equivalent degree of freedom is studied moreover a fast svd based numerical algorithm is developed that includes the optimization of the regularization parameter and the computation of confidence intervals the proposed techniques are validated on a benchmark problem and are shown to provide effective solutions to the three physiological case studies

generalized lyapunov equation approach to state dependent stochastic stabilization detectability criterion in this paper the generalized lyapunov equation approach is used to study stochastic stabilization detectability with state multiplicative noise some practical test criteria for stochastic stabilization and detectability such as stochastic popov belevitch hautus criterion for exact detectability are obtained moreover useful properties of the generalized lyapunov equation are derived based on critical stability and exact detectability introduced in this paper as applications first the stochastic linear quadratic regulator as well as the related generalized algebraic riccati equation are discussed extensively second the infinite horizon stochastic h 2 h infin control with state and control dependent noise is also investigated which extends and improves the recently published results

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

gibbsian dynamics and ergodicity for the stochastically forced navier stokes equation we study stationary measures for the two dimensional navier stokes equation with periodic boundary condition and random forcing we prove uniqueness of the stationary measure under the condition that all determining modes are forced the main idea behind the proof is to study the gibbsian dynamics of the low modes obtained by representing the high modes as functionals of the time history of the low modes

quantum state determination estimates for information gain and some exact calculations it is known that mutually unbiased bases mubs whenever they exist are optimal in an information theoretic sense for the determination of the unknown state of a quantum ensemble such bases may not exist for most dimensions the present paper deals with information gain in some generalizations and approximations of mubs we give estimates of the information loss relative to mubs in these suboptimal choice of bases for some generalization of mubs we give exact calculations for the information gain it is calculated directly in terms of transition probabilities among the measurement bases we also give the formal solutions for the problem of quantum state tomography in these cases 1

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

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

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

exponential convergence for the stochastically forced navier stokes equations and other partially dissipative dynamics we prove that the two dimensional navier stokes equations possess an exponentially attracting invariant measure this result is in fact the consequence of a more general harris like ergodic theorem applicable to many dissipative stochastic pdes and stochastic processes with memory a simple iterated map example is also presented to help build intuition and showcase the central ideas in a less encumbered setting to analyze the iterated map a general doeblin like theorem is proven one of the main features of this paper is the novel coupling construction used to examine the ergodic theory of the non markovian processes

the small scales of the stochastic navier stokes equations under rough forcing we prove that the small scale structures of the stochastically forced navier stokes equations approach those of the naturally associated ornstein uhlenbeck process as the scales get smaller precisely we prove that the rescaled kth spatial fourier mode converges weakly on path space to an associated ornstein uhlenbeck process as k in addition we prove that the navier stokes equations and the naturally associated ornstein uhlenbeck process induce equivalent transition densities if the viscosity is replaced with hyper viscosity this gives a simple proof of unique ergodicity for the hyperviscous navier stokes system we show how different strengthened hyperviscosity produce varying levels of equivalence

beyond the swap test optimal estimation of quantum state overlap we study the estimation of the overlap between two unknown pure quantum states of a finite dimensional system given m and n copies of each type this is a fundamental primitive in quantum information processing that is commonly accomplished from the outcomes of n swap tests a joint measurement on one copy of each type whose outcome probability is a linear function of the squared overlap we show that a more precise estimate can be obtained by allowing for general collective measurements on all copies we derive the statistics of the optimal measurement and compute the optimal mean square error in the asymptotic pointwise and finite bayesian estimation settings besides we consider two strategies relying on the estimation of one or both states and show that although they are suboptimal they outperform the swap test in particular the swap test is extremely inefficient for small values of the overlap which become exponentially more likely as the dimension increases finally we show that the optimal measurement is less invasive than the swap test and study the robustness to depolarizing noise for qubit states

ergodicity of the 2 d navier stokes equation under random perturbations a 2 dimensional navier stokes equation perturbed by a sufficiently distributed white noise is considered existence of invariant measures is known from previous works the aim is to prove uniqueness of the invariant measures strong law of large numbers and convergence to equilibrium

delta method in large deviations and moderate deviations for estimators the delta method is a popular and elementary tool for deriving limiting distributions of transformed statistics while applications of asymptotic distributions do not allow one to obtain desirable accuracy of approximation for tail probabilities the large and moderate deviation theory can achieve this goal motivated by the delta method in weak convergence a general delta method in large deviations is proposed the new method can be widely applied to driving the moderate deviations of estimators and is illustrated by examples including the wilcoxon statistic the kaplan meier estimator the empirical quantile processes and the empirical copula function we also improve the existing moderate deviations results for m estimators and l statistics by the new method some applications of moderate deviations to statistical hypothesis testing are provided

technical communique unbiased minimum variance input and state estimation for linear discrete time systems with direct feedthrough this paper extends previous work on joint input and state estimation to systems with direct feedthrough of the unknown input to the output using linear minimum variance unbiased estimation a recursive filter is derived where the estimation of the state and the input are interconnected the derivation is based on the assumption that no prior knowledge about the dynamical evolution of the unknown input is available the resulting filter has the structure of the kalman filter except that the true value of the input is replaced by an optimal estimate

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

a spectral test for observability and reachability of time varying systems a spectral test for the observability and reachability of linear time invariant systems the popov belevitch hautus test is well known and serves as a powerful characterization of these properties in this paper it is shown that similar tests exist for linear time varying systems the test presented here involves a check over a subset of the spectrum of the weighted block shift known as the set of almost eigenvalues

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

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