riccati equation and em algorithm convergence for inertial navigation alignment this correspondence investigates the convergence of a kalman filter based expectation maximization em algorithm for estimating variances it is shown that if the variance estimates and the error covariances are initialized appropriately the underlying riccati equation solution and the sequence of iterations will be monotonically nonincreasing further the process noise variance estimates converge to the actual values when the measurement noise becomes negligibly small conversely when the process noise variance becomes negligible the measurement noise variance estimates asymptotically approach the true values an inertial navigation application is discussed in which performance depends on accurately estimating the process variances

fast coupled adaptation for sparse impulse responses using a partial haar transform this work presents a novel scheme for identifying the impulse response of a sparse channel the scheme consists of two adaptive filters operating sequentially the first adaptive filter adapts using a partial haar transform of the input and yields an estimate of the location of the peak of the sparse impulse response the second adaptive filter is then centered about this estimate both filters are short in comparison to the delay uncertainty of the unknown channel the principle advantage of this scheme is that two short adaptive filters can be used instead of one long adaptive filter resulting in faster overall convergence and reduced computational complexity and storage the scheme is analyzed in detail for a least mean squares lms lms lms type of structure although it can be implemented using any combination of adaptive algorithms monte carlo simulations are shown to be in good agreement with the theoretical model for the behavior of the peak estimating filter as well as for the mean square error mse behavior of the second filter

a polynomial approach to robust estimation of uncertain discrete time systems the robust estimation problem for uncertain discrete time systems is treated in this paper considering parametric uncertainties in the polynomial framework the estimator is the minimiser of a cost function written in a epsilon contaminated form uncertainties are not formally modelled it is shown that in the present context the proposed approach can be connected to stochastic modelling of uncertainties the optimal robust estimator is obtained by computing a spectral factorisation and by solving a single diophantine equation an example shows the efficiency of the proposed method

a solution to the continuous time rm h _ infty fixed interval smoother problem the minimum variance fixed interval smoother is a state space realization of the wiener solution generalized for time varying problems it involves forward and adjoint wiener hopf factor inverses in which the gains are obtained by solving a riccati equation this technical note introduces a continuous time h smoother having the structure of the minimum variance version in which the gains are obtained by solving a riccati equation that possesses an indefinite quadratic term it is shown that the smoother exhibits an increase in mean square error the error is bounded and the upper error bound is greater than that for the h filter

robust state estimation for uncertain systems with averaged integral quadratic constraints this paper considers a robust state estimation problem for a new class of uncertain systems the new uncertainty class introduced in the paper involves structured uncertainties which are required to satisfy a certain averaged integral quadratic constraint this uncertainty class combines aspects of norm bounded and stochastic uncertainty descriptions the solution to the robust state estimation problem is obtained by solving a parametrized riccati differential equation of the game type

polynomial matrix solution of the h infinity filtering problem and the relationship to riccati equation state space results a solution to the standard suboptimal h filtering problem is presented using a new polynomial systems ap proach the polynomial matrix solution is closely related to the recent h state space based riccati equation results and the links between the polynomial and state equation methodologies are demonstrated the h filter is derived by solving a special type of minimum variance filtering problem using a technique based on game theory the solution of this game problem in a stochastic setting by polynomial methods is novel the cal culation of the h filter involves a j spectral factorization and the solution of two coupled diophantine equations there are several computational advantages over previous polynomial methods for calculating h filters

h output feedback control for linear discrete time varying systems via the bounded real lemma in this paper we develop a solution to the discrete time output feedback control problem for linear time varying ltv systems the solution is developed along the strategy set up by doyle et al in 1989 and the main ingredient in its derivation is the extension of the well known bounded real lemma to a discrete time varying context developed by van der veen and verhaegen in 1995 this approach contributes to the conceptual simplicity and hence to the accessibility of the solution apart from that we treat the infinite horizon case for ltv system of non uniform state dimension and varying input and output dimension both situations can easily occur in practice for example in multirate sampled data control systems the algorithm that can be derived from the solution presented in then applied to the output feedback of a dynamical system changing from one operation point in its operation envelope to another

brief h performance of preview control systems performance of the preview control is investigated in terms of h criterion in the infinite horizon time setting the limitation of h performance in preview control action is characterized with the hamiltonian matrix by employing the property of hamiltonian matrix the solvability and analytic solution for the preview full information control problem are clarified based on an auxiliary introduced matrix riccati equation the property of resulting control law is illustrated with a numerical example

adaptive reliable h_ infty filtering against sensor failures this paper is concerned with the adaptive reliable hinfin filtering problem against sensor failures for continuous time linear systems an adaptive hinfin performance index is defined to describe the disturbance attenuation performance of systems with time varying parameter estimations by combining the linear matrix inequality lmi approach for hinfin filter design and adaptive method a method of designing adaptive reliable hinfin filters is proposed where the filter parameter matrices are updated automatically to compensate the sensor failures effects on systems based on the online estimations of eventual faults it is shown that the design condition for the newly proposed adaptive hinfin filtering is more relaxed than that for the traditional fixed gain filter design based on lmi approach an illustrative example and its simulation results are given to illustrate the effectiveness of the proposed design method

h spl infin deconvolution filtering prediction and smoothing a krein space polynomial approach this correspondence is concerned with the infinite horizon h spl infin deconvolution for discrete time invariant systems described by polynomial equations a simple frequency domain approach in krein space is developed for the deconvolution problem with the help of an arma innovation model solutions to the problems of deconvolution filtering prediction and fixed lag smoothing are obtained the estimators are calculated by performing one j spectral factorization

minimizing euclidian state estimation error for linear uncertain dynamic systems based on multisensor and multi algorithm fusion in this paper a multisensor linear dynamic system with model uncertainty and bounded noises is considered based on previously developed set valued estimation methods in terms of convex optimization we propose several efficient algorithms of centralized sensor fusion distributed sensor fusion and multi algorithm fusion to minimize the euclidian estimation error of the state vector obviously an ellipsoid box with a larger size cannot be in general guaranteed to contain another ellipsoid box with a smaller size since centers and shapes of the two ellipsoids boxes may be different from each other this fact and the complementary advantages of multiple sensors and multiple algorithms motivate us to construct multiple estimation ellipsoids boxes squashed along each entry of the state vector as much as possible respectively by using the technique of multiple differently weighted objectives then intersection fusion of these estimation ellipsoids boxes yields a final euclidian error minimized state estimate numerical examples show that the new method with multi algorithm at both the sensors and the fusion center can significantly reduce the euclidian estimation error of the state

robust spl hscr sub spl infin filtering for uncertain discrete time state delayed systems this paper addresses the problem of robust spl hscr sub spl infin filtering for linear discrete time systems subject to parameter uncertainties in the system state space model and with multiple time delays in the state variables the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain a methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed spl hscr sub spl infin performance for the filtering error irrespective of the uncertainty and the time delays the proposed design is given in terms of linear matrix inequalities which has the advantage in that it can be implemented numerically very efficiently

game theory approach to h sub spl infin optimal discrete time fixed point and fixed lag smoothing optimal h sub spl infin fixed point and fixed lag discrete time smoothing estimators are developed by applying a game theory approach a deterministic discrete time game is defined where the estimator plays against nature nature determines the system initial condition the driving input and the measurement noise whereas the estimator tries to find an estimate that brings a prescribed cost function that is based on the error of the estimation at a fixed time instant to a saddle point equilibrium the latter estimate yields the h sub spl infin optimal fixed point smoothing differently from the usual case in h sub spl infin optimal estimation and control the critical value of the scalar design parameter of the smoothing game is obtained in closed form explicitly in the terms of the corresponding h sub 2 solution unlike the h sub 2 case the recursive application of the h sub spl infin fixed point smoothing algorithm does not lead to fixed lag smoothing in the h sub spl infin norm sense the h sub spl infin fixed lag smoothing filter is derived by augmenting the state vector of the system with additional delayed states

global optimal attitude estimation using uncertainty ellipsoids a deterministic attitude estimation problem for a rigid body in a potential field with bounded attitude and angular velocity measurement errors is considered an attitude estimation algorithm that globally minimizes the attitude estimation error is obtained assuming that the initial attitude the initial angular velocity and measurement noise lie within given ellipsoidal bounds an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained the center of the uncertainty ellipsoid provides point estimates and the size of the uncertainty ellipsoid measures the accuracy of the estimates the point estimates and the uncertainty ellipsoids are propagated using a lie group variational integrator and its linearization respectively the attitude and angular velocity estimates are optimal in the sense that the sizes of the uncertainty ellipsoids are minimized

h optimal multichannel linear deconvolution filters predictors and smoothers a solution is presented to the h optimal deconvolution filtering smoothing and prediction problems for multivariable discrete linear signal processing problems a weighted h cost function is minimized where the dynamic weighting function can be chosen for robustness improvement the signal and noise sources can be correlated and signal channel dynamics can be included in the system model a brief example is presented to demonstrate the approach

an innovation approach to h sub spl infin fixed lag smoothing for continuous time varying systems this note studies the finite horizon h sub spl infin fixed lag smoothing problem for linear continuous time varying systems a technique named as reorganized innovation analysis in krein space is developed to give a necessary and sufficient condition for the existence of an h sub spl infin fixed lag smoother the condition is given in terms of the boundedness of two matrix functions which are derived from the solutions of two riccati differential equations rdes one standard h sub spl infin filtering rde and one h sub 2 type of rde examples demonstrate the proposed h sub spl infin fixed lag smoother design and the fact that the existence of an h sub spl infin smoother does not depend on the solvability of h sub spl infin filtering

robust finite horizon minimax filtering for discrete time stochastic uncertain systems we study a finite horizon robust minimax filtering problem for time varying discrete time stochastic uncertain systems the uncertainty in the system is characterized by a set of probability measures under which the stochastic noises driving the system are defined the optimal minimax filter has been found by applying techniques of risk sensitive lqg control the structure and properties of resulting filter are analyzed and compared to h and kalman filters

robust inversion based fault estimation for discrete time lpv systems the article presents a state space based fault diagnosis fd method for discrete time affine linear parameter varying lpv systems the goal of the technical note is to develop a robust and dynamic inversion based technique for systems with parameter varying representations when an additive exogenous disturbance signal perturbs the system after applying geometric concepts for explicit fault inversion a robust strategy is proposed to attenuate the effect of the unknown disturbance input signal on the fault estimation error the proposed robust observer is derived as a solution of off line linear matrix inequality lmi conditions the technical note demonstrates the viability of the novel methodology through a numerical example

asymptotic optimality of the minimum variance fixed interval smoother this correspondence investigates the asymptotic performance of the discrete time and continuous time time varying minimum variance fixed interval smoothers comparison theorems are generalized to provide sufficient conditions for the monotonic convergence of the underlying riccati equations under these conditions the energy of the estimation errors asymptotically approach a lower bound and attain lscr2 l2 stability

wavelet transform domain adaptive fir filtering this paper presents and studies two new wavelet transform domain least mean square lms algorithms the algorithms exploit the special sparse structure of the wavelet transform of wide classes of correlation matrices and their cholesky factors in order to compute a whitening transformation of the input data in the wavelet domain and minimize computational complexity the procedures differ in the exact estimates they use and in the way they identify the data dependent whitening transformation the first approach explicitly computes a sparse estimate of the wavelet domain correlation matrix of the input process it then computes the cholesky factor of that matrix and uses its inverse to whiten the input the complexity of this first approach is o n log sup 2 n in contrast the second approach computes a sparse estimate of the cholesky factor of the wavelet domain correlation matrix of the input process directly this second approach has a computational complexity of o n log n floating point operations however it requires a more complex bookkeeping procedure both algorithms have a convergence rate that is faster than that of time domain lms and discrete fourier transform dft or discrete cosine transform dct based lms procedures the paper compares the two procedures and analyzes their mean and mean square performance

a game theory approach to robust discrete time h sub spl infin estimation the deterministic robust estimation problem is formulated in the discrete time case as a zero sum two person difference game in which a statistician plays against nature the statistician tries to estimate a linear combination of the states of an uncertain linear system which is driven by nature saddle point strategies for the statistician in the above game are difficult to find a suboptimal strategy is therefore considered which guarantees an h sub spl infin performance bound on the estimation error different patterns of the information that is available to the statistician are treated and the corresponding fixed point fixed lag and fixed interval smoothing strategies are derived

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

technical communique robust state estimation and model validation for discrete time uncertain systems with a deterministic description of noise and uncertainty the paper presents a new approach to robust state estimation for a class of uncertain discrete time systems with a deterministic description of noise and uncertainty the main result is a recursive scheme for constructing an ellipsoidal state estimation set of all states consistent with the measured output and the given noise and uncertainty description the paper also includes a result on model validation whereby it can be determined if the assumed model is consistent with measured data

region based wavelet packet adaptive algorithm for identification of sparse impulse responses identification of systems with sparse impulse response encounters large applicability numerous techniques have been proposed to identify such systems efficiently one strategy that leads to specially good results is to detect the active nonzero response samples and update only the corresponding adaptive coefficients wavelet based approaches have been shown to be specially effective to this end this paper proposes a new region based wavelet packet rbwp algorithm for efficient identification of systems with sparse impulse responses with arbitrary frequency spectra and with any delay of the effective response the discrete wavelet packet transform dwpt is adaptively tailored to the energy distribution of the unknown system s response spectrum the new algorithm leads to a reduced number of active weights and to a reduced computational complexity when compared with competing wavelet based algorithms monte carlo simulation results show good performances regarding convergence speed and robustness to design parameter choice

on discrete time h sub spl infin fixed lag smoothing the h sub spl infin fixed lag smoothing problem for discrete time linear systems is considered it is well known that such a problem can be reformulated as a filtering problem for a suitable augmented system however in order to check the solvability of the smoothing problem and compute the relevant gains one must solve a riccati equation involving the augmented system matrices which is an approach that may be inefficient especially for long lags in this paper efficient algorithms are worked out that permit checking of solvability and implementation of the smoother relying only on the solution of the h sub spl infin filtering riccati equation in particular this provides a fast method to compute the minimum lag guaranteeing a desired attenuation level

robust steady state filtering for systems with deterministic and stochastic uncertainties for uncertain systems containing both deterministic and stochastic uncertainties we consider two problems of optimal filtering the first is the design of a linear time invariant filter that minimizes an upper bound on the mean energy gain between the noise affecting the system and the estimation error the second is the design of a linear time invariant filter that minimizes an upper bound on the asymptotic mean square estimation error when the plant is driven by a white noise we present filtering algorithms that solve each of these problems with the filter parameters determined via convex optimization based on linear matrix inequalities we demonstrate the performance of these robust algorithms on a numerical example consisting of the design of equalizers for a communication channel

the use of fake algebraic riccati equations for co channel demodulation this paper describes a method for nonlinear filtering based on an adaptive observer which guarantees the local stability of the linearized error system a fake algebraic riccati equation is employed in the calculation of the filter gain the design procedure attempts to produce a stable filter at the expense of optimality this contrasts with the extended kalman filter ekf which attempts to preserve optimality via its linearization procedure at the expense of stability a passivity approach is applied to deduce stability conditions for the filter error system the performance is compared with an ekf for a co channel frequency demodulation application

h sub infinity minimum error state estimation of linear stationary processes a state estimator is derived which minimizes the h sub infinity norm of the estimation error power spectrum matrix two approaches are presented the first achieves the optimal estimator in the frequency domain by finding the filter transfer function matrix that leads to an equalizing solution the second approach establishes a duality between the problem of h sub infinity filtering and the problem of unconstrained input h sub infinity optimal regulation using this duality previously published results for the latter regulation problem are applied which lead to an optimal filter that possess the structure of the corresponding kalman filter the two approaches usually lead to different results they are compared by a simple example which also demonstrates a clear advantage of the h sub infinity estimate over the conventional l sub 2 estimate

transform domain lms algorithm the concept of transform domain adaptive filtering is introduced in certain applications filtering in the transform domain results in great improvements in convergence rate over the conventional time domain adaptive filtering the relationship between several existing frequency domain adaptive filtering algorithms is established applications of the discrete fourier transform dft and the discrete cosine transform dct domain adaptive filtering algorithms in the areas of speech processing and adaptive line enhancers are discussed

on linear h sup spl infin equalization of communication channels as an alternative to existing techniques and algorithms we investigate the merit of the h sup spl infin approach to the linear equalization of communication channels we first give the formulation of all causal h sup spl infin equalizers using the results of and then look at the finite delay ease we compare the risk sensitive h sup spl infin equalizer with the mmse equalizer with respect to both the average and the worst case ber performances and illustrate the improvement due to the use of the h sup spl infin equalizer

brief paper minimax fir smoothers for deterministic continuous time state space models in order to design a smoother for a deterministic continuous time state space model a new performance criterion is proposed which is given by a ratio of the current estimation error to the weighted energy of the deterministic disturbance applied during the recent finite horizon among smoothers with the deadbeat property and finite impulse response fir structure a minimax fir smoother mfs is obtained to optimize the proposed performance criterion to begin with the functional optimization problem is formulated with respect to kernel functions of the mfs and then its solution is explicitly presented the mfs depends only on inputs and outputs on the finite recent horizon and is independent of any a priori state information the mfs is first represented in an integral form for simple representation and then a differential form is introduced for efficient numerical computation as in h iir smoothing and h 2 iir filtering it is shown that the proposed mfs for a deterministic system can be interpreted as the minimum variance unbiased fir smoother for a stochastic system

l_ 2 e fir smoothers for deterministic discrete time state space signal models in this note a new type of l2 e performance criterion for a fixed lag smoother is introduced which is given by a gain between the energy of the external disturbances during the recent time horizon and the estimation error at the fixed delayed time from the current one by minimizing the maximum value of the l2 e performance criterion the l2 e finite impulse response fir smoother lefs is obtained for a deterministic discrete time state space signal model the lets is designed to meet requirements such as linearity and fir structure with respect to measured inputs and outputs unbiased property in the deterministic sense and independence of any state information simultaneously the proposed lets is represented in a batch form for simplicity the lets is compared with a conventional h infin infinite impulse response iir smoother via simulation

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

probability guaranteed h finite horizon filtering for a class of nonlinear time varying systems with sensor saturations in this paper the probability guaranteed h finite horizon filtering problem is investigated for a class of nonlinear time varying systems with uncertain parameters and sensor saturations the system matrices are functions of mutually independent stochastic variables that obey uniform distributions over known finite ranges attention is focused on the construction of a time varying filter such that the prescribed h performance requirement can be guaranteed with probability constraint by using the difference linear matrix inequalities dlmis approach sufficient conditions are established to guarantee the desired performance of the designed finite horizon filter the time varying filter gains can be obtained in terms of the feasible solutions of a set of dlmis that can be recursively solved by using the semi definite programming method a computational algorithm is specifically developed for the addressed probability guaranteed h finite horizon filtering problem finally a simulation example is given to illustrate the effectiveness of the proposed filtering scheme 2012 elsevier b v all rights reserved

h filter design for discrete delay systems a new parameter dependent approach this article revisits the problem of h filtering for discrete time systems with a time varying delay in the state and parameter uncertainties residing in a polytope by utilising the polynomially parameter dependent idea a new filter design procedure is proposed which formulates the existence of admissible robust h filters into a set of linear matrix inequalities these conditions are developed based on homogeneous polynomially parameter dependent matrices of an arbitrary degree as the degree grows test of increasing precision is obtained providing less conservative filter designs it is established that the results in the quadratic framework that entail fixed matrices for the entire uncertainty domain and the linearly parameter dependent framework that use linear convex combinations of matrices are special cases of the proposed conditions for the zeroth degree and the first degree respectively moreover in addition to parameter dependence the obtained conditions are also dependent on both

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

sampled data h optimal control of time varying systems the sampled data h optimal control problem is studied for time varying systems the problem consists of finding all sampled data controllers with a piece wise constant control signal for which the l2 induced norm from the continuous time disturbance to the continuous time output is less than a specified bound a game theoretic approach is used to obtain a complete solution to the problem in the finite horizon time varying case the solution involves a mixed discrete continuous riccati equation and a variable transformation which takes the problem to a standard discrete finite dimensional h filtering problem

optimal and robust noncausal filter formulations the paper describes an optimal minimum variance noncausal filter or fixed interval smoother the optimal solution involves a cascade of a kalman predictor and an adjoint kalman predictor a robust smoother involving h sub spl infin predictors is also described filter asymptotes are developed for output estimation and input estimation problems which yield bounds on the spectrum of the estimation error these bounds lead to a priori estimates for the scalar spl gamma in the h sub spl infin filter and smoother design the results of simulation studies are presented which demonstrate that optimal robust and extended kalman smoothers can provide performance benefits

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

brief on the h fixed lag smoothing how to exploit the information preview the problem of the continuous time h fixed lag smoothing over the infinite horizon is studied the first solution to the problem is derived in terms of one algebraic riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the h filtering occur is clarified it is shown that the h smoother exploits the information preview in an h 2 manner

a spectral factorization approach for h spl infin estimation problems in discrete time this note deals with the h filtering prediction and smoothing problems for discrete time linear systems the j spectral factorization approach is pursued and for each of the three problems a computationally efficient procedure to derive a j spectral factor is presented the construction of filter smoother and predictor hinges on the stabilizing solution of the same algebraic riccati equation this fact allows for the avoidance of any fictitious augmentation of the state space dimensions

prediction filtering smoothing and deconvolution in a discrete h infinity setting a game theory approach the problems of prediction filtering smoothing and deconvolution are formulated and solved for a discrete time linear system in an h infinity setting over a finite interval the measurement noise and process noise have bounded energies the case with known initial conditions is considered the approach uses a basic quadratic game theory in a discrete time domain h infinity setting

cal h _ infty control and estimation problems with delayed measurements state space solutions most physical processes exhibit transport delay in the measured output and it is well known that this can have disastrous effects on system stability and performance if it is not accounted for in this paper we give necessary and sufficient conditions for existence of estimators and controllers that achieve the desired cal h infty performance criterion when such a measurement delay is present we also give the complete characterization of all controllers and estimators that achieve the desired performance criterion the necessary and sufficient conditions are easy to check and are given in terms of the familiar pair of algebraic riccati equations that appear in the nondelay versions of the corresponding cal h infty problems along with an additional riccati differential equation explicit state space formulas for the controllers and estimators are also obtained they have a linear periodic structure and are easily implementable to obtain these results we first obtain state space results for a modified nehari problem which may be of independent interest see problem 5 in section 2

continuous time tracking problems in an h sub spl infin setting a game theory approach this paper investigates the problem of finite horizon h sub spl infin tracking for linear time varying systems three tracking problems are considered depending on whether the reference signal is perfectly known in advance measured on line or previewed in fixed interval of time ahead no a priori knowledge of a dynamic model for the reference signal is assumed a game theory approach to the latter tracking problems is presented where given a specific reference signal the controllers play against nature which can choose any initial state and any bounded energy disturbance input and measurement noise necessary and sufficient conditions for the existence of a saddle point equilibrium are determined and h sub spl infin tracking controllers for both the cases of state and output feedback are derived tracking problems for time invariant systems on infinite horizon are also analyzed and time invariant tracking controllers are obtained for zero initial conditions

a miscellany of results of an equation of count j f riccati a collection of results on the riccati equation is presented the questions addressed are the existence of strong solutions of the algebraic riccati equation and the convergence of solutions of the riccati difference equation to those of the algebraic equation the results derived utilize detestability conditions only

robust filtering for discrete time systems with bounded noise and parametric uncertainty this note presents a new approach to finite horizon guaranteed state prediction for discrete time systems affected by bounded noise and unknown but bounded parameter uncertainty our framework handles possibly nonlinear dependence of the state space matrices on the uncertain parameters the main result is that a minimal confidence ellipsoid for the state consistent with the measured output and the uncertainty description may be recursively computed in polynomial time using interior point methods for convex optimization with n states l uncertain parameters appearing linearly in the state space matrices with rank one matrix coefficients the worst case complexity grows as o l n l sup 3 5 with unstructured uncertainty in all system matrices the worst case complexity reduces to o n sup 3 5

adaptive robust h filter design for linear systems with time varying uncertainty this article studies the problem of designing robust h filters for linear uncertain systems the uncertainty parameters are assumed to be time varying unknown but bounded which appear affinely in the matrices of system models an adaptive mechanism is introduced to construct novel filters with variable gains which can reduce the conservativeness of the traditional robust h filters the proposed adaptive filter design conditions are given in terms of linear matrix inequalities a numerical example is presented to illustrate the effectiveness of the proposed strategy

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

robust extended kalman filtering linearization errors inherent in the specification of an extended kalman filter ekf can severely degrade its performance this correspondence presents a new approach to the robust design of a discrete time ekf by application of the robust linear design methods based on the h sub spl infin norm minimization criterion the results of simulations are presented to demonstrate an advantage for signal demodulation and nonlinear equalization applications

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

rapid identification of a sparse impulse response using an adaptive algorithm in the haar domain this paper proposes a fast convergence adaptive algorithm for identifying a sparse impulse response that is rich in spectral content a sparse impulse response is referred here as a discrete time impulse response that has a large number of zero or near zero coefficients the basic idea for rapid identification is to automatically determine the locations of the nonzero impulse response coefficients for their adaptation and eliminate the unnecessary adaptation of zero coefficients the proposed method which is called the haar basis algorithm employs a transform approach by modeling the sparse impulse response in the haar domain the haar transform has many basis sets and each of them contains basis vectors that span the entire time domain range this special nature of the haar transform allows for the selection of one small subset of adaptive filter coefficients whose basis vectors span the entire range of the impulse response these coefficients are adapted at the beginning and are then used subsequently to identify from the hierarchical structure of the haar transform the rest of the filter coefficients that must be adapted to correctly model the unknown sparse impulse response the consequence is avoiding adaptation of many zero coefficients leading to a dramatic improvement in either convergence speed or steady state excess mean square error ease while requiring no a priori knowledge such as the number of nonzero coefficients in the unknown sparse impulse response the proposed algorithm has been tested with a variety of unknown sparse systems using both white noise input and colored input whose spectrum closely resembles that of speech simulation results show that the new approach provides promising results

on designing h_ infty fault detection filter for linear discrete time varying systems this technical note deals with the problem of finite horizon h fault detection for linear discrete time varying systems using an observer based fault detection filter fdf with residual feedback as a residual generator a new problem formulation of fault detection is first presented then the design of finite horizon h fdf is converted into a minimum problem of certain quadratic form through building a relationship with krein space projection and applying innovation analysis a sufficient and necessary condition for the minimum is derived and a solution to the h fdf is obtained by recursively computing riccai recursions numerical examples are given to show the effectiveness of the proposed method

h sub infinity fixed lag smoothing filter for scalar systems the solution of the h sub infinity optimal linear fixed lag smoothing problem is considered using a polynomial matrix description for the discrete system the smoother is obtained from the solution of a linear equation and a spectral factorization calculation the pole zero properties of the optimal smoother are obvious in the polynomial representation and insights into the measurement noise rejection properties of the smoother are obtained allowance is made for both dynamic cost weighting and colored measurement noise the polynomial form of the smoothing filter may be incorporated into a self tuning algorithm and a simple adaptive smoother is discussed

optimal estimation for continuous time systems with delayed measurements this note focuses on the traditional problem of the kalman filtering for linear continuous time systems although the problem has been studied widely in the past decades little work has been done for the time delayed systems and some fundamental problems remain to be solved this note proposes a new tool namely reorganization innovation analysis approach to investigate the filtering problem for systems with delayed measurements the kalman filter is given in terms of the solution of standard riccati equations the performance is clearly demonstrated through analytical results and simulation the solved problem in this note is related with some more complicated problems such as h sub spl infin fixed lag smoothing h sub spl infin control with preview and control with input delays

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

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

a new parametrization of h suboptimal controllers elementary state space concepts are used to derive a transparent solution to the h control problem on an infinite horizon the main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric riccati equations with a coupling constraint unlike the classical parametrization in terms of linear fractional transformation this state space representation has a homogeneous riccati formulation which should help to make the most of the suboptimal controller diversity potential applications include the design of reduced order controllers and more generally the selection of suboptimal controllers to meet or optimize additional constraints

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

a transfer function approach to the problems of discrete time systems h sub infinity optimal linear control and filtering a solution is derived to the problems of h sub infinity optimal linear state regulation and filtering the solution method for both problems is based on a transfer function approach which applies standard spectral factorization return difference relations are given which are extensions of the relations associated with the linear quadratic problem

a frequency domain approach to the problems of h sub infinity minimum error state estimation and deconvolution the properties of the minimum h sub infinity norm filtering estimation error are investigated and the relation between the optimal estimator and the equalizing solution to the standard h sub infinity minimization problem is discussed the optimal estimation method is applied in the multivariable deconvolution problem a simple deconvolution filter of minimum order which minimizes the h sub infinity norm of the deconvolution error is obtained the proposed methods of optimal estimation and deconvolution are useful in cases where the statistics of the disturbance and the noise signals is not completely known or in cases where it is required to minimize the maximum singular value of the estimation or the deconvolution error problem

brief robust h filtering with error variance constraints for discrete time varying systems with uncertainty the robust h filtering problem with error variance constraints is considered for discrete time varying systems subject to norm bounded parameter uncertainties in both the state and the output matrices of the state space model sufficient conditions for a finite horizon filter to satisfy state estimation error variance constraints as well as prescribed h performance for all admissible perturbations are given in terms of two discrete riccati difference equations which are of a form suitable for recursive computation the results are extended to cover the case of stationary filtering over an infinite horizon for uncertain time invariant systems

bounded constrained filtering for gps ins integration this paper considers estimation problems where inequality constraints are imposed on the outputs of linear systems and can be modeled by nonlinear functions in this case censoring functions can be designed to constrain measurements for use by filters and smoothers it is established that the filter and smoother output estimates are unbiased provided that the underlying probability density functions are even and the censoring functions are odd the bounded real lemma is employed to ensure that the output estimates satisfy a performance criterion a global positioning system gps and inertial navigation system ins integration application is discussed in which a developed solution exhibits improved performance during gps outages when a priori information is used to constrain the altitude and velocity measurements

robust h filtering for discrete time varying uncertain systems with a known deterministic input in this paper a new discrete time dynamic game where two players seek to reinforce and suppress the output of a system under the influence of a known deterministic input is considered a necessary and sufficient condition for the existence of a saddle point solution to this game is derived in terms of a discrete time riccati difference equation the result of the game is used to solve the robust h x filtering problem for discrete time varying systems subject to a known deterministic input and norm bounded parameter uncertainties occurring in both the state and the output matrices of the state space model there is no restriction on the form of the filter this allows the effect of the known input on the estimation error due to system uncertainties to be optimally reduced without any prior assumption on the filter structure

time varying discrete riccati equation some monotonicity results abstract using a fre chet derivative based approach some monotonicity and comparison results concerning the solutions of the time varying discrete time riccati equation are obtained connections with the existence of the semistabilizing solution are made explicit as well

gain scheduled filtering for time varying discrete systems this paper deals with the design of gain scheduled filters whose state space realization depends on real time parameters of plants similar to well recognized advantages of gain scheduled controllers in control theory gain scheduled filters are expected to provide enhanced performance in comparison with customary nonadjustable filters our construction technique is based on nonlinear fractional transformation nft representations of systems that are a generalization of widely used linear fractional transformation lft representations both generalized h sub 2 and h sub spl infin discrete time filter design problems are investigated together with their extension to mixed designs this study leads to new linear matrix inequality lmi formulations which in turn provide an effective and reliable design tool the proposed design technique is finally evaluated in the light of simulation examples

h optimal sampled data control in continuous time systems we consider the design of h optimal discrete time digital controllers in continuous time systems an apparent difficulty especially in utilizing modern transform domain analysis in this context stems from the absence of an appropriate transfer function model for the hybrid time discrete and continuous closed loop system this difficulty is overcome through the introduction of an equivalent difference equation model for the continuous time system with distributed inputs and outputs equivalence being in the sense that the continuous and discrete time inputs and outputs are essentially identical using the interplay between the discrete and the continuous time models solutions of the well known purely continuous time and purely discrete time standard problems extend to solutions of the problem at hand they comprise riccati equation characterizations of feasible combinations of sampling rates and bounds on the closed loop induced input output norm and parameterization of compensators we consid