rank based tests for randomness against first order serial dependence abstract optimal rank based procedures were derived in hallin ingenbleek and puri 1985 1987 and hallin and puri 1988 for some fundamental testing problems arising in time series analysis the optimality properties of these procedures are of an asymptotic nature however whereas much of the attractiveness of rank based methods lies in their small sample applicability and robustness features accordingly the objective of this article is twofold a a study of the finite sample behavior of the asymptotically optimal tests for randomness against first order autoregressive moving average dependence proposed in hallin et al 1985 both under the null hypothesis tables of critical values and under alternatives of serial dependence evaluation of the power function and b an heuristic investigation of the robustness properties of the proposed procedures with emphasis on the identification problem in the presence of outliers we begin sec 2 with a brief description of the rank based measu

a note on time reversibility of multivariate linear processes we derive some readily verifiable necessary and sufficient conditions for a multivariate non gaussian linear process to be time reversible under two sets of conditions on the contemporaneous dependence structure of the innovations one set of conditions concerns the case of independent component innovations in which case a multivariate non gaussian linear process is time reversible if and only if the coefficients consist of essentially asymmetric columns with column specific origins of symmetry or symmetric pairs of columns with pair specific origins of symmetry on the other hand for dependent component innovations plus other regularity conditions a multivariate non gaussian linear process is time reversible if and only if the coefficients are essentially symmetric about some origin

improved mpeg 4 still texture image coding under noisy environment this paper describes the performance of the mpeg 4 still texture image codec in coding noisy images as will be shown when using the mpeg 4 still texture image codec to compress a noisy image increasing the compression rate does not necessarily imply reducing the peak signal to noise ratio psnr of the decoded image an optimal operating point having the highest psnr can be obtained within the low bit rate region nevertheless the visual quality of the decoded noisy image at this optimal operating point is greatly degraded by the so called cross shape artifact in this paper we analyze the reason for the existence of the optimal operating point and the cross shape artifact when using the mpeg 4 still texture image codec to compress noisy images we then propose an adaptive thresholding technique to remove the cross shape artifact of the decoded images it requires only a slight modification to the quantization process of the traditional mpeg 4 encoder while the decoder remains unchanged finally an analytical study is performed for the selection and validation of the threshold value used in the adaptive thresholding technique it is shown that the visual quality and psnr of the decoded images are much improved by using the proposed technique comparing with the traditional mpeg 4 still texture image codec in coding noisy images

testing time reversibility without moment restrictions in this paper we propose a class of new tests for time reversibility it is shown that this test has an asymptotic normal distribution under the null hypothesis and non trivial power under local alternatives a novel feature of this test is that it does not have any moment restriction in contrast with other time reversibility and linearity tests our simulations also confirm that the proposed test is very robust when data do not possess proper moments an empirical study of stock market indices is also included to illustrate the usefulness of the new test

embedded image coding using zerotrees of wavelet coefficients the embedded zerotree wavelet algorithm ezw is a simple yet remarkably effective image compression algorithm having the property that the bits in the bit stream are generated in order of importance yielding a fully embedded code the embedded code represents a sequence of binary decisions that distinguish an image from the null image using an embedded coding algorithm an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly also given a bit stream the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream in addition to producing a fully embedded bit stream the ezw consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images yet this performance is achieved with a technique that requires absolutely no training no pre stored tables or codebooks and requires no prior knowledge of the image source the ezw algorithm is based on four key concepts 1 a discrete wavelet transform or hierarchical subband decomposition 2 prediction of the absence of significant information across scales by exploiting the self similarity inherent in images 3 entropy coded successive approximation quantization and 4 universal lossless data compression which is achieved via adaptive arithmetic coding

unknown input observers for switched nonlinear discrete time descriptor systems in this paper a linear matrix inequality technique for the state estimation of discrete time nonlinear switched descriptor systems is developed the considered systems are composed of linear and nonlinear parts an observer giving a perfect unknown input decoupled state estimation is proposed sufficient conditions of global convergence of observers are proposed numerical examples are given to illustrate this method

observer based schemes for adaptive nonlinear state feedback control we combine recently proposed adaptive nonlinear controllers with two types of observer based identifiers the controllers guarantee an input to state stability property with respect to and and the observer based identifiers independently guarantee boundedness of a stability enhancement in the observer is crucial in establishing stability properties

thermodynamics of the general diffusion process time reversibility and entropy production we introduce an axiomatic thermodynamic theory for the general diffusion process and prove a theorem concerning entropy and irreversibility the equivalence among time reversibility zero entropy production symmetricity of the stationary diffusion process and a potential condition

brief paper adaptive observers for nonlinearly parameterized class of nonlinear systems in this paper one proposes adaptive observers for a class of uniformly observable mimo nonlinear systems with general nonlinear parameterizations the state and the unknown parameters of the considered systems are supposed to lie in bounded domains which size can be arbitrarily large and the exponential convergence of the observers is shown to result under a well defined persistent excitation condition moreover the gain of the observers involves a design function that has to satisfy a simple condition which is given different expressions of such a function are proposed and it is shown that adaptive high gain like observers and adaptive sliding mode like observers can be derived by considering particular expressions of the design function the theory is supported by simulation results related to the estimation of the biomass concentration and the contois model parameters in a bioreactor

on detailed balance and reversibility of semi markov processes and single molecule enzyme kinetics semi markov processes have found increasing applications in modeling the kinetics of single enzyme molecules detailed balance is a widely accepted condition for markov models of closed chemical systems and well known to be equivalent to the reversibility of a stationary markov process we show that for a semi markov process detailed balance is only a necessary condition but not sufficient for its time reversibility the statistical independence between the transition direction and the sojourn time is also necessary we show that the direction time independence naturally arises from the exit problem of markov models for enzyme kinetics with detailed balance detailed balance and the direction time independence together are equivalent to the time reversibility of a stationary semi markov process applications of the present theory to single molecule enzymology are also presented

a lyapunov based distributed consensus filter for a class of nonlinear stochastic systems abstract this paper considers the distributed state estimation problem for nonlinear stochastic systems over sensor networks it is assumed that the nonlinear functions are bounded in the pseudo lipschitz condition based on the stochastic lyapunov stability theory a distributed consensus filter dcf is proposed for both continuous and discrete nonlinear stochastic systems for each node in a sensor network it will be shown that the estimation errors of the proposed filters are exponentially ultimately bounded in the sense of mean square in terms of linear matrix inequality lmi furthermore a criterion is presented to optimize the filter gains based on minimizing the upper bound of mean square error numerical examples are used to verify the theoretical results

on nonparametric and semiparametric testing for multivariate linear time series we formulate nonparametric and semiparametric hypothesis testing of multivariate stationary linear time series in a unified fashion and propose new test statistics based on estimators of the spectral density matrix the limiting distributions of these test statistics under null hypotheses are always normal distributions and they can be implemented easily for practical use if null hypotheses are false as the sample size goes to infinity they diverge to infinity and consequently are consistent tests for any alternative the approach can be applied to various null hypotheses such as the independence between the component series the equality of the autocovariance functions or the autocorrelation functions of the component series the separability of the covariance matrix function and the time reversibility furthermore a null hypothesis with a nonlinear constraint like the conditional independence between the two series can be tested in the same way

on time reversibility and the uniqueness of moving average representations for non gaussian stationary time series a recent result by findley 1986 on the uniqueness of moving average representations for non gaussian time series is shown to establish a conjecture by weiss 1975 on the time reversibility of general linear processes 1988 biometrika trust

noncausal vector ar processes with application to economic time series abstract inference procedures for noncausal autoregressive ar models have been well studied and applied in a variety of applications from environmental to financial for such processes the observation at time t may depend on both past and future shocks in the system in this paper we consider extension of the univariate noncausal ar models to the vector ar var case the extension presents several interesting challenges since even a first order var can possess both causal and noncausal components assuming a non gaussian distribution for the noise we show how to compute an approximation to the likelihood function under suitable conditions it is shown that the maximum likelihood estimator mle of the vector of ar parameters is asymptotically normal the estimation procedure is illustrated with a simulation study for a var 1 process and with two real data examples

design of a unified adaptive fuzzy observer for uncertain nonlinear systems this paper presents an adaptive fuzzy observer for a class of uncertain nonlinear systems more precisely we propose a unified approach for designing such an observer with some design flexibility so that it can be easily adaptable and employed either as a high gain or a sliding mode observer by selecting its gain appropriately additionally we derive a suitable parameter adaptation law so that the proposed observer is robust with respect to ubiquitous fuzzy approximation errors and external disturbances we also show that the observation error is ultimately bounded using a lyapunov approach without having recourse to the usual strictly positive real spr condition or a suitable observation error filtering the effectiveness of the proposed observers is illustrated through two simulation case studies taken from the adaptive fuzzy control literature

adaptive state observer for lipschitz nonlinear systems abstract the problem of adaptive observer synthesis for lipschitz nonlinear systems is addressed in the case of known parameters the convergence property of state observer is first discussed based on a generalized lipschitz condition the sufficient conditions to ensure the stability of observer error dynamics are presented in terms of some lmis in the case of system dynamics with some unknown parameters the proposed conditions along with an equality constraint are then employed to guarantee the convergence property of an adaptive state observer moreover an adaptive observer form is derived which can be utilized in designing the reduced order state observer the simulation results are finally given to exhibit the effectiveness of proposed synthesis approaches in dealing with the practical systems

the explicit form of the rate function for semi markov processes and its contractions we derive the explicit form of the rate function for semi markov processes here the random time change trick plays an essential role also by exploiting the contraction principle of the large deviation theory to the explicit form we show that the fluctuation theorem gallavotti cohen symmetry holds for semi markov cases furthermore we elucidate that our rate function is an extension of the level 2 5 rate function for markov processes to semi markov cases

miscellanea on time reversibility of linear processes summary a necessary and sufficient condition for time reversibility of stationary linear processes is given which contrary to previous results does not require existence of moments of order higher than two

quantile spectral analysis for locally stationary time series summary classical spectral methods are subject to two fundamental limitations they can account only for covariance related serial dependences and they require second order stationarity much attention has been devoted lately to quantile based spectral methods that go beyond covariance based serial dependence features at the same time covariance based methods relaxing stationarity into much weaker local stationarity conditions have been developed for a variety of time series models here we combine those two approaches by proposing quantile based spectral methods for locally stationary processes we therefore introduce a time varying version of the copula spectra that have been recently proposed in the literature along with a suitable local lag window estimator we propose a new definition of local strict stationarity that allows us to handle completely general non linear processes without any moment assumptions thus accommodating our quantile based concepts and methods we establish a central limit theorem for the new estimators and illustrate the power of the proposed methodology by means of a simulation study moreover in two empirical studies namely of the standard poor s 500 series and a temperature data set recorded in hohenpeissenberg we demonstrate that the new approach detects important variations in serial dependence structures both across time and across quantiles such variations remain completely undetected and are actually undetectable via classical covariance based spectral methods

krein space based h adaptive smoother design for a class of lipschitz nonlinear discrete time systems in this paper the problem of h adaptive smoother design is addressed for a class of lipschitz nonlinear discrete time systems with l2 bounded disturbance input by comprehensively analyzing the h performance lipschitz conditions and unknown parameter s bounded condition a positive minimum problem for an indefinite quadratic form is introduced such that the h adaptive smoothing problem is achieved a krein space stochastic system with multiple fictitious outputs is constructed by associating with the minimum problem of the introduced indefinite quadratic form the minimum of indefinite quadratic form is derived in the form of innovations through utilizing krein space orthogonal projection and innovation analysis approach via choosing the suitable fictitious outputs to guarantee the minimum of indefinite quadratic form is positive the existence condition of the adaptive smoother and its analytical solutions are obtained in virtue of nonstandard riccati difference equations the quality of the estimator is checked on an example

adaptive observers for a class of uniformly observable systems with nonlinear parametrization and sampled outputs in this paper we propose an adaptive observer for a class of uniformly observable nonlinear systems with nonlinear parametrization and sampled outputs a high gain adaptive observer is first designed under the assumption that the output is continuously measured and its exponential convergence is investigated thanks to a well defined persistent excitation condition then we address the case where the output is available only at non uniformly spaced sampling instants to this end the continuous time output observer is redesigned leading to an impulsive observer with a corrective term involving instantaneous state impulses corresponding to the measured samples and their estimates moreover it is shown that the proposed impulsive observer can be put under the form of a hybrid system composed of a continuous time observer coupled with an inter sample output predictor two design features are worth to be emphasized firstly the observer calibration is achieved through the tuning of a scalar design parameter secondly the exponential convergence to zero of the observation and parameter estimation errors is established under a well defined condition on the maximum value of the sampling partition diameter more specifically the observer design is firstly carried out in the case of linear parametrization before being extended to the nonlinear one the theoretical results are corroborated through simulation results involving a typical bioreactor

lyapunov based adaptive state estimation for a class of nonlinear stochastic systems this paper is concerned with an adaptive state estimation problem for a class of nonlinear stochastic systems with unknown constant parameters these nonlinear systems have a linear in parameter structure and the nonlinearity is assumed to be bounded in a lipschitz like manner using stochastic counterparts of lyapunov stability theory we present adaptive state and parameter estimators with ultimately exponentially bounded estimator errors in the sense of mean square for both continuous time and discrete time nonlinear stochastic systems sufficient conditions are given in terms of the solvability of lmis moreover we also introduce a suboptimal design approach to optimizing the upper bound of the mean square error of parameter estimation this suboptimal design procedure is also realized by lmi computations by a martingale method we also show that the related lyapunov function has a non negative lyapunov exponent

a global high gain finite time observer a global finite time observer is designed for nonlinear systems which are uniformly observable and globally lipschitz this result is based on a high gain approach combined with recent advances on finite time stability using lyapunov function and homogeneity concepts

continuous time random walk for open systems fluctuation theorems and counting statistics we consider continuous time random walks ctrw for open systems that exchange energy and matter with multiple reservoirs each waiting time distribution wtd for times between steps is characterized by a positive parameter alpha which is set to alpha 1 if it decays at least as fast as t 2 at long times and therefore has a finite first moment a wtd with alpha 1 decays as t alpha 1 a fluctuation theorem for the trajectory quantity r defined as the logarithm of the ratio of the probability of a trajectory and the probability of the time reversed trajectory holds for any ctrw however r can be identified as a trajectory entropy change only if the wtds have alpha 1 and satisfy separability also called direction time independence for nonseparable wtds with alpha 1 r can only be identified as a trajectory entropy change at long times and a fluctuation theorem for the entropy change then only holds at long times for wtds with 0 alpha 1 no meaningful fluctuation theorem can be derived we also show that the experimentally accessible nth moments of the energy and matter transfers between the system and a given reservoir grow as t nalpha at long times

the uniqueness of moving average representations with independent and identically distributed random variables for non gaussian stationary time series summary full spectrum non gaussian stationary series can have at most one representation as a moving average of independent and identically distributed random variables having finite moments of all orders

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

brief paper robust adaptive observer for nonlinear systems with unmodeled dynamics unmodeled dynamics exist in almost all applications of observers due to the impossibility of using exact and detailed models it is highly desired that the observers can dominate the effects of unmodeled dynamics independently to prevent the state estimations from diverging and to get the precise estimations based on adaptive nonlinear damping this paper presents a robust adaptive observer for multiple input multiple output nonlinear systems with unknown parameters uncertain nonlinearities disturbances and unmodeled dynamics the observer only has one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are with the proposed observer neither estimating the unknown parameters or solving linear matrix inequalities is needed it is shown that the state estimation error is uniformly bounded and can be made arbitrarily small

time domain tests for gaussianity and time reversibility statistical signal processing algorithms often rely upon gaussianity and time reversibility two important notions related to the probability structure of stationary random signals and their symmetry parametric models obtained via second order statistics sos are appropriate when the available data is gaussian and time reversible on the other hand evidence of nonlinearity non gaussianity or time irreversibility favors the use of higher order statistics hos in order to validate gaussianity and time reversibility and quantify the tradeoffs between sos and hos consistent time domain chi squared statistical tests are developed exact asymptotic distributions are derived to estimate the power of the tests including a covariance expression for fourth order sample cumulants a modification of existing linearity tests in the presence of additive gaussian noise is discussed briefly the novel gaussianity statistic is computationally attractive leads to a constant false alarm rate test and is well suited for parametric modeling because it employs the minimal hos lags which uniquely characterize arma processes simulations include comparisons with an existing frequency domain approach and an application to real seismic data time reversibility tests are also derived and their performance is analyzed both theoretically and experimentally

nonlinear system fault diagnosis based on adaptive estimation an approach to fault diagnosis for a class of nonlinear systems is proposed in this paper it is based on a new adaptive estimation algorithm for recursive estimation of the parameters related to faults this algorithm is designed in a constructive manner through a nontrivial combination of a high gain observer and a recently developed linear adaptive observer without resort to any linearization its global exponential convergence is ensured by an easy to check persistent excitation condition a numerical example is presented for illustration

observer design for unknown input nonlinear descriptor systems via convex optimization this paper treats the design problem of full order observers for nonlinear descriptor systems with unknown input ui depending on the available knowledge on the ui dynamics two cases are considered first a ui proportional observer uipo is proposed when the spectral domain of the ui is unknown second a pio is proposed when the spectral domain of the ui is in the low frequency range sufficient conditions for the existence and stability of such observers are given and proved based on the linear matrix inequality lmi approach an algorithm is presented to compute the observer gain matrix that achieves the asymptotic stability objective an example is included to illustrate the method

brief paper redesign of adaptive observers for improved parameter identification in nonlinear systems we propose a method for redesigning adaptive observers for nonlinear systems the redesign uses an adaptive law that is based on delayed observers this increases the computational burden but gives significantly better parameter identification and robustness properties in particular given that a special persistency of excitation condition is satisfied we prove uniform global asymptotic stability and semi global exponential stability of the origin of the state and parameter estimation error and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics for initial conditions with a known upper bound we prove tunable exponential convergence rate to illustrate the use of the proposed method we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system the simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design

state and input simultaneous estimation for a class of nonlinear systems this paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems here the systems nonlinear part comprises a lipschitz nonlinear function with respect to the state and input and a state dependent unknown function including additive disturbance as well as uncertain nonlinear time varying terms upon satisfying some conditions the observer design problem can be solved via a riccati inequality or a lmi based technique with asymptotic estimation guaranteed a numerical example is included for illustration

adaptive redesign of nonlinear observers to estimate unmeasured states in dynamical systems with parametric uncertainties one can use adaptive observers in this technical note a new method for adaptive redesign of reduced order observers for nonlinear systems is presented the redesign makes the observer robust as it guarantees that the state estimation error converges to zero in the presence of parametric uncertainties to enable parameter adaption a new type of update law is derived using lyapunov analysis and a nonlinear coordinate transformation the uniqueness of the approach is that it allows terms containing both uncertainty and nonlinearity in the unmeasured states to appear in the dynamics of the unmeasured states and still achieves convergence of the state estimate without requiring persistent excitation two examples are presented that demonstrate these properties

a unified h adaptive observer synthesis method for a class of systems with both lipschitz and monotone nonlinearities abstract this paper investigates the problem of the h adaptive observer design for a class of nonlinear dynamical systems the main contribution consists in providing a unified synthesis method for systems with both lipschitz and monotone nonlinearities not necessarily lipschitz thanks to the innovation terms into the nonlinear functions m arcak p kokotovic observer based control of systems with slope restricted nonlinearities ieee transactions on automatic control 46 7 2001 1146 1150 and to the differential mean value theorem a zemouche m boutayeb g i bara observers for a class of lipschitz systems with extension to h performance analysis systems and control letters 57 1 2008 18 27 the stability analysis leads to the solvability of a linear matrix inequality lmi with several degrees of freedom for simplicity we start by presenting the result in an h adaptive free context furthermore we propose an h adaptive estimator that extends easily the obtained results to systems with unknown parameters in the presence of disturbances we show in particular that the matching condition in terms of an equality constraint required in several works is not necessary and therefore allows reducing the conservatism of the existing conditions performances of the proposed approach are shown through a numerical example with a polynomial nonlinearity

robustness design of nonlinear dynamic systems via fuzzy linear control this study introduces a fuzzy linear control design method for nonlinear systems with optimal h sup spl infin robustness performance first the takagi and sugeno fuzzy linear model 1985 is employed to approximate a nonlinear system next based on the fuzzy linear model a fuzzy controller is developed to stabilize the nonlinear system and at the same time the effect of external disturbance on control performance is attenuated to a minimum level thus based on the fuzzy linear model h sup spl infin performance design can be achieved in nonlinear control systems in the proposed fuzzy linear control method the fuzzy linear model provides rough control to approximate the nonlinear control system while the h sup spl infin scheme provides precise control to achieve the optimal robustness performance linear matrix inequality lmi techniques are employed to solve this robust fuzzy control problem in the case that state variables are unavailable a fuzzy observer based h sup spl infin control is also proposed to achieve a robust optimization design for nonlinear systems a simulation example is given to illustrate the performance of the proposed design method

adaptive impulsive observers for nonlinear systems this paper revisits the design of adaptive impulsive observers aios for nonlinear systems the dynamics of observer state of the proposed aio is modelled by an impulsive differential equation by which the observer state is updated in an impulsive fashion the parameter estimation law is modelled by an impulse free time varying differential equation associated with the impulse time sequence for determining when the observer state is updated unlike the previous work the convergence analysis of the estimation error system is performed by applying a time varying lyapunov function based method in conjunction with the application of a generalized version of barbalat s lemma a sufficient condition for the existence of aios is also derived for some special cases it is shown that the sufficient condition can be formulated in terms of linear matrix inequalities lmis and the observer matrices can be attained by solving a set of lmis furthermore with an additional persistence of excitation type constraint it is proved that the sufficient condition can guarantee the convergence of parameter estimation two examples of chaotic oscillators are provided to illustrate the design procedure of the proposed aios

dynamical fluctuations for semi markov processes wedevelopanonsager machlup typetheoryfornonequilibriumsemi markov processes our main result is an exact large time asymptotics for the joint probability of the occupation times and the currents in the system establishing some generic large deviation structures we discuss in detail how the nonequilibrium driving and the non exponential waiting time distribution influence the occupation current statistics the violation of the markov condition is reflected in the emergence of a new type of nonlocality in the fluctuations explicit solutions are obtained for some examples of driven random walks on the ring

quantization noise fixed point multiplicative roundoff noise and dithering the author considers the characteristics of the error resulting when a continuous amplitude signal x sub n is quantized and then multiplied by a constant multiplier a under fixed point roundoff arithmetic it is shown that the overall error of such an operation can be decomposed into two terms one being a scaled version of the error due to the quantization of x sub n and the other due to rounding off the product aq x sub n exact first and second order moments are derived for the quantization error the roundoff error and the overall error as a function of the multiplier a and the distribution of x sub n sufficient conditions are given for the quantization error and the roundoff error to be individually uniformly distributed and white up to the first and second order moments and also for them to be mutually uncorrelated it is also shown that regardless of the probability distribution of the input signal x sub n it is always possible to add a suitable dither signal to the input of the system so that both the quantization error and the roundoff error are uniformly distributed white and mutually uncorrelated for gaussian inputs the sufficient conditions given are not satisfied

bispectral analysis and model validation of texture images statistical approaches to texture analysis and synthesis have largely relied upon random models that characterize the 2 d process in terms of its first and second order statistics and therefore cannot completely capture phase properties of random fields that are non gaussian and or asymmetric in this paper higher than second order statistics are used to derive and implement 2 d gaussianity linearity and spatial reversibility tests that validate the respective modeling assumptions the nonredundant region of the 2 d bispectrum is correctly defined and proven a consistent parameter estimator for nonminimum phase asymmetric noncausal 2 d arma models is derived by minimizing a quadratic error polyspectrum matching criterion simulations on synthetic data are performed and the results of the bispectral analysis on real textures are reported

joint state and parameter estimation of non linearly parameterized discrete time nonlinear systems abstract simultaneous state and parameter estimation of nonlinear discrete time systems is addressed the developed procedure is dedicated to multiple input multiple output mimo bounded state nonlinear systems subject to either linear or nonlinear parametrization it is shown that under the persistent excitation condition the unmeasured states along with the system parameters can be reproduced asymptotically if the upper and the lower bounds of the system states are assumed to be known the existence of the observer gain is conditioned by the solvability of a linear matrix inequality lmi simulation results are provided to highlight the efficacy of the developed theoretical results

noncausal vector autoregressive process representation identification and semi parametric estimation abstract this paper introduces a representation theorem for a mixed var p process by distinguishing its causal and noncausal components that representation is used to discuss the advantages and limitations of second order identification in a mixed var we show that it is possible to find the numbers of causal or noncausal components of the process from its multivariate autocovariance function while nonlinear autocovariances are needed to distinguish between them the paper introduces also a consistent semi parametric estimator for mixed causal noncausal multivariate non gaussian processes called the generalized covariance gcov estimator which relies on combined standard and nonlinear autocovariances of the process the gcov does not require any distributional assumptions on the errors the approach is illustrated by a simulation study and applied to commodity prices

stationary bubble equilibria in rational expectation models abstract a linear rational expectation model with current expectations admits a unique linear stationary dynamic equilibrium only under specific restrictions on the parameter values this paper shows that in general there is a multiplicity of stationary dynamic equilibria due to the existence of nonlinear stationary equilibria these nonlinear stationary equilibria are consistent with the self fulfilling prophecies that characterize the rational expectation equilibria and can display speculative bubbles volatility induced mean reversion and or stochastic autoregressive patterns they are also compatible with the transversality conditions when the model involves intertemporal optimization the stationary nonlinear dynamic equilibria are economically relevant their analysis requires revised methods of identification for the stationary equilibrium impulse response analysis and estimation techniques which are presented in this paper standard econometric and economic methods which ignore the nonlinear stationary solutions provide misleading outcomes which may affect the validity of an economic policy or portfolio strategy

adapting to unknown smoothness via wavelet shrinkage abstract we attempt to recover a function of unknown smoothness from noisy sampled data we introduce a procedure sureshrink that suppresses noise by thresholding the empirical wavelet coefficients the thresholding is adaptive a threshold level is assigned to each dyadic resolution level by the principle of minimizing the stein unbiased estimate of risk sure for threshold estimates the computational effort of the overall procedure is order n log n as a function of the sample size n sureshrink is smoothness adaptive if the unknown function contains jumps then the reconstruction essentially does also if the unknown function has a smooth piece then the reconstruction is essentially as smooth as the mother wavelet will allow the procedure is in a sense optimally smoothness adaptive it is near minimax simultaneously over a whole interval of the besov scale the size of this interval depends on the choice of mother wavelet we know from a previous paper by the authors that traditional smoot

visibility of wavelet quantization noise the discrete wavelet transform dwt decomposes an image into bands that vary in spatial frequency and orientation it is widely used for image compression measures of the visibility of dwt quantization errors are required to achieve optimal compression uniform quantization of a single band of coefficients results in an artifact that we call dwt uniform quantization noise it is the sum of a lattice of random amplitude basis functions of the corresponding dwt synthesis filter we measured visual detection thresholds for samples of dwt uniform quantization noise in y cb and cr color channels the spatial frequency of a wavelet is r2 sup spl lambda where r is the display visual resolution in pixels degree and spl lambda is the wavelet level thresholds increase rapidly with wavelet spatial frequency thresholds also increase from y to cr to cb and with orientation from lowpass to horizontal vertical to diagonal we construct a mathematical model for dwt noise detection thresholds that is a function of level orientation and display visual resolution this allows calculation of a perceptually lossless quantization matrix for which all errors are in theory below the visual threshold the model may also be used as the basis for adaptive quantization schemes

an adaptive fuzzy hybrid state observer for bioprocesses in order to monitor and control bioprocesses online measurements of certain biological variables like biomass concentration are normally required unfortunately there is a lack of highly reliable and low cost instruments for online measuring these important variables these limitations have motivated the use of observers this paper describes a state observer for bioprocesses based on a hybrid fuzzy model the model combines the mass balances and a fuzzy inference system for approximating the uncertain dynamic of the kinetic reactions the convergence stability and robustness of the observer are analyzed the main features of this observer are illustrated by considering a lactic fermentation

nonlinear observer for simultaneous states and unknown parameter estimation this paper presents the design of an observer for the simultaneous estimation of states and unknown parameter for a class of nonlinear systems whose nonlinearity satisfies a bounded jacobian condition the paper presents two alternate observers based on the structure of the system the conditions for the existence of these observers can be expressed as a linear matrix inequality and solved using standard solvers the case of time varying parameter and multiple unknown parameter have also been investigated the use of the developed methodology is demonstrated through illustrative examples

adaptive observers for single output nonlinear systems an adaptive version of the nonlinear observer obtained by a j krener et al 1983 is presented this version involves the cancellation of nonlinear terms by output injection as an intermediate step necessary and sufficient conditions are given for transforming a nonlinear system by state space change of coordinates into the special adaptive observer form that was used by y bastin et al 1988 to design adaptive observers

maximum standardized cumulant deconvolution of non gaussian linear processes a linear process is represented as a driving white noise convolved with a system response sequence the concept of natural peakedness of a system response sequence is defined and its properties are investigated utilizing natural peakedness the convergence theory of maximum standardized cumulant deconvolution is established and the uniqueness theorem of non gaussian linear process representations is proved in addition autoregressive models on a countable abelian group are defined and the relation between cumulant deconvolution and autoregressive models is given

technical communique continuous discrete adaptive observers for state affine systems the observation of a class of multi input multi output mimo state affine systems with constant unknown parameters and discrete time output measurements is addressed assuming some persistent excitation conditions to hold and the sampling steps to satisfy some boundedness hypotheses system observability is ensured and a class of global exponential observers is synthesized

a versatile and robust metric entropy test of time reversibility and other hypotheses abstract we examine the performance of a metric entropy statistic as a robust test for time reversibility tr symmetry and serial dependence it also serves as a measure of goodness of fit the statistic provides a consistent and unified basis in model search and is a powerful diagnostic measure with surprising ability to pinpoint areas of model failure we provide empirical evidence comparing the performance of the proposed procedure with some of the modern competitors in nonlinear time series analysis such as robust implementations of the bds and characteristic function based tests of tr along with correlation based competitors such as the ljung box q statistic unlike our procedure each of its competitors is motivated for a different specific context and hypothesis our evidence is based on monte carlo simulations along with an application to several stock indices for the us equity market

mathematical formalism for isothermal linear irreversibility we prove the equivalence among symmetricity time reversibility and zero entropy production of the stationary solutions of linear stochastic differential equations a sufficient and necessary rever

adaptive nonlinear observer for state and unknown parameter estimation in noisy systems this paper proposes a novel adaptive observer for lipschitz nonlinear systems and dissipative nonlinear systems in the presence of disturbances and sensor noise the observer is based on an h observer that can estimate both the system states and unknown parameters by minimising a cost function consisting of the sum of the square integrals of the estimation errors in the states and unknown parameters the paper presents necessary and sufficient conditions for the existence of the observer and the equations for determining observer gains are formulated as linear matrix inequalities lmis that can be solved offline using commercially available lmi solvers the observer design has also been extended to the case of time varying unknown parameters the use of the observer is demonstrated through illustrative examples and the performance is compared with extended kalman filtering compared to previous results on nonlinear observers the proposed observer is more computationally efficient and guarantees state

fitness response relation of a multitype age structured population dynamics we construct a pathwise formulation for a multitype age structured population dynamics which involves an age dependent cell replication and transition of gene or phenotypes by employing the formulation we derive a variational representation of the stationary population growth rate the representation comprises a tradeoff relation between growth effects and a single cell intrinsic dynamics described by a semi markov process this variational representation leads to a response relation of the stationary population growth rate in which statistics on a retrospective history work as the response coefficients these results contribute to predicting and controlling growing populations based on experimentally observed cell lineage information

identification and estimation of non gaussian structural vector autoregressions abstract conventional structural vector autoregressive svar models with gaussian errors are not identified and additional identifying restrictions are needed in applied work we show that the gaussian case is an exception in that a svar model whose error vector consists of independent non gaussian components is without any additional restrictions identified and leads to essentially unique impulse responses building upon this result we introduce an identification scheme under which the maximum likelihood estimator of the parameters of the non gaussian svar model is consistent and asymptotically normally distributed as a consequence additional economic identifying restrictions can be tested in an empirical application we find a negative impact of a contractionary monetary policy shock on financial markets and clearly reject the commonly employed recursive identifying restrictions

lossy compression of noisy images noise degrades the performance of any image compression algorithm this paper studies the effect of noise on lossy image compression the effect of gaussian poisson and film grain noise on compression is studied to reduce the effect of the noise on compression the distortion is measured with respect to the original image not to the input of the coder results of noisy source coding are then used to design the optimal coder in the minimum mean square error mmse sense this is equivalent to an mmse estimator followed by an mmse coder the coders for the poisson noise and the film grain noise cases are derived and their performance is studied the effect of this preprocessing step is studied using standard coders e g jpeg also as is demonstrated higher quality is achieved at lower bit rates

a hierarchical kinetic theory of birth death and fission in age structured interacting populations we develop mathematical models describing the evolution of stochastic age structured populations after reviewing existing approaches we formulate a complete kinetic framework for age structured interacting populations undergoing birth death and fission processes in spatially dependent environments we define the full probability density for the population size age chart and find results under specific conditions connections with more classical models are also explicitly derived in particular we show that factorial moments for non interacting processes are described by a natural generalization of the mckendrick von foerster equation which describes mean field deterministic behavior our approach utilizes mixed type multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy bbgky like equation hierarchies

a note on observers for lipschitz nonlinear systems this note deals with the design of reduced order observers for lipschitz nonlinear systems it shows that the conditions under which a full order observer exists also guarantee the existence of a reduced order observer a design method of the reduced order observer that is dependent on the solution of the riccati equation is then presented and an example is given to illustrate effects of the design method

polyspectra of ordered signals polyspectra are related to fourier transforms of moment or cumulant functions of any order of random signals they play an important role in many problems of signal analysis and processing however there are only a few statistical models giving explicitly the expression of polyspectra ordered signals are signals for which the explicit expression of the moment functions requires that the time instants appearing in these moments are put in an increasing order there are many examples of such signals the best known being the random telegraph signal constructed from a poisson process some of these examples are presented and analyzed the origin of the ordering structure is related with the point that real time is an oriented variable making a difference between past and future this especially appears in markov processes the calculation of polyspectra is difficult because ordering is not adapted to fourier analysis by an appropriate grouping of various terms the explicit expression of spectral moment functions is obtained it shows in particular that many ordered signals present a normal density on the normal manifolds of the frequency domain and another contribution on the stationary manifold that is explicitly calculated the analysis of the structure of this expression allows us to discuss some relationships with normal distribution central limit theorem and time reversibility

the transient fluctuation theorem of sample entropy production for general stochastic processes the transient fluctuation theorem for stochastic processes was first put forward by d j searles and d j evans 1999 in the present paper it is rigorously proved that the transient fluctuation theorem tft of sample entropy production which is previously defined by jiang et al 2003 and reid et al 2005 and also called the general action functional up to boundary terms by lebowitz and spohn 1999 holds for general stochastic processes without the assumption of markovian homogeneous or stationary properties then the condition of our theorem is verified for various stochastic processes including homogeneous inhomogeneous markov chains and general diffusion processes among these cases the transient fluctuation theorems for inhomogeneous markov chains and general diffusion processes are rigorously derived for the first time

image compression via joint statistical characterization in the wavelet domain we develop a probability model for natural images based on empirical observation of their statistics in the wavelet transform domain pairs of wavelet coefficients corresponding to basis functions at adjacent spatial locations orientations and scales are found to be non gaussian in both their marginal and joint statistical properties specifically their marginals are heavy tailed and although they are typically decorrelated their magnitudes are highly correlated we propose a markov model that explains these dependencies using a linear predictor for magnitude coupled with both multiplicative and additive uncertainties and show that it accounts for the statistics of a wide variety of images including photographic images graphical images and medical images in order to directly demonstrate the power of the model we construct an image coder called epwic embedded predictive wavelet image coder in which subband coefficients are encoded one bitplane at a time using a nonadaptive arithmetic encoder that utilizes conditional probabilities calculated from the model bitplanes are ordered using a greedy algorithm that considers the mse reduction per encoded bit the decoder uses the statistical model to predict coefficient values based on the bits it has received despite the simplicity of the model the rate distortion performance of the coder is roughly comparable to the best image coders in the literature

on observers for nonlinear differential algebraic systems we extend a recent approach to observer design for linear differential algebraic systems to systems with lipschitz nonlinearities the observer design further extends the standard luenberger type observer design we show that the design parameters for the observer can be obtained by the solution of a riccati type inequality the solutions of the latter can in turn be obtained by solving a set of linear matrix inequalities lmis and bilinear matrix inequalities bmis which provides a computational procedure a feature of the presented observer design is the possibility of reformulation as an ordinary differential equation

on the reversibility of the observed process of three state hidden markov model for the continuous time and the discrete time three state hidden markov model the flux of the likelihood function up to 3 dimensional of the observed process is shown explicitly as an application the sufficient and necessary condition of the reversibility of the observed process is shown

remarks on nonlinear adaptive observer design abstract a solution to the problem of state estimation for systems with unknown parameters is to use some on line adaptation of the observer parameters on the basis of various existing results for such adaptive observer designs a unifying adaptive observer form is proposed in this paper this form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters as well as additional properties which further allow parameter estimation as an example it is shown how an adaptive observer can be designed for a class of state affine systems

a unified approach for encoding clean and noisy sources by means of waveform and autoregressive model vector quantization data compression by vector quantization is considered for sources which have been degraded by noise it is shown that by appropriately modifying the given distortion measure the problem becomes a standard quantization problem for the noisy source and the modified distortion measure for the special case of sources corrupted by statistically independent additive noise the authors provide sufficient conditions on the original distortion measure and probability distributions of the source and the noise for convergence of the generalized lloyd algorithm in designing the quantizers the results are specialized to waveform and autoregressive model vector quantization using the weighted quadratic and the itakura saito distortion measures respectively

a systematic approach to adaptive observer synthesis for nonlinear systems geometric techniques of controller design for nonlinear systems have enjoyed great success a serious shortcoming however has been the need for access to full state feedback this paper addresses the issue of state estimation from limited sensor measurements in the presence of parameter uncertainty an adaptive nonlinear observer is suggested for lipschitz nonlinear systems and the stability of this observer is shown to be related to finding solutions to a quadratic inequality involving two variables a coordinate transformation is used to reformulate this inequality as a linear matrix inequality a systematic algorithm is presented which checks for feasibility of a solution to the quadratic inequality and yields an observer whenever the solution is feasible the state estimation errors then are guaranteed to converge to zero asymptotically the convergence of the parameters however is determined by a persistence of excitation type constraint