linear estimation of boundary value stochastic processes part ii 1 d smoothing problems this paper addresses the fixed interval smoothing problem for linear two point boundary value stochastic processes of the type introduced by krener 5 as these models are not markovian kalman filtering and associated smoothing algorithms are not applicable the smoothing problem for this class of noncausal processes is solved here by an application of the estimator solution which is developed in part i of this paper 3 via the method of complementary models for an n th order model this approach yields the smoother as a 2 n th order two point boundary value problem it is shown that this smoother can be realized in a stable two filter form which is remarkably similar to two filter smoothers for causal processes in addition expressions for the smoothing error and smoothing error covariance are developed these equations are employed to perform a covariance analysis of estimating the temperature and heat flow in a cooling fin

convergence analysis of an online approach to parameter estimation problems based on binary observations in this paper we present an online identification method to the problem of parameter estimation from binary observations a recursive identification algorithm with low storage requirements and computational complexity is derived we prove the convergence of this method provided that the input signal satisfies a strong mixing property some simulation results are then given in order to illustrate the properties of this method under various scenarios this method is appealing in the context of micro electronic devices since it only requires a 1 bit analog to digital converter with low power consumption and minimal silicon area

stochastic gradient identification of polynomial wiener systems analysis and application this paper presents analytical numerical and experimental results for a stochastic gradient adaptive scheme that identifies a polynomial type nonlinear system with memory for noisy output observations the analysis includes the computation of the stationary points the mean square error surface and the stability regions of the algorithm for gaussian data convergence of the mean is studied using l sub 2 and euclidian norms monte carlo simulations confirm the theoretical predictions that show a small sensitivity to the observation noise an application is presented for the identification of a nonlinear time delayed feedback system

complementary models and smoothing the authors apply the concept of complementary models introduced by weinert and desai 1983 to derive forwards and backwards markovian models for the smoothing error process by exploring the structure of the complementary models they show that under certain restrictions only two simple structured models exist one that runs forwards in time and another than runs backwards in time the forwards complementary model leads to a forwards rauch tung striebel rts smoothing formula and to a backwards markovian model for the error whereas the backwards model leads to a backwards rts formula and to a forwards error model the two models for the smoothing error can be derived one from the other by a forwards backwards transformation that preserves the sample paths finally by using a combination of the two complementary models another proof of the two filter smoothing formula is given

design of exponentially weighted moving average control charts for autocorrelated processes with model uncertainty residual based control charts are popular methods for statistical process control of autocorrelated processes to implement these methods a time series model of the process is required the model must be estimated from data in practice and model estimation errors can cause the actual in control average run length to differ substantially from the desired value this article develops a method for designing residual based exponentially weighted moving average ewma charts under consideration of the uncertainty in the estimated model parameters the resulting ewma control limits are widened by an amount that depends on a number of factors including the level of model uncertainty

minimal representations of semiseparable kernels and systems with separable boundary conditions abstract the simplest representations of triangular parts of finite rank kernels are analysed criteria for uniqueness up to similarity are given the results are applied to the problem of minimal realization of systems with separable boundary conditions

strong consistence of recursive identification for wiener systems the paper concerns identification of the wiener system consisting of a linear subsystem followed by a static nonlinearity f with no invertibility and structure assumption recursive estimates are given for coefficients of the linear subsystem and for the value f v at any fixed v the main contribution of the paper consists in establishing convergence with probability one of the proposed algorithms to the true values this probably is the first strong consistency result for this kind of wiener systems a numerical example is given which justifies the theoretical analysis

correspondence a note on efficient smoothing for boundary value models abstract the smoothing problem for two point boundary value models is investigated it is shown that by triangularizing the relevant hamiltonian system a new smoothing algorithm can be derived which is twice as fast as that obtained by diagonalizing the hamiltonian

linear estimation of boundary value stochastic processes part i the role and construction of complementary models this paper presents a substantial extension of the method of complementary models for minimum variance linear estimation introduced by weinert and desai in their important paper 1 specifically the method of complementary models is extended to solve estimation problems for both discrete and continuous parameter linear boundary value stochastic processes in one and higher dimensions a major contribution of this paper is an application of green s identity in deriving a differential operator representation of the estimator to clarify the development and to illustrate the range of applications of our approach two brief examples are provided one is a 1 d discrete two point boundary value process and the other is a 2 d process governed by poisson s equation on the unit disk

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

nonlinear system identification via direct weight optimization a general framework for estimating nonlinear functions and systems is described and analyzed in this paper identification of a system is seen as estimation of a predictor function the considered predictor function estimate at a particular point is defined to be affine in the observed outputs and the estimate is defined by the weights in this expression for each given point the maximal mean square error or an upper bound of the function estimate over a class of possible true functions is minimized with respect to the weights which is a convex optimization problem this gives different types of algorithms depending on the chosen function class it is shown how the classical linear least squares is obtained as a special case and how unknown but bounded disturbances can be handled most of the paper deals with the method applied to locally smooth predictor functions it is shown how this leads to local estimators with a finite bandwidth meaning that only observations in a neighborhood of the target point will be used in the estimate the size of this neighborhood the bandwidth is automatically computed and reflects the noise level in the data and the smoothness priors the approach is applied to a number of dynamical systems to illustrate its potential

adaptive filtering using quantized output measurements a normalized stochastic gradient adaptive filtering algorithm based on a finite impulse response fir model is discussed the algorithm identifies the system exactly given only coarsely quantized output measurements a description of the quantizer is included in the overall input output model and the scheme exploits an approximation of the derivative of the quantizer using an associated differential equation global convergence is established to a zero output error except for possible colored measurement disturbances parameter setting or to the boundary of the model set

performance of cusum control schemes for serially correlated observations this article discusses situations in which one is interested in evaluating the run length characteristics of a cumulative sum control scheme when the underlying data show the presence of serial correlation in practical applications situations of this type are common in problems associated with monitoring such characteristics of data as forecasting errors measures of model adequacy and variance components the discussed problem is also relevant in situations in which data transformations are used to reduce the magnitude of serial correlation the basic idea of analysis involves replacing the sequence of serially correlated observations by a sequence of independent and identically distributed observations for which the runlength characteristics of interest are roughly the same applications of the proposed method for several classes of processes arising in the area of statistical process control are discussed in detail and it is shown that it leads to approximations that can be considered acceptable in

monitoring processes that wander using integrated moving average models often the least appropriate assumption in traditional control charting technology is that process data constitute a random sample in reality most process data are correlated either temporally spatially or due to nested sources of variation one approach to monitoring temporally correlated data uses a control chart on the forecast errors from a time series model of the process with possibly a transfer function term to model compensatory adjustments if the time series term is an integrated moving average then a sudden level shift in the process results in a patterned shift in the mean of forecast errors initially the mean shifts by the same amount as the process level but then it decays geometrically back to 0 corresponding to the ability of the forecast to recover from the upset we study four monitoring schemes umulative sums cusum s exponentially weighted moving averages shewhart individuals charts and a likelihood ratio scheme comparisons of signaling probabilities and average run lengt

boundary value descriptor systems well posedness reachability and observability in this paper we introduce the class of two point boundary value descriptor systems tpbvds discrete time systems described by possibly linear dynamics and a set of boundary conditions constraining the values of the system state at the two endpoints of the system s interval of definition by introducing a standard form for regular pencils we obtain a new and simple generalized cayley hamilton theorem that simplifies our investigation of well posedness green s function solutions and reachability and observability for tpbvds there are two distinct notions of reachability and observability that one can define for tpbvds associated with processes that propagate inward from and outward toward the boundaries we investigate each of these in detail obtaining among other things far simpler forms for the reachability and observability results than found previously in the literature in addition we describe several methods for the efficient solution of tpbvds one involving recursions from each end of t

smoothing for random fields modeled by partial differential equations the authors present an efficient numerically reliable smoothing algorithm for random fields modeled by linear constant coefficient partial differential equations the estimate is computed from discrete measurements by using the discrete fourier transform to convert the two dimensional 2d problem to a collection of uncoupled one dimensional 1d problems which are then solved using stable iterations

asymptotically efficient parameter estimation using quantized output observations this paper studies identification of systems in which only quantized output observations are available an identification algorithm for system gains is introduced that employs empirical measures from multiple sensor thresholds and optimizes their convex combinations strong convergence of the algorithm is first derived the algorithm is then extended to a scenario of system identification with communication constraints in which the sensor output is transmitted through a noisy communication channel and observed after transmission the main results of this paper demonstrate that these algorithms achieve the cramer rao lower bounds asymptotically and hence are asymptotically efficient algorithms furthermore under some mild regularity conditions these optimal algorithms achieve error bounds that approach optimal error bounds of linear sensors when the number of thresholds becomes large these results are further extended to finite impulse response and rational transfer function models when the inputs are designed to be periodic and full rank

kalman filtering and riccati equations for descriptor systems a general formulation of a discrete time filtering problem for descriptor systems is considered it is shown that the nature of descriptor systems leads directly to the need to examine singular estimation problems using a dual approach to estimation the authors derive a so called 3 block form for the optimal filter and a corresponding 3 block riccati equation for a general class of time varying descriptor models which need not represent a well posed system in that the dynamics may be either over or under constrained specializing in the time invariant case they examine the asymptotic properties of the 3 block filter and in particular analyze in detail the resulting 3 block algebraic riccati equation the noncausal nature of discrete time descriptor dynamics implies that future dynamics may provide some information about the present state a modified form for the descriptor kalman filter that takes this information into account is presented

brief fast approximate identification of nonlinear systems in this paper a method is presented to extend the classical identification methods for linear systems towards nonlinear modelling of linear systems that suffer from nonlinear distortions a well chosen general nonlinear model structure is proposed that is identified in a two step procedure first a best linear approximation is identified using the classical linear identification methods in the second step the nonlinear extensions are identified with a linear least squares method the proposed model not only includes wiener and hammerstein systems it is also suitable to model nonlinear feedback systems the stability of the nonlinear model can be easily verified the method is illustrated on experimental data

curve evolution implementation of the mumford shah functional for image segmentation denoising interpolation and magnification we first address the problem of simultaneous image segmentation and smoothing by approaching the mumford shah 1989 paradigm from a curve evolution perspective in particular we let a set of deformable contours define the boundaries between regions in an image where we model the data via piecewise smooth functions and employ a gradient flow to evolve these contours each gradient step involves solving an optimal estimation problem for the data within each region connecting curve evolution and the mumford shah functional with the theory of boundary value stochastic processes the resulting active contour model offers a tractable implementation of the original mumford shah model i e without resorting to elliptic approximations which have traditionally been favored for greater ease in implementation to simultaneously segment and smoothly reconstruct the data within a given image in a coupled manner various implementations of this algorithm are introduced to increase its speed of convergence we also outline a hierarchical implementation of this algorithm to handle important image features such as triple points and other multiple junctions next by generalizing the data fidelity term of the original mumford shah functional to incorporate a spatially varying penalty we extend our method to problems in which data quality varies across the image and to images in which sets of pixel measurements are missing this more general model leads us to a novel pde based approach for simultaneous image magnification segmentation and smoothing thereby extending the traditional applications of the mumford shah functional which only considers simultaneous segmentation and smoothing

on the markov chain approach to the two sided cusum procedure a markov chain representation is given for the two sided possibly asymmetric cumulative sum cusum procedure of ewan and kemp 1960 for integer valued random variables the approach taken by brook and evans 1972 for the one sided cusum procedure to determine exact and approximate expressions for the run length distribution its moments and its percentage points is extended to the two sided cusum procedure the number of states included in the markov chain is minimized in order to make the methods as efftcient as possible

optimal brightness functions for optical flow estimation of deformable motion estimation accuracy of horn and schunck s 1981 classical optical flow algorithm depends on many factors including the brightness pattern of the measured images since some applications can select brightness functions with which to paint the object it is desirable to know what patterns will lead to the best motion estimates the paper presents a method for determining this pattern a priori using mild assumptions about the velocity field and imaging process the method is based on formulating horn and schunck s algorithm as a linear smoother and rigorously deriving an expression for the corresponding error covariance function the authors then specify a scalar performance measure and develop an approach to select an optimal brightness function which minimizes this performance measure from within a parametrized class conditions for existence of an optimal brightness function are also given the resulting optimal performance is demonstrated using simulations and a discussion of these results and potential future research is given

an optimal two stage identification algorithm for hammerstein wiener nonlinear systems abstract an optimal two stage identification algorithm is presented for hammerstein wiener systems where two static nonlinear elements surround a linear block the proposed algorithm consists of two steps the first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases moreover the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise

δ entropy definition properties and applications in system identification with quantized data recently the minimum error entropy criterion an information theoretic alternative to the traditional mean square error criterion has been successfully used in the contexts of machine learning and signal processing for system identification however the mee criterion will be no longer suitable if the training data are discrete valued since minimizing error s discrete entropy cannot constrain error s dispersion in this paper to make the mee criterion suitable for the discrete valued data cases we give a new entropy definition for the discrete random variables i e the d entropy based on riemann sums for finite size partitions a probability weighted formula is established to calculate the average partition this new entropy retains some important properties of the differential entropy and reduces to discrete entropy under certain conditions unlike discrete entropy the d entropy is sensitive to the dynamic range of the data and can be used as a superior optimality criterion in system identification problems also we present a plug in estimate of d entropy analyze its asymptotic behavior and explore the links to the kernel based and m spacing based estimates for differential entropy finally the d entropy criterion is applied in system identification with coarsely quantized input output data to search for the optimum parameter set monte carlo simulations demonstrate the performance improvement that may be achieved with the d entropy criterion

stability stochastic stationarity and generalized lyapunov equations for two point boundary value descriptor systems the authors introduce the concept of internal stability for two point boundary value descriptor systems tpbvdss since tpbvdss are defined only over a finite interval the concept of stability is not easy to formulate the definition which is used consists of requiring that as the length of the interval of definition increases the effect of boundary conditions on states located close to the center of the interval should go to zero stochastic tpbvdss are studied and the property of stochastic stationarity is characterized in terms of a generalized lyapunov equation satisfied by the variance of the boundary vector a second generalized lyapunov equation satisfied by the state variance of a stochastically stationary tpbvds is also introduced and the existence and uniqueness of positive definite solutions to this equation are then used to characterize the property of internal stability

stationarity and reciprocity in stochastic multipoint boundary value systems investigates certain statistical properties of the state vector in a stochastic multipoint boundary value system the authors give necessary and sufficient conditions for the state vector to be stationary and prove that the state vector is locally reciprocal

linear stochastic differential equations with boundary conditions we study linear stochastic differential equations with affine boundary conditions the equation is linear in the sense that both the drift and the diffusion coefficient are affine functions of the solution the solution is not adapted to the driving brownian motion and we use the extended stochastic calculus of nualart and pardoux 16 to analyse them we give analytical necessary and sufficient conditions for existence and uniqueness of a solution we establish sufficient conditions for the existence of probability densities using both the malliavin calculus and the co aera formula and give sufficient conditions that the solution be either a markov process or a markov field

estimation of quantized linear errors in variables models we present an estimation algorithm for dynamic shock error models dsem given 1 bit quantized noisy measurements of the input and output the algorithm is called the binary series estimation algorithm bsea bsea is computationally inexpensive since it involves counting the number of occurrences of particular patterns of zeros and ones in the input and output sequences it yields consistent parameter estimates that are asymptotically normal

asymptotically efficient identification of fir systems with quantized observations and general quantized inputs this paper introduces identification algorithms for finite impulse response systems under quantized output observations and general quantized inputs while asymptotically efficient algorithms for quantized identification under periodic inputs are available their counterpart under general inputs has encountered technical difficulties and evaded satisfactory resolutions under quantized inputs this paper resolves this issue with constructive solutions a two step algorithm is developed which demonstrates desired convergence properties including strong convergence mean square convergence convergence rates asymptotic normality and asymptotical efficiency in terms of the cramer rao lower bound some essential conditions on input excitation are derived that ensure identifiability and convergence it is shown that by a suitable selection of the algorithm s weighting matrix the estimates become asymptotically efficient the strong and mean square convergence rates are obtained optimal input design is given also the joint identification of noise distribution functions and system parameters is investigated numerical examples are included to illustrate the main results of this paper

run length distributions of special cause control charts for correlated processes we derive run length distributions of the special cause control chart proposed by alwan and roberts for correlated observations given that the assignable cause to be detected is a shift in the process mean both recursive and closed form solutions are derived for the run length distribution average run length arl and standard deviation of the run length srl for any ar p process and approximate solutions are derived for the more general arma p q processes the expressions derived do not depend on the type of shift in the process mean numerical results are illustrated for the arl and srl of the arma l l model given that the shift in the mean is a step shift these results show that the arl and srl of the specialcause control chart are relatively smaller when the process is negatively rather than positively autocorrelated regardless of the sign of the autocorrelation the shape of the probability mass function of the run length reveals that the probability of detecting shifts very early is subs

internal models and recursive estimation for 2 d isotropic random fields efficient recursive smoothing algorithms are developed for isotropic random fields that can be obtained by passing white noise through rational filters the estimation problem is shown to be equivalent to a countably infinite set of 1 d separable two point boundary value smoothing problems the 1 d smoothing problems are solved using a markovianization approach followed by a standard 1 d smoothing algorithm the desired field estimate is then obtained as properly weighted sum of the 1 d smoothed estimates the 1 d two point boundary value problems are also shown to have the same asymptotic properties and yield a stable spectral factorization of the power spectrum of the isotropic random fields

construction and applications of discrete time smoothing error models we present a unified perspective on techniques for constructing both forward and backward markovian realizations of the error process associated with discrete time fixed interval smoothing several alternative approaches are presented each of which provides additional insight and connections with other results in linear estimation theory in addition two applications of such models are described the first is a problem in the validation of an error model for a measurement system while the second concerns the problems of updating and combining smoothed estimates we also present an example of the use of our updating solution for the mapping of random fields based on several sets of data tracks

trajectory planning for systems with a multiplicative stochastic uncertainty a trajectory planning problem for linear stochastic differential equations is considered in this paper the aim is to control the system such that the expected value of the output interpolates given points at given times while the variance and an integral cost of the control effort are minimized the solution is obtained by using the dynamic programming technique which allows for several possible generalizations the results of this paper can be used for control of systems with a multiplicative stochastic disturbance on the state vector and systems with a stochastic growth rate this is frequently the case in investment problems biomathematics and control theory

recursive identification for wiener model with discontinuous piece wise linear function this paper deals with identification of wiener systems with nonlinearity being a discontinuous piece wise linear function recursive estimation algorithms are proposed to estimate six unknown parameters contained in the nonlinearity and all unknown coefficients of the linear subsystem by using the iid gaussian inputs the estimates are proved to converge to the corresponding true values with probability one a numerical example is given to justify the obtained theoretical results

smoothing for multipoint boundary value models abstract we show how to solve the linear least squares smoothing problem for multipoint boundary value models the complementary model is derived and is used to determine the hamiltonian equations for the smoothed state estimate and its error covariance stable algorithms are obtained using an invariant imbedding multiple shooting procedure

frequency domain identification of wiener models this paper proposes a frequency domain algorithm for wiener model identifications based on exploring the fundamental frequency and harmonics generated by the unknown nonlinearity the convergence of the algorithm is established in the presence of white noise no a priori knowledge of the structure of the nonlinearity is required and the linear part can be nonparametric

variable selection and identification of high dimensional nonparametric additive nonlinear systems this paper considers variable selection and identification of dynamic additive nonlinear systems via kernel based nonparametric approaches where the number of variables and additive functions may be large variable selection aims to find which additive functions contribute and which do not the proposed variable selection consists of two successive steps at the first step one estimates each additive function by kernel based nonparametric identification approaches without suffering from the curse of dimensionality at the second step a nonnegative garrote estimator is applied to identify which additive functions are nonzero by utilizing the obtained nonparametric estimates of each function under weak conditions the nonparametric estimates of each additive function can achieve the same asymptotic properties as for 1d nonparametric identification based on kernel functions it is also established that the nonnegative garrote estimator turns a consistent estimate for each additive function into a consistent variable selection with probability one as the number of samples tends to infinity two simulation examples are presented to verify the effectiveness of the variable selection and identification approaches proposed in the paper

proportional integral derivative charts for process monitoring we introduce a new class of monitoring procedures based on the relationship between a proportional integral derivative pid feedback control scheme and the corresponding prediction scheme the charts are obtained by applying the pid predictor to the autocorrelated data to get residuals and then monitoring the residuals this class of procedures includes as special cases several charts that have been recently proposed in the literature and thus provides a unifying framework the pid charts have three parameters that can be suitably tuned to achieve good average run length arl performance for large or small mean shifts methods for determining chart parameters to obtain good arl performance are discussed simulation studies for autoregressive moving average 1 1 models show that pid charts are competitive with the special cause charts of alwan and roberts for detecting large shifts and perform better in detecting small to moderate shifts the effects of model parameter misspecification and bias in esti

optimal smoothing for finite state hidden reciprocal processes this technical note addresses modelling and estimation of a class of finite state random processes called hidden reciprocal chains hrc a hidden reciprocal chain consists of a finite state reciprocal process together with an observation process conditioned on the reciprocal process much as in the case of a hidden markov model hmm the key difference between markov models and reciprocal models is that reciprocal models are non causal the technical note presents a characterization of a hrc by a finite set of hidden markov bridges which are hmms with the final state fixed the technical note then uses this characterization to derive the optimal fixed interval smoother for a hrc performance of linear and optimal smoothers derived for both hmm and hrc are compared using simulations for a class of hrc derived from underlying markov transitions these experiments suggest that not surprisingly the performance of the optimal hmm and hrc smoothers are signifcantly better than their linear counterparts and that some performance improvement is obtained using the hrc smoothers compared to the hmm smoothers the technical note concludes by mentioning some ongoing and future work which exploits this new markov bridge characterization of a hrc

a hamiltonian formulation of risk sensitive linear quadratic gaussian control we consider the optimal control problem with time homogeneous linear and in general non markov dynamics and risk sensitive criterion appeal to the extremal principle prescribed by the risk sensitive certainty equivalence principle rscep yields a symmetric equation system indicating that the extended hamiltonian formulation generalizes naturally to the risk sensitive case the conjugate variable of a hamiltonian formulation now has an interpretation in terms of forecasted process noise and the rscep in fact provides a stochastic maximum principle for which all variables have a clear interpretation and the desired measurability properties in the infinite horizon case meaningful under generalized controllability conditions optimal control is determined explicitly in terms of a canonical factorization for the case of imperfect process observation the rscep leads to coupled equation systems that can again be solved in terms of canonical factorizations in the time invariant stationary case

modeling and estimation of discrete time gaussian reciprocal processes discrete time gaussian reciprocal processes are characterized in terms of a second order two point boundary value nearest neighbor model driven by a locally correlated noise whose correlation is specified by the model dynamics this second order model is the analog for reciprocal processes of the standard first order state space models for markov processes the model is used to obtain a solution to the smoothing problem for reciprocal processes the resulting smoother obeys second order equations whose structure is similar to that of the kalman filter for gauss markov processes it is shown that the smoothing error is itself a reciprocal process

weak approximations a malliavin calculus approach we introduce a variation of the proof for weak approximations that is suitable for studying the densities of stochastic processes which are evaluations of the flow generated by a stochastic differential equation on a random variable that may be anticipating our main assumption is that the process and the initial random variable have to be smooth in the malliavin sense furthermore if the inverse of the malliavin covariance matrix associated with the process under consideration is sufficiently integrable then approximations for densities and distributions can also be achieved we apply these ideas to the case of stochastic differential equations with boundary conditions and the composition of two diffusions

modelling and estimation for finite state reciprocal processes a reciprocal equation is a kind of descriptor linear discrete index stochastic system which is well known be satisfied pathwise by all gaussian reciprocal processes from a system theoretic point of view it is a kind of noncausal linear system in the sense that the solution of it cannot be determined by only an initial condition indeed requiring the terminal state as well besides all the input function between initial and terminal states also nice properties are known of a reciprocal equation such as the equivalence of it with a couple of ordinary causal dynamic systems running in opposite directions for these reasons here we assume a reciprocal equation as the target of stochastic realization for the class of finite state reciprocal processes also named reciprocal chains the central result of the present paper is showing that any canonical reciprocal chain i e valued in the canonical base of realrn n being the cardinality of the set of chain s states satisfies pathwise a reciprocal equation in a n2 dimensional canonical variable or in other word a quadratic reciprocal equation named augmented state reciprocal model asrm also for a partially observed reciprocal chain a linear optimal smoother is derived all the results here presented are based upon the idea that a reciprocal chain is a combination of markov bridges to this purpose other forms besides the asrm are presented in order to make clear the meaning of this combination as well as to prove that the linear smoother can be actually implemented as n smoothers all operating independently on each markov bridge component

smoothing and likelihood ratio for gaussian boundary value processes a new derivation which does not need the invertibility assumption of the covariance matrix of the boundary data is given for the smoothing of gaussian two point boundary value processes tpbvp the likelihood ratio for tpbv processes is then derived in terms of the system parameters by using the krein factorization the likelihood ratio involves the smoother of the process an alternate expression for the likelihood ratio based on the filtered estimate of the state is also given

on complementary models and fixed interval smoothing a new algorithm is derived for the standard fixed interval linear smoothing problem in which the signal is generated by a state model the structure of this new algorithm allows the smoothed estimate to be easily updated in response to a change in the initial state covariance matrix pi 0 since unlike in existing algorifiuns the relevant riccati equation is entirely independent of pi 0 the derivation of the algorithm is based on properties of complementary models

boundary value processes estimation and identification recent results obtained for boundary value processes and the associated smoothing and identification problems are presented in this paper both lumped and distributed parameter models are considered some open problems are discussed and the fundamental mathematical difficulties that arise in studying nonlinear extensions of the proposed models are mentioned

a new characterization for multivariate gaussian reciprocal processes established a new necessary and sufficient condition for a multivariate gaussian random process to be reciprocal this result is then used to prove that the state vector of a two point boundary value system is reciprocal the authors do not impose any nonsingularity conditions on the covariance function of the state vector

exponentially weighted moving average control schemes properties and enhancements roberts 1959 first introduced the exponentially weighted moving average ewma control scheme using simulation to evaluate its properties he showed that the ewma is useful for detecting small shifts in the mean of a process the recognition that an ewma control scheme can be represented as a markov chain allows its properties to be evaluated more easily and completely than has previously been done in this article we evaluate the properties of an ewma control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value a design procedure for ewma control schemes is given parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process in addition several enhancements to ewma control schemes are considered these include a fast initial response feature that makes the ewma control scheme more sensitive to start up problems a combined shewhart ewma that provides protection against both larg

multiscale systems kalman filters and riccati equations an algorithm analogous to the rauch tung striebel algorithm spl minus consisting of a fine to coarse kalman filter like sweep followed by a coarse to fine smoothing step spl minus was developed previously by the authors ibid vol 39 no 3 p 464 78 1994 in this paper they present a detailed system theoretic analysis of this filter and of the new scale recursive riccati equation associated with it while this analysis is similar in spirit to that for standard kalman filters the structure of the dyadic tree leads to several significant differences in particular the structure of the kalman filter error dynamics leads to the formulation of an ml version of the filtering equation and to a corresponding smoothing algorithm based on triangularizing the hamiltonian for the smoothing problem in addition the notion of stability for dynamics requires some care as do the concepts of reachability and observability using these system theoretic constructs the stability and steady state behavior of the fine to coarse kalman filter and its riccati equation are analysed

optimal smoothing for noncausal 2 d systems based on a descriptor model an optimal smoothing problem for noncausal two dimensional systems is formulated and solved based on the descriptor model with coefficient functions using this model a forward and backward recursion procedure is obtained it is shown that for the existence of solutions pointwise reachability and observability of the descriptor model at infinite poles are important

some new smoother implementations for discrete time gaussian reciprocal processes abstract the smoothing problem for discrete time gaussian reciprocal processes is examined for this class of process the smoother takes the form of a second order two point boundary value nearest neighbour model this smoother is non causal but admits causal implementations which extend the two filter and rauch tung striebel smoothing formulae of gauss markov processes a multi rate implementation based on a block cyclic reduction method is also described

joint identification of plant rational models and noise distribution functions using binary valued observations system identification of plants with binary valued output observations is of importance in understanding modeling capability and limitations for systems with limited sensor information establishing relationships between communication resource limitations and identification complexity and studying sensor networks this paper resolves two issues arising in such system identification problems first regression structures for identifying a rational model contain non smooth nonlinearities leading to a difficult nonlinear filtering problem by introducing a two step identification procedure that employs periodic signals empirical measures and identifiability features rational models can be identified without resorting to complicated nonlinear searching algorithms second by formulating a joint identification problem we are able to accommodate scenarios in which noise distribution functions are unknown convergence of parameter estimates is established recursive algorithms for joint identification and their key properties are further developed

nonlinear black box modeling in system identification a unified overview a nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics there has been considerable recent interest in this area with structures based on neural networks radial basis networks wavelet networks and hinging hyperplanes as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules this paper describes all these approaches in a common framework from a user s perspective it focuses on what are the common features in the different approaches the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques it is pointed out that the nonlinear structures can be seen as a concatenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space these mappings are discussed separately the latter mapping is usually formed as a basis function expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection

identification of wiener systems with binary valued output observations this work is concerned with identification of wiener systems whose outputs are measured by binary valued sensors the system consists of a linear fir finite impulse response subsystem of known order followed by a nonlinear function with a known parametrization structure the parameters of both linear and nonlinear parts are unknown input design identification algorithms and their essential properties are presented under the assumptions that the distribution function of the noise is known and the nonlinearity is continuous and invertible it is shown that under scaled periodic inputs identification of wiener systems can be decomposed into a finite number of core identification problems the concept of joint identifiability of the core problem is introduced to capture the essential conditions under which the wiener system can be identified with binary valued observations under scaled full rank conditions and joint identifiability a strongly convergent algorithm is constructed the algorithm is shown to be asymptotically efficient for the core identification problem hence achieving asymptotic optimality in its convergence rate for computational simplicity recursive algorithms are also developed

a simple method for studying run length distribution of exponentially weighted moving average charts a numerical procedure using integral equations is presented for the tabulation of moments of run lengths of exponentially weighted moving average ewma charts both average run lengths arl s and standard deviations of run lengths sdrl s are presented for the twosided ewma chart assuming normal observations along with an example illustrating how to design such a chart the procedure given extends easily to many nonnormal cases and to one sided versions of the ewma chart