a state predictor for continuous time stochastic systems abstract this work investigates the state prediction problem for nonlinear stochastic differential systems affected by multiplicative state noise this problem is relevant in many state estimation frameworks such as filtering of continuous discrete systems i e stochastic differential systems with discrete measurements and time delay systems a very common heuristic to achieve the state prediction exploits the numerical integration of the deterministic nonlinear equation associated to the noise free system unfortunately these methods provide the exact solution only for linear systems instead here we provide the exact state prediction for nonlinear system in terms of the series expansion of the expected value of the state conditioned to the value in a previous time instant obtained according to the carleman embedding technique the truncation of the infinite series allows to compute the prediction at future times with an arbitrary approximation simulations support the effectiveness of the proposed state prediction algorithm in comparison to the aforementioned heuristic method

adaptive ode solvers in extended kalman filtering algorithms this paper studies numerical methods that are used to treat ordinary differential equations arising in extended kalman filtering algorithms such problems are called the moment equations and constitute an important subclass of differential equations they all possess a number of specific properties that make the standard available software ineffective for some mathematical models in this area for instance we show that built in matlab ode solvers are not able to cope with a number of tests considered here in contrast the hybrid method developed by mazzoni 2007 exhibits much better performance on the same examples the latter means that specially designed numerical schemes are needed for efficient solution of the moment equations instead of the standard software designed for general systems of ordinary differential equations

design and analysis of a fuzzy proportional integral derivative controller abstract this paper describes the design principle tracking performance and stability analysis of a fuzzy proportional integral pi plus a derivative d controller first the fuzzy pi d controller is derived from the conventional continuous time linear pi d controller then the fuzzification control rule base and defuzzification in the design of the fuzzy controller are discussed in detail the resulting controller is a discrete time fuzzy version of the conventional pi d controller which has the same linear structure in the proportional integral and derivative parts but has nonconstant gains the proportional integral and derivative gains are nonlinear functions of the input signals the new fuzzy pi d controller thus preserves the simple linear structure of its conventional counterpart yet enhances the self tuning control capability computer simulation results have demonstrated the advantages of the fuzzy controller particularly when the process to be controlled is nonlinear after a brief stability analysis where a simple and realistic sufficient condition for the bounded input bounded output stability of the overall feedback control system was derived several computer simulation results are shown to compare with the conventional pi d controller computer simulation results have shown the new fuzzy controller indeed has satisfactory tracking performance

score confidence intervals and sample sizes for stratified comparisons of binomial proportions in a series of articles gart and nam construct the efficient score tests and confidence intervals with or without skewness correction for stratified comparisons of binomial proportions on the risk difference relative risk and odds ratio effect metrics however the stratified score methods and their properties are not well understood we rederive the efficient score tests which reveals their theoretical relationship with the contrast based score tests and provides a basis for adapting the method by using other weighting schemes the inverse variance weight is optimal for a common treatment effect in large samples we explore the behavior of the score approach in the presence of extreme outcomes when either no or all subjects in some strata are responders and provide guidance on the choice of weights in the analysis of rare events the score method is recommended for studies with a small number of moderate or large sized strata a general framework is proposed to calculate the asymptotic power and sample size for the score test in superiority noninferiority and equivalence clinical trials or case control studies we also describe a nearly exact procedure that underestimates the exact power but the degree of underestimation can be controlled to a negligible level the proposed methods are illustrated by numerical examples

a gaussian approximation recursive filter for nonlinear systems with correlated noises this paper proposes a gaussian approximation recursive filter gasf for a class of nonlinear stochastic systems in the case that the process and measurement noises are correlated with each other through presenting the gaussian approximations about the two step state posterior predictive probability density function pdf and the one step measurement posterior predictive pdf a general gasf framework in the minimum mean square error mmse sense is derived based on the framework the gasf implementation is transformed into computing the multi dimensional integrals which is solved by developing a new divided difference filter ddf with correlated noises simulation results demonstrate the superior performance of the proposed ddf as compared to the standard ddf the existing ukf and ekf with correlated noises

moving horizon state estimation for nonlinear systems using neural networks moving horizon mh state estimation is addressed for nonlinear discrete time systems affected by bounded noises acting on system and measurement equations by minimizing a sliding window least squares cost function such a problem is solved by searching for suboptimal solutions for which a certain error is allowed in the minimization of the cost function nonlinear parameterized approximating functions such as feedforward neural networks are employed for the purpose of design thanks to the offline optimization of the parameters the resulting mh estimation scheme requires a reduced online computational effort simulation results are presented to show the effectiveness of the proposed approach in comparison with other estimation techniques

discrete time solutions to the continuous time differential lyapunov equation with applications to kalman filtering prediction and filtering of continuous time stochastic processes often require a solver of a continuous time differential lyapunov equation cdle for example the time update in the kalman filter

moving horizon estimation for switching nonlinear systems this paper is concerned with moving horizon estimation for a class of constrained switching nonlinear systems where the system mode is regarded as an unknown discrete state to be estimated together with the continuous state in this work we establish the observability framework of switching nonlinear systems by proposing a series of concepts about observability and analyzing the properties of such concepts by fully applying the observability properties we prove the stability of the proposed moving horizon estimators simulation results are reported to verify the derived results

correspondence author s reply to comments on performance evaluation of ukf based nonlinear filtering it is stated in the above mentioned comment that the main result of the paper xiong zhang et al 2006 performance evaluation of ukf based nonlinear filtering automatica 42 2 261 270 can be extended to a class of filters such as the extended kalman filter ekf as we show here this belief can be justified in a rigorous way even for the nonlinear stochastic system with a nonlinear measurement equation

unscented kalman filter over unreliable communication networks with markovian packet dropouts the paper investigates the stability of the discrete time modified unscented kalman filter mukf in transmitting measurement outputs to the filter via a network since the communication channel states do not always vary in time the arrival of the observations is modeled as a two state time homogeneous markov process k the stability of the estimation error covariance matrices at packet reception times is analyzed sufficient conditions related to hk and the initial conditions for the peak covariance stability and the usual covariance stability are given also the relationship between the different types of stability notions is illustrated for systems with i i d observation dropouts numerical example is given to illustrate the effectiveness of the techniques developed

stochastic stability of the extended kalman filter with intermittent observations in this technical note we analyze the error behavior of the discrete time extended kalman filter for nonlinear systems with intermittent observations modelling the arrival of the observations as a random process we show that given a certain regularity of the system the estimation error remains bounded if the noise covariance and the initial estimation error are small enough we also study the effect of different measurement models on the bounds for the error covariance matrices

moving horizon estimation for hybrid systems we propose a state smoothing algorithm for hybrid systems based on moving horizon estimation mhe by exploiting the equivalence between hybrid systems modeled in the mixed logic dynamical form and piecewise affine systems we provide sufficient conditions on the time horizon and the penalties on the state at the beginning of the estimation horizon to guarantee asymptotic convergence of the mhe scheme moreover we propose two practical algorithms for the computation of penalties that allow us to implement mhe by solving a mixed integer quadratic program

paper the role of the interactor matrix in multivariable stochastic adaptive control this paper is concerned with the extension of the well known minimum variance control strategy to the multi input multi output case it is shown that this extension is straightforward when the system interactor matrix is diagonal but presents some unexpected difficulties in the general case we develop a suitable stochastic controller for the general case as a logical extension of the single input algorithm we also explore the properties of the algorithm in detail we also address the question of adaptive control of multivariable stochastic systems and investigate one possible strategy for overcoming the requirement of knowing the system interactor matrix a priori

convergence analysis of the extended kalman filter used as an observer for nonlinear deterministic discrete time systems in this paper convergence analysis of the extended kalman filter ekf when used as an observer for nonlinear deterministic discrete time systems is presented based on a new formulation of the first order linearization technique sufficient conditions to ensure local asymptotic convergence are established furthermore it is shown that the design of the arbitrary matrix plays an important role in enlarging the domain of attraction and then improving the convergence of the modified ekf significantly the efficiency of this approach compared to the classical version of the ekf is shown through a nonlinear identification problem as well as a state and parameter estimation of nonlinear discrete time systems

brief paper derivative free estimation methods new results and performance analysis the derivative free nonlinear estimation methods exploiting the stirling s interpolation and the unscented transformation for discrete time nonlinear stochastic systems are treated the divided difference and unscented filters smoothers and predictors based on the methods are introduced in the unified framework the new relations among the first order stirling s interpolation the second order stirling s interpolation and the unscented transformation are derived and their impact on the covariance matrices of the state estimates of the corresponding filters is analysed the theoretical results are illustrated and used for the explanation of the unexpected behaviour of the sigma point gaussian sum filters given as a mixture of the derivative free filters

accurate numerical implementation of the continuous discrete extended kalman filter this paper addresses an accurate and effective implementation of the continuous discrete extended kalman filtering method the technique under discussion is grounded in numerical solution of the moment differential equations to predict the state mean of the stochastic dynamical system and the corresponding error covariance matrix here we apply an efficient embedded runge kutta pair possessing superior stability and many other attractive features including automatic global error control in order to improve performance of the complex computational procedure consisting of the extended kalman filter and the underlying adaptive ode solver thus we introduce a new continuous discrete adaptive extended kalman filter and show its advantage over the standard variant on two test examples in practice this technique allows for much longer sampling intervals without any loss of accuracy and that improves the applied potential of the extended kalman filtering method significantly

observability of autonomous discrete time non linear systems a geometric approach in this paper the observability of autonomous discrete time systems is studied from a purely differential geometric point of view as with continuous time systems this approach leads to a local canonical form for an observable system a proposal for the generalization of an invariant subspace is made

various ways to compute the continuous discrete extended kalman filter the extended kalman filter ekf is a very popular tool dealing with state estimation its continuous discrete version cd ekf estimates the state trajectory of continuous time nonlinear models whose internal state is described by a stochastic differential equation and which is observed through a noisy nonlinear form of the sampled state the prediction step of the cd ekf leads to solve a differential equation that cannot be generally solved in a closed form this technical note presents an overview of the numerical methods including recent works usually implemented to approximate this filter comparisons of theses methods on two different nonlinear models are finally presented the first one is the van der pol oscillator which is widely used as a benchmark the second one is a neuronal population model this more original model is used to simulate eeg activity of the cortex experiments showed better stability properties of implementations for which the positivity of the prediction matrix is guaranteed

state estimation incorporating infrequent delayed and integral measurements this paper investigates the problem of state estimation incorporating infrequent delayed and integral measurements in chemical process there often exist two types of measurements on one hand the measurements for process variables such as flow rates and pressures are sampled frequently and are available nearly instantaneously on the other hand the measurements for quality variables such as concentration are sampled infrequently and are available with a delay due to long analysis time involved moreover due to the interval time taken by chemical sample collection the measurements for some quality variables have another important characteristic it is a function of the states of the compositions over a period of time this paper formulates the process with infrequent delayed and integral measurements as an equivalent variable dimension system whose measurements are both delay and integration free based on the new model a variable dimension unscented kalman filter vd ukf is proposed to estimate the states furthermore the stability of the proposed vd ukf is analyzed compared with the existing results the proposed stability condition is significantly relaxed and the invertibility condition of jacobian matrices is no longer needed finally a simulation example demonstrates the effectiveness of the proposed method

speed and rotor flux estimation of induction machines using a two stage extended kalman filter this paper presents an effective implementation of an extended kalman filter used for the estimation of both rotor flux and rotor velocity of an induction motor an algorithm proposed by hsieh and chen in hsieh c s chen f c 1999 optimal solution of the two stage kalman estimator ieee transactions on automatic control 44 1 194 199 for linear parameter estimation is extended to non linear estimation where parameters such as the velocity of an induction machine are present in the transition matrix and in the augmented state space compared to a straightforward implementation of an extended kalman filter our modified optimal two stage kalman estimator reduces the number of arithmetic operations by 25 allowing higher sampling rate or the use of a cheaper microcontroller

numerical methods for stochastic differential equations stochastic differential equations sde s play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability a general strategy for developing accurate and efficient schemes for solving stochastic equations is outlined here high order numerical methods are developed for the integration of stochastic differential equations with strong solutions we demonstrate the accuracy of the resulting integration schemes by computing the errors in approximate solutions for sde s which have known exact solutions

analysis of kalman filter approximations for nonlinear measurements a theoretical analysis is presented of the correction step of the kalman filter kf and its various approximations for the case of a nonlinear measurement equation with additive gaussian noise the kf is based on a gaussian approximation to the joint density of the state and the measurement the analysis metric is the kullback leibler divergence of this approximation from the true joint density the purpose of the analysis is to provide a quantitative tool for understanding and assessing the performance of the kf and its variants in nonlinear scenarios this is illustrated using a numerical example

the stability of nonlinear least squares problems and the cramer rao bound a number of problems of interest in signal processing can be reduced to nonlinear parameter estimation problems the traditional approach to studying the stability of these estimation problems is to demonstrate finiteness of the cramer rao bound crb for a given noise distribution we review an alternate deterministic notion of stability for the associated nonlinear least squares nls problem from the realm of nonlinear programming i e that the global minimizer of the least squares problem exists and varies smoothly with the noise furthermore we show that under mild conditions identifiability of the parameters along with a finite crb for the case of gaussian noise is equivalent to the deterministic stability of the nls problem finally we demonstrate the application of our result which is general to the problems of multichannel blind deconvolution and sinusoid retrieval to generate new stability results for these problems with little additional effort

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

methods for finding feasible points in constrained optimization methods for finding feasible points are needed in some numerical optimization algorithms to initiate the search for a local minimum other methods perform more efficiently if a nearly feasible starting point is used in addition a feasible solution may be acceptable as the final design in some practical applications therefore constraint correction methods are quite useful such methods based on penalty functions and primal approach are described and discussed to gain insight into the methods a two variable problem is used to analyze the methods several structural design problems are used to study the numerical behavior of the methods and compare their performance it is concluded that in general the primal methods are more efficient than the penalty function methods also no method has been found that is guaranteed to find a feasible point for general constrained nonlinear problems starting from an arbitrary point in case a method fails random points should be used to restart the procedure to search for a feasible point

recursive bayesian estimation using piece wise constant approximations abstract in bayesian estimation the objective is to calculate the complete density function for an unknown quantity conditioned on noisy observations of that quantity this work considers recursive estimation of a nonlinear discrete time system state using successive observations the formal recursion for the density function is easily written but generally there is no closed form solution the numerical solution proposed here is obtained by modifying the recursion and using a simple piece wise constant approximation to the density functions the approach also allows detailed analysis of error propagation through the algorithm yielding a bound on the maximum error growth and a characterization of the situations with potential for large errors the stability of the algorithm is demonstrated by comparing its long term performance to a kalman filter for a linear system with gaussian noises comparison to the point mass algorithm shows improved estimation accuracy and for moderately dense grids faster computation as an example the algorithm is applied to a system identification problem and the results compared to a popular second order minimum variance estimator the optimal estimate derived from the approximate density is seen to be far superior

technical communique stochastic stability of the unscented kalman filter with intermittent observations in this paper the stochastic stability of the discrete time unscented kalman filter for general nonlinear stochastic systems with intermittent observations is proposed it is shown that the estimation error remains bounded if the system satisfies some assumptions and the statistical convergence property of the estimation error covariance is studied showing the existence of a critical value for the arrival rate of the observations an upper bound on this expected state error covariance is given a numerical example is given to illustrate the effectiveness of the techniques developed

brief paper a maximum likelihood kalman filter for switching discrete time linear systems state estimation is addressed for a class of discrete time systems that may switch among different modes taken from a finite set the system and measurement equations of each mode are assumed to be linear and perfectly known but the current mode of the system is unknown moreover additive independent normally distributed noises are assumed to affect the dynamics and the measurements first relying on a well established notion of mode observability developed ad hoc for switching systems an approach to system mode estimation based on a maximum likelihood criterion is proposed second such a mode estimator is embedded in a kalman filtering framework to estimate the continuous state under the unique assumption of mode observability stability properties in terms of boundedness of the mean square estimation error are proved for the resulting filter simulation results showing the effectiveness of the proposed filter are reported

self tuning pid controllers algorithms and implementation a class of controllers with integral action is shown to arise directly from appropriate system models via the zero gain predictor approach a corresponding class of hybrid self tuning controllers is shown to have both integral action in the controller and offset removal in the tuning algorithm implementation details and some experimental results are given

brief paper adaptive divided difference filtering for simultaneous state and parameter estimation a novel adaptive version of the divided difference filter ddf applicable to non linear systems with a linear output equation is presented in this work in order to make the filter robust to modeling errors upper bounds on the state covariance matrix are derived the parameters of this upper bound are then estimated using a combination of offline tuning and online optimization with a linear matrix inequality lmi constraint which ensures that the predicted output error covariance is larger than the observed output error covariance the resulting sub optimal high gain filter is applied to the problem of joint state and parameter estimation simulation results demonstrate the superior performance of the proposed filter as compared to the standard ddf

performance evaluation of ukf based nonlinear filtering the performance of the modified unscented kalman filter ukf for nonlinear stochastic discrete time system with linear measurement equation is investigated it is proved that under certain conditions the estimation error of the ukf remains bounded furthermore it is shown that the design of noise covariance matrix plays an important role in improving the stability of the algorithm error behavior of the ukf is then derived in terms of mean square error mse and the cramer rao lower bound crlb is introduced as a performance measure the modified ukf is found to approach the crlb if the difference between the real noise covariance matrix and the selected one is small enough these results are verified by using monte carlo simulations on two example systems

posterior cramer rao bounds for discrete time nonlinear filtering a mean square error lower bound for the discrete time nonlinear filtering problem is derived based on the van trees 1968 posterior version of the cramer rao inequality this lower bound is applicable to multidimensional nonlinear possibly non gaussian dynamical systems and is more general than the previous bounds in the literature the case of singular conditional distribution of the one step ahead state vector given the present state is considered the bound is evaluated for three important examples the recursive estimation of slowly varying parameters of an autoregressive process tracking a slowly varying frequency of a single cisoid in noise and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation

a class of stable square root nonlinear information filters information filters can process nonlinear systems with uncertain prior knowledge and the particular square root form of adaptive filters can improve numerical stability based on a square root decomposition of information matrix and an extra positive definite matrix the unscented transform and the cubature rule are applied to the information filtering architecture for nonlinear estimation a class of stable square root nonlinear information filters is then proposed in this technical note in addition the boundedness of their estimation errors is also proven results from simulations of filtering a chaotic map demonstrate that the proposed square root nonlinear filters can improve numerical stability and has better filtering performance than other information filters

paper parameterization issues in multivariable adaptive control this paper gives both an overview of multivariable adaptive control algorithms which have evolved to date and presents some new approaches to the design of indirect multivariable adaptive control systems all algorithms are presented using a unified pole placement approach furthermore the emphasis is on parameterization issues such as types of control structures necessary for implementation required prior information necessary for implementation and techniques for reducing the size of the resulting parameter estimation problem

robust control on saturated markov jump systems with missing information in this paper a robust h controller is designed for saturated markov jump systems with uncertainties and time varying transition probabilities the time varying transition probability uncertainty is described as a polytope set stochastic stability is analyzed for the underlying systems by lyapunov function approach and a sufficient condition is derived to design controllers such that the resulting closed loop system is stochastically stable and a prescribed h performance is also achieved furthermore the attraction domain of this markov jump system is estimated and evaluated a simulation example is given to show the effectiveness of the developed techniques

a direct algebraic approach to observer design under switching measurement equations based on the algebraic transformation of a switched linear measurement equation into a nonlinear yet deterministic equation an asymptotic state observer is constructed for discrete time linear systems whose observations are generated according to randomly switching measurement modes the observer which combines the algebraic transformation with a newton observer applied to the resulting nonlinear measurement equation is shown to be locally exponentially convergent under arbitrary mode sequences

noninferiority trial designs for odds ratios and risk differences this study presents constrained maximum likelihood derivations of the design parameters of noninferiority trials for binary outcomes with the margin defined on the odds ratio or risk difference scale the derivations show that for trials in which the group specific response rates are equal under the point alternative hypothesis the common response rate n is a fixed design parameter whose value lies between the control and experimental rates hypothesized at the point null c e we show that setting n equal to the value of c that holds under h 0 underestimates the overall sample size requirement given c or c and the type i and ii error rates or algorithm finds clinically meaningful design values of n and the corresponding minimum asymptotic sample size n n e n c and optimal allocation ratio n e n c we find that optimal allocations are increasingly imbalanced as increases with 2 5 trial results that are presented on both scales will differ in power with more power lost if the study is designed on the risk difference scale and reported on the odds ratio scale than vice versa

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

a multivariable self tuning pid controller abstract a multivariable self tuning controller with a proportional plus integral plus derivative pid structure is derived the algorithm features a combination of the self tuning property in which the controller parameters are tuned automatically on line and also the structure of a multivariable pid controller making it more favourable to be used in industry a stability proof of the algorithm is also presented here comparison of the performance of the algorithm with a fixed tuned multivariable pid controller in the simulation examples demonstrates the effectiveness of the proposed algorithm

a tutorial on particle filters for online nonlinear non gaussian bayesian tracking increasingly for many application areas it is becoming important to include elements of nonlinearity and non gaussianity in order to model accurately the underlying dynamics of a physical system moreover it is typically crucial to process data on line as it arrives both from the point of view of storage costs as well as for rapid adaptation to changing signal characteristics in this paper we review both optimal and suboptimal bayesian algorithms for nonlinear non gaussian tracking problems with a focus on particle filters particle filters are sequential monte carlo methods based on point mass or particle representations of probability densities which can be applied to any state space model and which generalize the traditional kalman filtering methods several variants of the particle filter such as sir asir and rpf are introduced within a generic framework of the sequential importance sampling sis algorithm these are discussed and compared with the standard ekf through an illustrative example

planning and analysis of three arm non inferiority trials with binary endpoints three arm trials including an experimental treatment an active control and a placebo group are frequently preferred for the assessment of non inferiority in contrast to two arm non inferiority studies these designs allow a direct proof of efficacy of a new treatment by comparison with placebo as a further advantage the test problem for establishing non inferiority can be formulated in such a way that rejection of the null hypothesis assures that a pre defined portion of the unknown effect the reference shows versus placebo is preserved by the treatment under investigation we present statistical methods for this study design and the situation of a binary outcome variable asymptotic test procedures are given and their actual type i error rates are calculated approximate sample size formulae are derived and their accuracy is discussed furthermore the question of optimal allocation of the total sample size is considered power properties of the testing strategy including a pre test for assay sensitivity are presented the derived methods are illustrated by application to a clinical trial in depression

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

new developments in state estimation for nonlinear systems based on an interpolation formula accurate state estimators for nonlinear systems can be derived the estimators do not require derivative information which makes them simple to implement

an extended kalman filter frequency tracker for high noise environments the problem of constructing a frequency tracker for weak narrowband signals with slowly varying frequency is considered an extended kalman filter is proposed that uses prior knowledge of the nature of the signal to overcome the difficulties presented by the inherent nonlinearity of the problem and the very low signal to noise ratios

improved cubature kalman filter for gnss ins based on transformation of posterior sigma points error tightly coupled gnss ins has been widely approved as a promising substitute for standalone gnss in urban areas navigation however due to the frequent gnss signal outages the filter used in gnss ins should be insensitive to the less informative observations in this paper a novel sigma points update method is proposed to enhance the robustness of cubature kalman filter ckf under the circumstance of unavailable observations first the problems of existing sampling based filters are analyzed then by transforming the posterior sigma points error matrix from prediction phase of filtering to the posterior domain of update the updated sigma points are expected to capture the covariance more precisely than traditional sigma points finally an improved ckf ickf is developed by embedding these points into the bayesian estimation framework and the upper bounds of error covariance matrices are analyzed theoretically signal outages with different durations are simulated and results demonstrate that ickf outperforms state of the art methods

nonlinear estimation applying an unscented transformation in systems with correlated uncertain observations an approximation to the least squares filter is proposed for discrete signals whose evolution is governed by nonlinear functions when the estimation is based on nonlinear observations with additive noise which can consist only of random noise this uncertainty in the observation process is modelled by bernoulli random variables which are correlated at consecutive time instants and are otherwise independent the proposed recursive approximation is based on the unscented principle successive applications of the unscented transformation to a suitable augmented state vector enable us to approximate the one stage state and observation predictors from the state filter at the previous time instant the performance of the proposed algorithm is compared with that of an extended algorithm in a numerical simulation example

comparison of tests and sample size formulae for proving therapeutic equivalence based on the difference of binomial probabilities to prove the hypothesis that a new treatment is as effective as a standard one a possibility is to test the one sided null hypothesis of a clear inferiority of the new treatment against the alternative hypothesis that if at all it is only negligibly inferior such a problem is of clinical relevance if for instance a new treatment with an effectiveness which is comparable to that of the standard one would be preferred if it is less toxic if the difference between the two treatments is measured by the difference of failure rates approximate statistical tests and sample size formulae have to be used this paper reports the results of an extensive empirical investigation comparing the well known calculations proposed by blackwelder rodary comnougue and tournade which propose a sample size formula for the test of dunnett and gent and farrington and manning the investigation was conducted in order to allow more comprehensive conclusions than those which may be drawn from the limited examples given by the last authors for the usual settings in clinical trials the formulae of farrington and manning are recommended however there are combinations of statistical parameters for which they are not preferred

test statistics and sample size formulae for comparative binomial trials with null hypothesis of non zero risk difference or non unity relative risk when it is required to establish a materially significant difference between two treatments or alternatively to show that two treatments are equivalent standard test statistics and sample size formulae based on a null hypothesis of no difference no longer apply this paper reviews some of the test statistics and sample size formulae proposed for comparative binomial trials when the null hypothesis is of a specified non zero difference or non unity relative risk methods based on restricted maximum likelihood estimation are recommended and applied to studies of pertussis vaccine

luenberger observers for switching discrete time linear systems state estimation is considered for a class of switching discrete time linear systems the switching is assumed to be unknown among the various system modes associated with different known matrices the proposed scheme relies on the combination of the estimation of the system mode with the application of a luenberger like observer whose gain is a function of the estimated mode in the absence of noises the estimate of the mode can be chosen among the ones that are consistent with the measurements and the stability of the estimation error is ensured under suitable conditions on the observer gains such conditions can be expressed by means of linear matrix inequalities lmis the presence of bounded disturbances is also taken explicitly into consideration in this situation a novel method based on a minimum distance criterion is proposed in order to estimate the system mode also in this case the error of the resulting estimator is proved to be exponentially bounded

constrained state estimation for nonlinear discrete time systems stability and moving horizon approximations state estimator design for a nonlinear discrete time system is a challenging problem further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances one strategy for constrained state estimation is to employ online optimization using a moving horizon approximation we propose a general theory for constrained moving horizon estimation sufficient conditions for asymptotic and bounded stability are established we apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation examples are used to illustrate the benefits of constrained state estimation our framework is deterministic

moving horizon observer with regularisation for detectable systems without persistence of excitation a constrained moving horizon observer is developed for nonlinear discrete time systems the algorithm is proved to converge exponentially under a detectability assumption with the data being exciting at all times however in many practical estimation problems such as combined state and parameter estimation the data may not be exciting for every period of time the algorithm therefore has regularisation mechanisms to ensure robustness and graceful degradation of performance in cases when the data are not exciting this includes the use of a priori estimates in the moving horizon cost function and the use of thresholded singular value decomposition to avoid ill conditioned or ill posed inversion of the associated nonlinear algebraic equations that define the moving horizon cost function the latter regularisation relies on monitoring of the rank of an estimate of a hessian like matrix and conditions for uniform exponential convergence are given the method is in particular useful with augmented state sp

a multivariable self tuning controller with integral action abstract in this paper a novel stochastic self tuning control algorithm for multivariable linear systems described by controlled autoregressive integrating moving average carima models is proposed in particular the presence of an integral action on each component of the error vector ensures the robust offset rejection for any constant load disturbance acting on the plant the leading assumption is made that the system interactor matrix is known a priori the algorithm is derived by resorting to the generalized minimum variance approach two simulation examples illustrate the main features of the method

a strong tracking extended kalman observer for nonlinear discrete time systems the authors show how the extended kalman filter used as an observer for nonlinear discrete time systems or extended kalman observer eko becomes a useful state estimator when the arbitrary matrices namely r sub k and q sub k are adequately chosen as a first step we use the linearization technique given by boutayed et al 1997 which consists of introducing unknown diagonal matrices to take the approximation errors into account it is shown that the decreasing lyapunov function condition leads to a linear matrix inequality lmi problem which points out the connection between a good convergence behavior of the eko and the instrumental matrices r sub k and q sub k in order to satisfy the obtained lmi a particular design of q sub k is given high performances of the proposed technique are shown through numerical examples under the worst conditions

design and implementation of gaussian filter for nonlinear system with randomly delayed measurements and correlated noises abstract in this paper we focus on the nonlinear state estimation problem with both one step randomly delayed measurements and correlated noises firstly a general framework of gaussian filter is designed under gaussian assumption on the conditional density furthermore the implementation of gaussian filter is transformed into the computation of the nonlinear numerical integrals in the proposed framework secondly a new cubature kalman filtering ckf algorithm is developed on the basis of the spherical radial cubature rule for approximating such nonlinear integrals finally the performance of the modified ckf is verified by a numerical simulation example

moving horizon state estimation for nonlinear discrete time systems new stability results and approximation schemes a moving horizon state estimation problem is addressed for a class of nonlinear discrete time systems with bounded noises acting on the system and measurement equations as the statistics of such disturbances and of the initial state are assumed to be unknown we use a generalized least squares approach that consists in minimizing a quadratic estimation cost function defined on a recent batch of inputs and outputs according to a sliding window strategy for the resulting estimator the existence of bounding sequences on the estimation error is proved in the absence of noises exponential convergence to zero is obtained moreover suboptimal solutions are sought for which a certain error is admitted with respect to the optimal cost value the approximate solution can be determined either on line by directly minimizing the cost function or off line by using a nonlinear parameterized function simulation results are presented to show the effectiveness of the proposed approach in comparison with the extended kalman filter

further results on the uniform observability of discrete time nonlinear systems in this technical note the relation between notions of uniform observability of discrete time nonlinear systems based on injectivity of an observation map window the full rankness of its jacobian and a k function is investigated it is proven that a system is uniformly observable in the sense of injectivity of the observation map together with the full rankness of its jacobian if and only if it is so in some k function senses

a new continuous discrete particle filter for continuous discrete nonlinear systems abstract the continuous discrete version of particle filter cd pf for continuous discrete nonlinear systems is proposed in this paper firstly the continuous discrete extended kalman filter cd ekf and the cd pf are described in detail then some comparisons of these two methods are carried out the simulation results show that the performance of the cd pf is better than that of the cd ekf then higher order stochastic runge kutta schemes are proposed to improve the stability and precision of the filter furthermore the cd pf is applied to nonlinear systems with nongaussian noise finally some simulations are provided to illustrate the effectiveness of the proposed filter

the extended kalman filter as an exponential observer for nonlinear systems we analyze the behavior of the extended kalman filter as a state estimator for nonlinear deterministic systems using the direct method of lyapunov we prove that under certain conditions the extended kalman filter is an exponential observer i e the dynamics of the estimation error is exponentially stable furthermore we discuss a generalization of the kalman filter with exponential data weighting to nonlinear systems

minimization of sample size when comparing two small probabilities in a non inferiority safety trial in clinical trials success rates of two treatments to be compared often range from 10 to 90 per cent when the comparison probabilities are much smaller than 10 per cent standard methods for sample size and power calculations may provide invalid results this situation may occur when there is interest in safety rather than in efficacy in such trials no more patients should be included than strictly necessary we compared the results of maximum likelihood methods for the computation of sample sizes in a non inferiority trial including exact procedures and considered unequal sample sizes for experimental and reference treatment an exact unequal sample size maximum likelihood procedure is advocated when the specified non zero risk difference under the null hypothesis is not too large such a procedure is also indicated when the parameter of interest is the relative risk rather than the risk difference

predictive control of switched nonlinear systems with scheduled mode transitions in this work a predictive control framework is proposed for the constrained stabilization of switched nonlinear systems that transit between their constituent modes at prescribed switching times the main idea is to design a lyapunov based predictive controller for each constituent mode in which the switched system operates and incorporate constraints in the predictive controller design which upon satisfaction ensure that the prescribed transitions between the modes occur in a way that guarantees stability of the switched closed loop system this is achieved as follows for each constituent mode a lyapunov based model predictive controller mpc is designed and an analytic bounded controller using the same lyapunov function is used to explicitly characterize a set of initial conditions for which the mpc irrespective of the controller parameters is guaranteed to be feasible and hence stabilizing then constraints are incorporated in the mpc design which upon satisfaction ensure that 1 the state of the closed loop system at the time of the transition resides in the stability region of the mode that the system is switched into and 2 the lyapunov function for each mode is nonincreasing wherever the mode is reactivated thereby guaranteeing stability the proposed control method is demonstrated through application to a chemical process example

correspondence comments on performance evaluation of ukf based nonlinear filtering this note points out that the main result of the paper xiong k zhang h y chan c w 2006 performance evaluation of ukf based nonlinear filtering automatica 42 2 261 270 can be extended to a class of so called gaussian filters it justifies a practical countermeasure of the divergence i e adding small quantities to the noise covariance matrix to stabilize the filter

simultaneous state and input estimation of hybrid systems with unknown inputs this paper addresses the problem of the simultaneous state and input estimation for hybrid systems when subject to input disturbances the proposed algorithm is based on the moving horizon estimation mhe method and uses mixed logical dynamical mld systems as equivalent representations of piecewise affine pwa systems so far the mhe method has been successfully applied for the state estimation of linear hybrid and nonlinear systems the proposed extension of the mhe algorithm enables the estimation of unknown inputs or disturbances acting on the hybrid system the new algorithm is shown to improve the convergence characteristics of the mhe method by reducing the delay of convergent estimates while assuring convergence for every possible sequence of input disturbances to ensure convergence the system is required to be incrementally input observable which is an extension to the classical incremental observability property