matrix representations of sturm liouville problems with transmission conditions we identify a class of sturm liouville equations with transmission conditions such that any sturm liouville problem consisting of such an equation with transmission condition and an arbitrary separated or real coupled self adjoint boundary condition has a representation as an equivalent finite dimensional matrix eigenvalue problem conversely given any matrix eigenvalue problem of certain type and an arbitrary separated or real coupled self adjoint boundary condition and transmission condition we construct a class of sturm liouville problems with this specified boundary condition and transmission condition each of which is equivalent to the given matrix eigenvalue problem

state estimation for discrete time markov jump linear systems with time correlated measurement noise abstract in this paper the state estimation problem for discrete time markov jump linear systems affected by time correlated measurement noise is considered where the time correlated measurement noise is described by a linear system model with white noise as a result two algorithms are proposed to estimate the state of the system under consideration based on a measurement sequence the first algorithm is optimal in the sense of minimum mean square error which is obtained based on the measurement differencing method bayes rule and some results derived in this paper the second algorithm is a suboptimal algorithm obtained by using a lot of gaussian hypotheses the proposed suboptimal algorithm is finite dimensionally computable and does not increase computational and storage load with time computer simulations are carried out to evaluate the performance of the proposed suboptimal algorithm

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

dynamic quantizer design for hidden markov state estimation via multiple sensors with fusion center feedback this paper considers the state estimation of hidden markov models by sensor networks the objective is to minimize the long term average of the mean square estimation error for the underlying finite state markov chain by employing feedback from the fusion center a dynamic quantization scheme for the sensor nodes is proposed and analyzed by a stochastic control approach dynamic rate allocation is also considered when the sensor nodes generate mode dependent measurements

multiple model estimation with variable structure existing multiple model mm estimation algorithms have a fixed structure i e they use a fixed set of models an important fact that has been overlooked for a long time is how the performance of these algorithms depends on the set of models used limitations of the fixed structure algorithms are addressed first in particular it is shown theoretically that the use of too many models is performance wise as bad as that of too few models apart from the increase in computation this paper then presents theoretical results pertaining to the two ways of overcoming these limitations select construct a better set of models and or use a variable set of models this is in contrast to the existing efforts of developing better implementable fixed structure estimators both the optimal mm estimator and practical suboptimal algorithms with variable structure are presented a graph theoretic formulation of multiple model estimation is also given which leads to a systematic treatment of model set adaptation and opens up new avenues for the study and design of the mm estimation algorithms the new approach is illustrated in an example of a nonstationary noise identification problem

formulas for calculating the extremum ranks and inertias of a four term quadratic matrix valued function and their applications abstract this paper studies the quadratic matrix valued function x dxax d dxb b x d c through some expansion formulas for ranks and inertias of hermitian matrices where a b c and d are given complex matrices with a and c hermitian x is a variable matrix and denotes the conjugate transpose of a complex matrix we first introduce an algebraic linearization method for studying this matrix valued function and establish a group of explicit formulas for calculating the global maximum and minimum ranks and inertias of this matrix valued function with respect to the variable matrix x we then use these rank and inertia formulas to derive i necessary and sufficient conditions for the matrix equation x 0 to have a solution as well as the four matrix inequalities x 0 in the lowner partial ordering to be feasible respectively ii necessary and sufficient conditions for the four matrix inequalities x 0 in the lowner partial ordering to hold for all matrices x respectively iii the two matrices x and x such that the inequalities x x and x x hold for all matrices x in the lowner partial ordering respectively an application of the quadratic matrix valued function in control theory is also presented

robust state estimation and fault diagnosis for uncertain hybrid systems abstract robust state estimation and fault diagnosis are challenging problems in the research into hybrid systems in this paper a novel robust hybrid observer is proposed for a class of hybrid systems with unknown inputs and faults model uncertainties disturbances and faults are represented as structured unknown inputs the robust hybrid observer consists of a mode observer for mode identification and a continuous observer for continuous state estimation and mode transition detection it is shown that the mode can be identified correctly and the continuous state estimation error is exponentially uniformly bounded robustness to model uncertainties and disturbances can be guaranteed for the hybrid observer by disturbance decoupling furthermore the detectability and mode identifiability conditions are rigorously analyzed on the basis of the robust hybrid observer a robust fault detection and isolation scheme is presented also in the paper simulations of a hybrid four tank system show the proposed approach is effective

matrix representations of sturm liouville problems with coupled eigenparameter dependent boundary conditions abstract we study the matrix representations of sturm liouville problems with coupled eigenparameter dependent boundary conditions with a finite spectrum we prove for any positive integer n the considered problems have at most n 3 eigenvalues and show that this kind of sturm liouville problems with coupled eigenparameter dependent boundary conditions is equivalent to a class of matrix eigenvalue problems in the sense that they have exactly the same eigenvalues

the study of jacobi and cyclic jacobi matrix eigenvalue problems using sturm liouville theory abstract we study the eigenvalues of matrix problems involving jacobi and cyclic jacobi matrices as functions of certain entries of particular interest are the limits of the eigenvalues as these entries approach infinity our approach is to use the recently discovered equivalence between these problems and a class of sturm liouville problems and then to apply the sturm liouville theory

state estimation for discrete time markov jump linear systems with time correlated and mode dependent measurement noise abstract the state estimation problem for discrete time markov jump linear systems corrupted by time correlated and mode dependent measurement noise is considered where the time correlated and mode dependent measurement noise is described via a discrete time stochastic system with markov parameter and kronecker delta function by defining the measurement noise in this manner both time correlation and periodic step change caused by the change of system environment or structure can be embodied in the measurement noise a novel distributed measurement differencing method is applied to the problem of state estimation under consideration so that two algorithms are obtained using some results presented in this paper the first algorithm is optimal in the sense of minimum mean square error which can exactly compute the minimum mean square error estimate of system state the second algorithm is suboptimal and the suboptimality of the algorithm is caused by using some gaussian hypotheses the two proposed algorithms are recursive and the proposed suboptimal algorithm has a time independent complexity the performance of the proposed suboptimal algorithm is illustrated using computer simulations

dependence of the nth sturm liouville eigenvalue on the problem abstract we consider the nth eigenvalue as a function on the space of self adjoint regular sturm liouville problems with positive leading coefficient and weight functions the discontinuity of the nth eigenvalue is completely characterized

brief paper risk sensitive filtering for jump markov linear systems in this paper a risk sensitive multiple model filtering algorithm is derived using the reference probability methods first the approximation of the interacting multiple model imm algorithm is identified in the reference probability domain then the same type of approximation is used to derive the finite dimensional risk sensitive filtering algorithm the derived algorithm reduces to the imm filter when the risk sensitive parameter goes to zero and reduces to the risk sensitive filter for linear gauss markov systems when the number of models is unity the algorithm performs better in a simulated uncertain parameter scenario than the imm filter

further characterizations of design optimality and admissibility for partial parameter estimation in linear regression the paper gives a contribution to the problem of finding optimal linear regression designs when only s out of k regression parameters are to be estimated also a treatment of design admissibility for the parameters of interest is included previous results of kiefer and wolfowitz 1959 karlin and studden 1966 and atwood 1969 are generalized in particular a connection to tchebycheff type approximation of ri valued functions is found which has been known in case s 1 strengthened versions of the results are obtained for invariant designs in situations when invariance properties of the regression setup are available applications are given to multiple quadratic regression and to one dimensional polynomial regression 1 introduction consider a linear regression y x a f x x e with an unknown coefficient vector a e r k and a known r valued function f on the experimental region y the range f y is assumed to be compact as usual observations y1 yn on the dependent variable y taken at points xl xn e e x respectively are assumed to have expectations y x 1 0 and to be pairwise uncorrelated suppose that the experiment aims at estimating ka where k is a given s x k matrix of rank s for example when the first s components of a are to be estimated one has k is 0 where it denotes the unit matrix of order s we will study design optimality and admissibility for estimating ka within the approximate design theory an approximate design is a probability measure on x with finite support the infornation matrix per observation and unit of variance of f is m t ff x f x dd x e f x f x ox f x supp

general model set design methods for multiple model approach multiple model approach provides the state of the art solutions to many problems involving estimation filtering control and or modeling one of the most important problems in the application of the multiple model approach is the design of the model set used in a multiple model algorithm to our knowledge however it has never been addressed systematically in the literature this paper deals with this challenging topic in a general setting general problems of model set design are considered a concept of a random model is introduced in other words modeling of models used in a multiple model mm algorithm as well as the true model as random variables is proposed three classes of general methods for optimal design of model sets by minimizing distribution mismatch minimizing modal distance and moment matching respectively are proposed theoretical results that address many of the associated issues are presented examples that demonstrate how some of these theoretical results can be used as well as their effectiveness are given many of the general results presented in this paper are also useful for performance evaluation of mm algorithms

an em algorithm for nonlinear state estimation with model uncertainties in most solutions to state estimation problems e g target tracking it is generally assumed that the state transition and measurement models are known a priori however there are situations where the model parameters or the model structure itself are not known a priori or are known only partially in these scenarios standard estimation algorithms like the kalman filter and the extended kalman filter ekf which assume perfect knowledge of the model parameters are not accurate in this paper the nonlinear state estimation problem with possibly non gaussian process noise in the presence of a certain class of measurement model uncertainty is considered it is shown that the problem can be considered as a special case of maximum likelihood estimation with incomplete data thus in this paper we propose an em type algorithm that casts the problem in a joint state estimation and model parameter identification framework the expectation e step is implemented by a particle filter that is initialized by a monte carlo markov chain algorithm within this step the posterior distribution of the states given the measurements as well as the state vector itself are estimated consequently in the maximization m step we approximate the nonlinear observation equation as a mixture of gaussians mog model during the m step the mog model is fit to the observed data by estimating a set of mog parameters the proposed procedure called em pf expectation maximization particle filter algorithm is used to solve a highly nonlinear bearing only tracking problem where the model structure is assumed unknown a priori it is shown that the algorithm is capable of modeling the observations and accurately tracking the state vector in addition the algorithm is also applied to the sensor registration problem in a multi sensor fusion scenario it is again shown that the algorithm is successful in accommodating an unknown nonlinear model for a target tracking scenario

matrix representations of sturm liouville problems with eigenparameter dependent boundary conditions abstract we show that a class of regular self adjoint sturm liouville problems with eigenparameter dependent boundary conditions are equivalent to a certain class of matrix problems equivalent here means that they have exactly the same eigenvalues

a new inverse three spectra theorem for jacobi matrices abstract this paper deals with an inverse three spectra problem for jacobi matrices where the spectrum of the full n n jacobi matrix t is prescribed together with the spectra of two matrices obtained from the principal submatrices of t denoted by t 1 n and t n 1 n by modifying the lower right entry of t 1 n and the upper left entry of t n 1 n here n satisfying 1 n n is fixed denote by t 1 n and t n 1 n the modified principal submatrices we give conditions for three given sets of points to be the spectra of a matrix t and of its two modified principal submatrices t 1 n and t n 1 n to uniquely reconstruct the original matrix t where the matrix t is a rank 2 perturbation of t 1 n t n 1 n

solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method abstract we establish in this paper a group of closed form formulas for calculating the global maximum and minimum ranks and inertias of the quadratic hermitian matrix function x q x p x with respect to the variable matrix x by using a linearization method and some known formulas for extremum ranks and inertias of linear hermitian matrix functions where both p and q are complex hermitian matrices and x is the conjugate transpose of x we then derive the global maximum and minimum ranks and inertias of the two quadratic hermitian matrix functions 1 x q 1 x p 1 x and 2 x q 2 x p 2 x subject to a consistent matrix equation a x b respectively by using some pure algebraic operations of matrices and their generalized inverses as consequences we establish necessary and sufficient conditions for the solutions of the matrix equation a x b to satisfy the quadratic hermitian matrix equalities x p 1 x q 1 and x p 2 x q 2 respectively and for the quadratic matrix inequalities x p 1 x q 1 and x p 2 x q 2 in the lowner partial ordering to hold respectively in addition we give complete solutions to four lowner partial ordering optimization problems on the matrix functions 1 x and 2 x subject to a x b examples are also presented to illustrative applications of the equality constrained quadratic optimizations in some matrix completion problems

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

mixture based extension of the ar model and its recursive bayesian identification an extension of the autoregressive ar model is studied which allows transformations and distortions on the regressor to be handled many important signal processing problems are amenable to this extended ar i e ear model it is shown that bayesian identification and prediction of the ear model can be performed recursively in common with the ar model itself the ear model does however require that the transformation be known when it is unknown the associated transformation space is represented by a finite set of candidates what follows is a mixture based ear model i e the mear model an approximate identification algorithm for mear is developed using a restricted variational bayes vb method this restores the elegant recursive update of sufficient statistics the mear model is applied to the robust identification of ar processes corrupted by outliers and burst noise respectively and to click removal for speech

an iterative algorithm for simulation error based identification of polynomial input output models using multi step prediction effective identification of polynomial input output models for applications requiring long range prediction or simulation performance relies on both careful model selection and accurate parameter estimation the simulation error minimisation sem approach has been shown to provide significant advantages in the model selection phase by ruling out candidate models with good short term prediction capabilities but unsuitable long term dynamics however sem based parameter estimation has been generally avoided due to excessive computational effort this article extends to the nonlinear case a computationally efficient approach for this task that was previously developed for linear models based on the iterative estimation of predictors with increasing prediction horizon conditions for the applicability of the approach to various model classes are also discussed finally some examples are provided to show the effectiveness and computational convenience of the proposed algorithm for polynomial input output

parameter and state estimation of nonlinear systems using a multi observer under the supervisory framework we present a hybrid scheme for the parameter and state estimation of nonlinear continuous time systems which is inspired by the supervisory setup used for control state observers are synthesized for some nominal parameter values and a criterion is designed to select one of these observers at any given time instant which provides state and parameter estimates assuming that a persistency of excitation condition holds the convergence of the parameter and state estimation errors to zero is ensured up to a margin which can be made as small as desired by increasing the number of observers to reduce the potential computational complexity of the scheme we explain how the sampling of the parameter set can be dynamically updated using a zoom in procedure this strategy typically requires a fewer number of observers for a given estimation error margin compared to the static sampling policy the results are shown to be applicable to linear systems and to a class of nonlinear systems we illustrate the applicability of the approach by estimating the synaptic gains and the mean membrane potentials of a neural mass model

matrix representations of fourth order boundary value problems with finite spectrum abstract we show that a class of regular self adjoint fourth order boundary value problems is equivalent to a certain class of matrix problems equivalent here means that they have exactly the same eigenvalues such an equivalence was previously known only in the second order case

an optimizing design strategy for multiple model adaptive estimation and control a method is proposed for designing multiple model adaptive estimators to provide combined state and parameter estimation in the presence of an uncertain parameter vector it is assumed that the parameter varies over a continuous region and a finite number of constant gain filters are available for the estimation the estimator elemental filters are shown by minimizing a cost functional representing the average state prediction error autocorrelation with the average taken as the true parameter ranges over the admissible parameter set an analogous method is proposed for designing multiple model adaptive regulators to provide stabilizing control in the presence of an uncertain parameter vector by minimizing a cost functional representing the average regulation error autocorrelation with the average taken as the true parameter ranges over the admissible parameter set an example is used to demonstrate the improvement in performance over previously accepted design methods

a method for recovering jacobi matrices with mixed spectral data abstract in this paper we employ the euclidean division for polynomials to recover uniquely a jacobi matrix in terms of the mixed spectral data consisting of its partial entries and the information given on its full spectrum together with a subset of eigenvalues of its truncated matrix obtained by deleting the last row and last column or its rank one modification matrix modified by adding a constant to the last element a necessary and sufficient condition is provided for the existence of the inverse problem a numerical algorithm and a numerical example are given

online bayesian estimation of transition probabilities for markovian jump systems markovian jump systems mjss evolve in a jump wise manner by switching among simpler models according to a finite markov chain whose parameters are commonly assumed known this paper addresses the problem of state estimation of mjs with unknown transition probability matrix tpm of the embedded markov chain governing the jumps under the assumption of a time invariant but random tpm an approximate recursion for the tpms posterior probability density function pdf within the bayesian framework is obtained based on this recursion four algorithms for online minimum mean square error mmse estimation of the tpm are derived the first algorithm for the case of a two state markov chain computes the mmse estimate exactly if the likelihood of the tpm is linear in the transition probabilities its computational load is however increasing with the data length to limit the computational cost three alternative algorithms are further developed based on different approximation techniques truncation of high order moments quasi bayesian approximation and numerical integration respectively the proposed tpm estimation is naturally incorporable into a typical online bayesian estimation scheme for mjs e g generalized pseudo bayesian gpb or interacting multiple model imm thus adaptive versions of mjs state estimators with unknown tpm are provided simulation results of tpm adaptive imm algorithms for a system with failures and maneuvering target tracking are presented

sturm liouville problems with finite spectrum abstract for every positive integer n we construct a class of regular self adjoint and non self adjoint sturm liouville problems with exactly n eigenvalues these n eigenvalues can be located anywhere in the complex plane in the non self adjoint case and anywhere along the real line in the self adjoint case the latter complements the well known general result for right definite sturm liouville problems with an infinite number of eigenvalues which must go to infinity asymptotically like n2 does with an appropriate and natural interpretation of a zero the eigenfunctions have the usual zero properties