cramer rao induced bounds for candecomp parafac tensor decomposition this paper presents a cramer rao lower bound crlb on the variance of unbiased estimates of factor matrices in canonical polyadic cp or candecomp parafac cp decompositions of a tensor from noisy observations i e the tensor plus a random gaussian i i d tensor a novel expression is derived for a bound on the mean square angular error of factors along a selected dimension of a tensor of an arbitrary dimension the expression needs less operations for computing the bound o nr6 than the best existing state of the art algorithm o n3r6 operations where n and r are the tensor order and the tensor rank insightful expressions are derived for tensors of rank 1 and rank 2 of arbitrary dimension and for tensors of arbitrary dimension and rank where two factor matrices have orthogonal columns the results can be used as a gauge of performance of different approximate cp decomposition algorithms prediction of their accuracy and for checking stability of a given decomposition of a tensor condition whether the crlb is finite or not a novel expression is derived for a hessian matrix needed in popular damped gauss newton method for solving the cp decomposition of tensors with missing elements beside computing the crlb for these tensors the expression may serve for design of damped gauss newton algorithm for the decomposition

design of robust controllers for time delay systems the problem of stabilizing linear dynamical time delay systems subject to bounded uncertainties is investigated two memoryless feedback controllers are considered it is established that when the matching conditions are met and certain bounding relations are satisfied then the linear controller renders the zero response of the system asymptotically stable saturation type controllers are shown to guarantee that all system responses are uniformly ultimately bounded

asymptotic global confidence regions for 3 d parametric shape estimation in inverse problems this paper derives fundamental performance bounds for statistical estimation of parametric surfaces embedded in ropf3 unlike conventional pixel based image reconstruction approaches our problem is reconstruction of the shape of binary or homogeneous objects the fundamental uncertainty of such estimation problems can be represented by global confidence regions which facilitate geometric inference and optimization of the imaging system compared to our previous work on global confidence region analysis for curves two dimensional 2 d shapes computation of the probability that the entire surface estimate lies within the confidence region is more challenging because a surface estimate is an inhomogeneous random field continuously indexed by a 2 d variable we derive an asymptotic lower bound to this probability by relating it to the exceedence probability of a higher dimensional gaussian random field which can in turn be evaluated using the tube formula due to sun simulation results demonstrate the tightness of the resulting bound and the usefulness of the three dimensional global confidence region approach

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

fast maximum likelihood for blind identification of multiple fir channels this paper develops a fast maximum likelihood method for estimating the impulse responses of multiple fir channels driven by an arbitrary unknown input the resulting method consists of two iterative steps where each step minimizes a quadratic function the two step maximum likelihood tsml method is shown to be high snr efficient i e attaining the cramer rao lower bound crb at high snr the tsml method exploits a novel orthogonal complement matrix of the generalized sylvester matrix simulations show that the tsml method significantly outperforms the cross relation cr method and the subspace ss method and attains the crb over a wide range of snr this paper also studies a fisher information fi matrix to reveal the identifiability of the m channel system a strong connection between the fi based identifiability and the cr based identifiability is established

on the number of signals resolvable by a uniform linear array an algebraic limitation on the maximum number of directions of arrival of plane waves that can be resolved by a uniform linear sensor array is studied achievable lower and upper bounds are derived on that number as a function of the number of elements in the array number of snapshots and the rank of the source sample correlation matrix the signals are assumed narrow band and of identical and known center frequency the results are also applicable in the coherent signal case and when directions of arrival are estimated from few snapshots while in the multiple snapshot case the lower bounds coincide with known asymptotic results the upper bounds indicate the potential for resolving more signals than by present methods of array processing

feasibility of tomography with unknown view angles in the standard two dimensional 2 d parallel beam tomographic formulation it is generally assumed that the angles at which the projections were acquired are known we have previously demonstrated however that under fairly mild conditions these view angles can be uniquely recovered from the projections themselves we address the question of reliability of such solutions to the angle recovery problem using moments of the projections we demonstrate that under mild conditions the angle recovery problem has unique solutions and is stable with respect to perturbations in the data furthermore we determine the cramer rao lower bounds on the variance of the estimates of the angles when the projection are corrupted by additive gaussian noise we also treat the case in which each projection is shifted by some unknown amount which must be jointly estimated with the view angles motivated by the stability results and relatively small values of the error bounds we construct a simple algorithm to approximate the ml estimator and demonstrate that the problem can be feasibly solved in the presence of noise simulations using this simple estimator on a variety of phantoms show excellent performance at low to moderate noise levels essentially achieving the cramer rao bounds

perturbed optimization in banach spaces i a general theory based on a weak directional constraint qualification using a directional form of constraint qualification weaker than robinson s we derive an implicit function theorem for inclusions and use it for first and second order sensitivity analyses of the value function in perturbed constrained optimization we obtain holder and lipschitz properties and under a no gap condition first order expansions for exact and approximate solutions as an application differentiability properties of metric projections in hilbert spaces are obtained using a condition generalizing polyhedricity we also present in the appendix a short proof of a generalization of the convex duality theorem in banach spaces

no gap second order optimality conditions for optimal control problems with a single state constraint and control the paper deals with optimal control problems with only one control variable and one state constraint of arbitrary order we consider the case of finitely many boundary arcs and touch times we obtain a no gap theory of second order conditions allowing to characterize second order quadratic growth

stability analysis of optimal control problems with a second order state constraint this paper gives stability results for nonlinear optimal control problems subject to a regular state constraint of second order the strengthened legendre clebsch condition is assumed to hold and no assumption on the structure of the contact set is made under a weak second order sufficient condition taking into account the active constraints we show that the solutions are lipschitz continuous w r t the perturbation parameter in the l 2 norm and holder continuous in the l infty norm we use a generalized implicit function theorem in metric spaces by dontchev and hager siam j control optim 36 1998 pp 698 718 the difficulty is that multipliers associated with second order state constraints have a low regularity they are only bounded measures we obtain lipschitz stability of a primitive of the state constraint multiplier

on unique localization of multiple sources by passive sensor arrays necessary and sufficient conditions are derived for the unique localization of narrowband sources having the same known center frequency by passive sensor arrays the conditions specify the maximum number of sources that can be uniquely localized by a general array that satisfies some mild geometric constraints the conditions are expressed in terms of the number of sensors and the rank of the correlation matrix of the sources two different conditions are presented the first guarantees uniqueness for every batch of sampled data the second which is weaker guarantees uniqueness for almost every batch of sampled data with the exception of a set of batches of measure zero it is shown that a condition that is slightly weaker than the second one is also necessary

tensor decomposition for signal processing and machine learning tensors or multiway arrays are functions of three or more indices i j k ldots similar to matrices two way arrays which are functions of two indices r c for row column tensors have a rich history stretching over almost a century and touching upon numerous disciplines but they have only recently become ubiquitous in signal and data analytics at the confluence of signal processing statistics data mining and machine learning this overview article aims to provide a good starting point for researchers and practitioners interested in learning about and working with tensors as such it focuses on fundamentals and motivation using various application examples aiming to strike an appropriate balance of breadth and depth that will enable someone having taken first graduate courses in matrix algebra and probability to get started doing research and or developing tensor algorithms and software some background in applied optimization is useful but not strictly required the material covered includes tensor rank and rank decomposition basic tensor factorization models and their relationships and properties including fairly good coverage of identifiability broad coverage of algorithms ranging from alternating optimization to stochastic gradient statistical performance analysis and applications ranging from source separation to collaborative filtering mixture and topic modeling classification and multilinear subspace learning

strict identifiability of multiple fir channels driven by an unknown arbitrary sequence the problem of blind identification of multiple finite impulse response fir channels driven by a common input arises in a wide range of applications it has received increasing attention in the signal processing community a system of multiple fir channels driven by an unknown input is said to be strictly identifiable if in the absence of noise the given channel outputs can only be realized by a unique up to a constant system impulse response and a unique input sequence we show necessary and sufficient conditions for strict identifiability and establish a connection among strict identifiability a cross relation based cr based identifiability and a fisher information based fi based identifiability

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

linear parameter varying discrete time delay systems stability and l 2 gain controllers in this paper we investigate a class of linear parameter varying discrete time delay lpvdtd systems where the state space matrices depend on time varying parameters and the delay is unknown but bounded we treat both notions of quadratic stability based on a single quadratic lyapunov function and affine quadratic stability using parameter dependent lyapunov functions in both cases we develop lmi based results of stability testing for time delay as well as delayless discrete time systems then we design state feedback controllers which guarantee quadratic stability and an induced l 2 norm bound for the case of dynamic output feedback control we use a parameter independent quadratic lyapunov krasovskii function to develop lmi based solvability conditions which are evaluated at the extreme points of the admissible parameter set throughout the paper complementary results for linear parameter varying discrete lpvd systems without delay are presented

some relaxation problems in optimal control theory usually the space u r is a space lp q endowed with its weak topology the space y g is a sobolev space w y q endowed with its weak topology or with the l q topology in the one dimensional case and condition ii is guaranteed by some boundedness or growth hypotheses on j and a when condition i is not fulfilled in general the existence of a solution of 1 1 may fail nevertheless it may be interesting to study the asymptotic 212 0022 247x 87 3 00

fir perfect signal reconstruction from multiple convolutions minimum deconvolver orders given p co prime finite impulse response fir filters h sub i spl isin r m sub h it well known that there exist q sub i spl isin r m sub q such that spl sigma sub i h sub i q sub i spl delta importantly this enables signal recovery from its convolutions with p spl ges 2 co prime fir filters by fir filtering we show that such q sub i exist almost surely if and only if m sub q spl ges m sub h 1 p 1 where x is the smallest integer greater than or equal to x the results also provide conditions for full rank of certain key matrices arising in the blind multichannel deconvolution problem

cramer rao lower bounds for low rank decomposition of multidimensional arrays unlike low rank matrix decomposition which is generically nonunique for rank greater than one low rank three and higher dimensional array decomposition is unique provided that the array rank is lower than a certain bound and the correct number of components equal to array rank is sought in the decomposition parallel factor parafac analysis is a common name for low rank decomposition of higher dimensional arrays this paper develops cramer rao bound crb results for low rank decomposition of three and four dimensional 3 d and 4 d arrays illustrates the behavior of the resulting bounds and compares alternating least squares algorithms that are commonly used to compute such decompositions with the respective crbs simple to check necessary conditions for a unique low rank decomposition are also provided

discontinuous control problems with state constraints linear formulations and dynamic programming principles abstract this paper aims at studying a class of discontinuous deterministic control problems under state constraints using a linear programming approach as for classical control problems gaitsgory and quincampoix 2009 16 goreac and serea 2011 19 the primal linear problem is stated on some appropriate space of probability measures naturally the support of these measures is contained in the set of constraints this linearized value function and its dual can alternatively be seen as the limit of standard penalized problems second we provide a semigroup property for this set of probability measures leading to dynamic programming principles for control problems under state constraints an abstract principle is provided for general bounded costs linearized versions are obtained under further semi continuity assumptions

worst case cramer rao bounds for parametric estimation of superimposed signals with applications the problem of parameter estimation of superimposed signals in white gaussian noise is considered the effect of the correlation structure of the signals on the cramer rao bounds is studied for both the single and multiple experiment cases the best and worst conditions are found using various criteria the results are applied to the example of parameter estimation of superimposed sinusoids or plane wave direction finding in white gaussian noise and best and worst conditions on the correlation structure and relative phase of the sinusoids are found this provides useful information on the limits of the resolvability of sinusoid signals in time series analysis or of plane waves in array processing the conditions are also useful for designing worst case simulation studies of estimation algorithms and for the design of minimax signal acquisition and estimation procedures as demonstrated by an example

relaxation of constrained control problems the problem of relaxation of optimal control problems with state and control constraints is formulated in this paper we determine that if the original problem consists of minimizing over control functions z g x t subject to d x ds f s x z t s leq t and h s x s z s leq 0 for a e t leq s leq t then the relaxed problem consists of minimizing over measure valued control functions m g xhat t subject to d xhat ds int z f s xhat s z m s dz and m s esssup z h s xhat s z leq 0 for a e t leq s leq t for each s this is the essential supremum of h in z with respect to the measure m s

resilient control of non linear discrete time state delay systems a class of non linear discrete time systems with state delay is considered we develop an lmi based analysis and design procedures to check primarily into the robust stability of discrete time systems with state delay and bounded non linearities then we address the robust stabilization using nominal and resilient feedback designs in both cases the trade off between the size of the controller gains and the bounding factors is illuminated and incorporated into the design formalism seeking computational convenience all the developed results are cast in the format of linear matrix inequalities lmis and several numerical examples are presented throughout the paper to illustrate the feasibility of the theoretical developments

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

second order necessary conditions in pontryagin form for optimal control problems in this article we state and prove first and second order necessary conditions in pontryagin form for optimal control problems with pure state and mixed control state constraints we say that a lagrange multiplier of an optimal control problem is a pontryagin multiplier if it is such that pontryagin s minimum principle holds and we call optimality conditions in pontryagin form those which only involve pontryagin multipliers our conditions rely on a technique of partial relaxation and apply to pontryagin local minima

sensitivity analysis for relaxed optimal control problems with final state constraints in this article we compute a second order expansion of the value function of a family of relaxed optimal control problems with final state constraints parameterized by a perturbation variable the sensitivity analysis is performed for controls that we call r strong solutions they are optimal solutions with respect to the set of feasible controls with a uniform norm smaller than a given r and having an associated trajectory in a small neighborhood for the uniform norm in this framework relaxation enables us to consider a wide class of perturbations and therefore to derive sharp estimates of the value function

relaxation of control systems under state constraints in this paper we provide a relaxation result for control systems under both equality and inequality constraints involving the state and the control in particular we show that the mangasarian fromowitz constraint qualification allows us to rewrite constrained systems as differential inclusions with locally lipschitz right hand side then the filippov wazewski relaxation theorem may be applied to show that ordinary solutions are dense in the set of relaxed solutions if besides agreeing with the above constraints the state has to remain in a control independent set k then the mangasarian fromowitz condition cannot hold this case is investigated as well by means of a condition on the feasible velocities on the boundary of k

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

stabilization analysis for discrete time systems with time delay the stabilization problem for a class of discrete time systems with time varying delay is investigated by constructing an augmented lyapunov function some sufficient conditions guaranteeing exponential stabilization are established in forms of linear matrix inequality lmi technique when norm bounded parameter uncertainties appear in the delayed discrete time system a delay dependent robust exponential stabilization criterion is also presented all of the criteria obtained in this paper are strict linear matrix inequality conditions which make the controller gain matrix can be solved directly three numerical examples are provided to demonstrate the effectiveness and improvement of the derived results

brief non fragile h control for linear systems with multiplicative controller gain variations this paper is concerned with the problem of non fragile h controller design for linear time invariant systems the controller to be designed is assumed to have multiplicative gain variations design methods are presented in terms of symmetric positive definite solutions of algebraic riccati inequalities the resulting design is such that the closed loop system is robustly stable and has an h disturbance attenuation bound with respect to the multiplicative controller gain variations a numerical example is given to illustrate the design methods

technical communique robust h control of discrete systems with uncertain parameters and unknown delays in this paper we address the problems of robust h performance analysis and control synthesis for a class of discrete time systems with norm bounded parameter uncertainty and unknown constant state delay through finite dimensional algebraic riccati equations we provide a necessary and sufficient condition for designing a memoryless state feedback controller which stabilizes the discrete time delay system under consideration and guarantees an h norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown delays an example is worked out to illustrate the developed theory