identification for control optimal input design with respect to a worst case nu gap cost function parameter identification experiments deliver an identified model together with an ellipsoidal uncertainty region in parameter space the objective of robust controller design is thus to stabilize all plants in the identified uncertainty region the subject of the present contribution is to design an identification experiment such that the worst case nu gap over all plants in the resulting uncertainty region between the identified plant and plants in this region is as small as possible the experiment design is performed via input power spectrum optimization two cost functions are investigated which represent different levels of trade off between accuracy and computational complexity it is shown that the input optimization problem with respect to these cost functions is amenable to standard numerical algorithms used in convex analysis

super resolution on the sphere using convex optimization this paper considers the problem of recovering an ensemble of diracs on a sphere from its low resolution measurements the diracs can be located at any location on the sphere not necessarily on a grid we show that under a separation condition one can recover the ensemble with high precision by a three stage algorithm which consists of solving a semi definite program root finding and least square fitting the algorithm s computation time depends solely on the number of measurements and not on the required solution accuracy we also show that in the special case of non negative ensembles a sparsity condition is sufficient for recovery furthermore in the discrete setting we estimate the recovery error in the presence of noise as a function of the noise level and the super resolution factor

relative entropy and the multivariable multidimensional moment problem entropy like functionals on operator algebras have been studied since the pioneering work of von neumann umegaki lindblad and lieb the best known are the von neumann entropy rho trace rhologrho and a generalization of the kullback leibler distance s rhoparsigma trace rhologrho rhologsigma referred to as quantum relative entropy and used to quantify distance between states of a quantum system the purpose of this paper is to explore and s as regularizing functionals in seeking solutions to multivariable and multidimensional moment problems it will be shown that extrema can be effectively constructed via a suitable homotopy the homotopy approach leads naturally to a further generalization and a description of all the solutions to such moment problems this is accomplished by a renormalization of a riemannian metric induced by entropy functionals as an application we discuss the inverse problem of describing power spectra which are consistent with second order statistics which has been the main motivation behind the present work

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

a useful input parameterization for optimal experiment design optimal inputs are usually determined by minimizing a scalar valued function of the inverse fisher information matrix the function should be monotonically increasing this is the case e g for the trace and the determinant the minimization must be performed under some constraints to prevent the input or output amplitude to blow up in this note it is proved that assuming open loop experiments the optimal input signal can be realized as a certain arma process of low order or at least can be approximated with any degree of accuracy by such a process this allows the optimal input design problem to be reformulated as a standard static optimization problem of low dimension

factorization of finite rank hankel and toeplitz matrices the main purpose of this paper is to prove factorization results for finite hankel and toeplitz matrices that generalize known results for the positive semidefinite case generalized vandermonde matrices appear in the factorizations factorization theorems are proved for infinite hankel and toeplitz matrices of finite rank and the results for finite matrices are deduced via a technique of rank preserving extension

variance error quantifications that are exact for finite model order this paper is concerned with the frequency domain quantification of noise induced errors in dynamic system estimates preceding and seminal work on this problem has suggested general expressions that are approximations whose accuracy increases with observed data length and model order in the interests of improved accuracy this paper provides new expressions whose accuracy depends only on data length they are therefore exact for arbitrarily small true model order other authors have recognized the importance of such expressions and have derived them for the case of finite impulse response like model structures in which denominators are fixed at true values and only numerator terms are estimated this paper progresses beyond this situation to address the more general output error and box jenkins structures in which full dynamics models both numerator and denominator terms and noise models may be estimated a key aspect of the work here is that it establishes that the variance quantification problem is equivalent to that of deriving the reproducing kernel for a subspace that depends on the model structure being employed

on the georgiou lindquist approach to constrained kullback leibler approximation of spectral densities we consider the georgiou lindquist constrained approximation of spectra in the kullback leibler sense we propose an alternative iterative algorithm to solve the corresponding convex optimization problem the lagrange multiplier is computed as a fixed point of a nonlinear matricial map simulation indicates that the algorithm is extremely effective

sensitivity to basis mismatch in compressed sensing the theory of compressed sensing suggests that successful inversion of an image of the physical world broadly defined to include speech signals radar sonar returns vibration records sensor array snapshot vectors 2 d images and so on for its source modes and amplitudes can be achieved at measurement dimensions far lower than what might be expected from the classical theories of spectrum or modal analysis provided that the image is sparse in an apriori known basis for imaging problems in spectrum analysis and passive and active radar sonar this basis is usually taken to be a dft basis however in reality no physical field is sparse in the dft basis or in any apriori known basis no matter how finely we grid the parameter space the sources may not lie in the center of the grid cells and consequently there is mismatch between the assumed and the actual bases for sparsity in this paper we study the sensitivity of compressed sensing to mismatch between the assumed and the actual sparsity bases we start by analyzing the effect of basis mismatch on the best k term approximation error which is central to providing exact sparse recovery guarantees we establish achievable bounds for the l1 error of the best k term approximation and show that these bounds grow linearly with the image or grid dimension and the mismatch level between the assumed and actual bases for sparsity we then derive bounds with similar growth behavior for the basis pursuit l1 recovery error indicating that the sparse recovery may suffer large errors in the presence of basis mismatch although we present our results in the context of basis pursuit our analysis applies to any sparse recovery principle that relies on the accuracy of best k term approximations for its performance guarantees we particularly highlight the problematic nature of basis mismatch in fourier imaging where spillage from off grid dft components turns a sparse representation into an incompressible one we substantiate our mathematical analysis by numerical examples that demonstrate a considerable performance degradation for image inversion from compressed sensing measurements in the presence of basis mismatch for problem sizes common to radar and sonar

a multivariate generalization of prony s method abstract prony s method is a prototypical eigenvalue analysis based method for the reconstruction of a finitely supported complex measure on the unit circle from its moments up to a certain degree in this note we give a generalization of this method to the multivariate case and prove simple conditions under which the problem admits a unique solution provided the order of the moments is bounded from below by the number of points on which the measure is supported as well as by a small constant divided by the separation distance of these points stable reconstruction is guaranteed in its simplest form the reconstruction method consists of setting up a certain multilevel toeplitz matrix of the moments compute a basis of its kernel and compute by some method of choice the set of common roots of the multivariate polynomials whose coefficients are given in the second step all theoretical results are illustrated by numerical experiments

randomized interpolation and approximationof sparse polynomials we present a randomized algorithm that interpolates a sparse polynomial in polynomial time in the bit complexity model the algorithm can be also applied to approximate polynomials that can be approximated by sparse polynomials the approximation is in the l 2 norm

closed loop experiment design for linear time invariant dynamical systems via lmis all stationary experimental conditions corresponding to a discrete time linear time invariant causal internally stable closed loop with real rational system and feedback controller are characterized using the youla kucera parametrization finite dimensional parametrizations of the input spectrum and the youla kucera parameter allow a wide range of closed loop experiment design problems based on the asymptotic in the sample size covariance matrix for the estimated parameters to be recast as computationally tractable convex optimization problems such as semi definite programs in particular for box jenkins models a finite dimensional parametrization is provided which is able to generate all possible asymptotic covariance matrices as a special case the very common situation of a fixed controller during the identification experiment can be handled and optimal reference signal spectra can be computed subject to closed loop signal constraints finally a brief numerical comparison with closed loop experiment design based on a high model order variance expression is presented

a sensitivity analysis of the music algorithm a first order analysis of the sensitivity of the music algorithm to system errors which cause differences between the array manifold used by music and the true array manifold is presented the effect of such errors on the direction of arrival estimates is investigated the ability of the music algorithm to resolve two closely spaced sources in the presence of phase and gain errors in the array elements or the receivers or errors in the element locations is analyzed a formula for computing the failure threshold of music as a function of source separation and other system parameters is derived and tested by simulation the analysis assumes that the exact covariance matrix of array element outputs is known the infinite data case

efficient multidimensional diracs estimation with linear sample complexity estimating diracs in continuous two or higher dimensions is a fundamental problem in imaging previous approaches extended one dimensional 1 d methods like the ones based on finite rate of innovation fri sampling in a separable manner e g along the horizontal and vertical dimensions separately in 2 d the separate estimation leads to a sample complexity of mathcal o left k d right for k diracs in d dimensions despite that the total degrees of freedom only increase linearly with respect to d we propose a new method that enforces the continuous domain sparsity constraints simultaneously along all dimensions leading to a reconstruction algorithm with linear sample complexity mathcal o k or a gain of mathcal o left k d 1 right over previous fri based methods the multi dimensional dirac locations are subsequently determined by the intersections of hypersurfaces e g curves in 2 d which can be computed algebraically from the common roots of polynomials we first demonstrate the performance of the new multidimensional algorithm on simulated data multidimensional dirac location retrieval under noisy measurements then we show results on real data radio astronomy point source reconstruction from lofar telescope measurements and the direction of arrival estimation of acoustic signals using pyramic microphone arrays

music for multidimensional spectral estimation stability and super resolution this paper presents a performance analysis of the multiple signal classification music algorithm applied on d dimensional single snapshot spectral estimation while s true frequencies are located on the continuum of a bounded domain inspired by the matrix pencil form we construct a d fold hankel matrix from the measurements and exploit its vandermonde decomposition in the noiseless case music amounts to identifying a noise subspace evaluating a noise space correlation function and localizing frequencies by searching the s smallest local minima of the noise space correlation function in the noiseless case 2s d measurements guarantee an exact reconstruction by music as the noise space correlation function vanishes exactly at true frequencies when noise exists we provide an explicit estimate on the perturbation of the noise space correlation function in terms of noise level dimension d the minimum separation among frequencies the maximum and minimum amplitudes while frequencies are separated by 2 rayleigh length rl at each direction as a by product the maximum and minimum non zero singular values of the multidimensional vandermonde matrix whose nodes are on the unit sphere are estimated under a gap condition of the nodes under the 2 rl separation condition if noise is i i d gaussian we show that perturbation of the noise space correlation function decays like sqrt log bf n bf n as the sample size bf n increases when the separation among frequencies drops below 2 rl our numerical experiments show that the noise tolerance of music obeys a power law with the minimum separation of frequencies

identification for control of multivariable systems controller validation and experiment design via lmis this paper presents a new controller validation method for linear multivariable time invariant models classical prediction error system identification methods deliver uncertainty regions which are nonstandard in the robust control literature our controller validation criterion computes an upper bound for the worst case performance measured in terms of the h norm of a weighted closed loop transfer matrix achieved by a given controller over all plants in such uncertainty sets this upper bound on the worst case performance is computed via an lmi based optimization problem and is deduced via the separation of graph framework our main technical contribution is to derive within that framework a very general parametrization for the set of multipliers corresponding to the nonstandard uncertainty regions resulting from pe identification of mimo systems the proposed approach also allows for iterative experiment design the results of this paper are asymptotic in the data length and it is assumed that the model structure is flexible enough to capture the true system

brief paper identification and control joint input design and h state feedback with ellipsoidal parametric uncertainty via lmis one obstacle in connecting robust control with models generated from prediction error identification is that very few control design methods are able to directly cope with the ellipsoidal parametric uncertainty regions that are generated by such identification methods in this contribution we present a joint robust state feedback control input design procedure which guarantees stability and prescribed closed loop performance using models identified from experimental data this means that given h specifications on the closed loop transfer function are translated into sufficient requirements on the input signal spectrum used to identify the process the condition takes the form of a linear matrix inequality

sampling signals with finite rate of innovation the authors consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation examples of signals with a finite rate of innovation include streams of diracs e g the poisson process nonuniform splines and piecewise polynomials even though these signals are not bandlimited we show that they can be sampled uniformly at or above the rate of innovation using an appropriate kernel and then be perfectly reconstructed thus we prove sampling theorems for classes of signals and kernels that generalize the classic bandlimited and sinc kernel case in particular we show how to sample and reconstruct periodic and finite length streams of diracs nonuniform splines and piecewise polynomials using sinc and gaussian kernels for infinite length signals with finite local rate of innovation we show local sampling and reconstruction based on spline kernels the key in all constructions is to identify the innovative part of a signal e g time instants and weights of diracs using an annihilating or locator filter a device well known in spectral analysis and error correction coding this leads to standard computational procedures for solving the sampling problem which we show through experimental results applications of these new sampling results can be found in signal processing communications systems and biological systems

numerical solution of bivariate and polyanalytic polynomial systems finding the real solutions of a bivariate polynomial system is a central problem in robotics computer modeling and graphics computational geometry and numerical optimization we propose an efficient and numerically robust algorithm for solving bivariate and polyanalytic polynomial systems using a single generalized eigenvalue decomposition in contrast to existing eigen based solvers the proposed algorithm does not depend on grobner bases or normal sets nor does it require computing eigenvectors or solving additional eigenproblems to recover the solution the method transforms bivariate systems into polyanalytic systems and then uses resultants in a novel way to project the variables onto the real plane associated with the two variables solutions are returned counting multiplicity and their accuracy is maximized by means of numerical balancing and newton raphson refinement numerical experiments show that the proposed algorithm consistently recovers a higher percentage of solutions and is at the sa

structured low rank decomposition of multivariate hankel matrices abstract we present a new algorithm for the decomposition of a multivariate hankel matrix h as a sum of hankel matrices of small rank this decomposition corresponds to the decomposition of its symbol as a sum of polynomial exponential series by exploiting the properties of the associated artinian gorenstein quotient algebra a we obtain new ways to compute the frequencies and the weights of the decomposition from generalized eigenvectors of sub matrices of h the new method is a multivariate generalization of the so called pencil method for solving prony type problems we analyse its numerical behaviour in the presence of noisy input moments we describe rescaling techniques and newton iterations which improve the numerical quality of the reconstruction and show their impact for correcting errors on input moments

a performance analysis of subspace based methods in the presence of model errors i the music algorithm application of subspace based algorithms to narrowband direction of arrival doa estimation requires that both the array response in all directions of interest and the spatial covariance of the noise must be known in practice however neither of these quantities is known precisely depending on the degree to which they deviate from their nominal values serious performance degradation can result the performance of the music algorithm is examined for situations in which the noise covariance and array response are perturbed from their assumed values theoretical expressions for the error in the music doa estimates are derived and compared with simulations performed for several representative cases and with the appropriate cramer rao bound an optimally weighted version of music is proposed for a particular class of array errors

a globally convergent matricial algorithm for multivariate spectral estimation in this paper we first describe a matricial newton type algorithm designed to solve the multivariable spectrum approximation problem we then prove its global convergence finally we apply this approximation procedure to multivariate spectral estimation and test its effectiveness through simulation simulation shows that in the case of short observation records this method may provide a valid alternative to standard multivariable identification techniques such as matlab s pem and matlab s n4sid

subjective probability assessment in decision analysis partition dependence and bias toward the ignorance prior decision and risk analysts have considerable discretion in designing procedures for eliciting subjective probabilities one of the most popular approaches is to specify a particular set of exclusive and exhaustive events for which the assessor provides such judgments we show that assessed probabilities are systematically biased toward a uniform distribution over all events into which the relevant state space happens to be partitioned so that probabilities are partition dependent we surmise that a typical assessor begins with an ignorance prior distribution that assigns equal probabilities to all specified events then adjusts those probabilities insufficiently to reflect his or her beliefs concerning how the likelihoods of the events differ in five studies we demonstrate partition dependence for both discrete events and continuous variables studies 1 and 2 show that the bias decreases with increased domain knowledge studies 3 and 4 and that top experts in decision analysis are susceptible to this bias study 5 we relate our work to previous research on the pruning bias in fault tree assessment e g fischhoff et al 1978 and show that previous explanations of pruning bias enhanced availability of events that are explicitly specified ambiguity in interpreting event categories and demand effects cannot fully account for partition dependence we conclude by discussing implications for decision analysis practice

information matrix and d optimal design with gaussian inputs for wiener model identification we present a closed form expression for the fischer s information matrix associated with the identification of wiener models in the derivation we assume that the input signal is gaussian the analysis allows the linear sub system in the wiener model to have a generic rational transfer function of arbitrary order it also allows the static nonlinearity of the wiener model to be a polynomial of arbitrary degree in addition we show how this analysis can be used to design tractable algorithms for d optimal input design the idea is further extended to design optimal inputs consisting of a sequence of gaussian signals with different mean values and variances by combining gaussian inputs with different means we can tune the amplitude distribution of the input to achieve the best identification accuracy in d optimal sense the analytical results are also illustrated with some numerical simulations

technical communique asymptotic variance expressions for closed loop identification asymptotic variance expressions are analyzed for models that are identified on the basis of closed loop data the considered methods comprise the classical direct method as well as the more recently developed indirect methods employing coprime factorized models dual youla kucera parametrizations and the two stage approach the variance expressions are compared with the open loop situation and evaluated in terms of their relevance for subsequent model based control design

a generalized entropy criterion for nevanlinna pick interpolation with degree constraint we present a generalized entropy criterion for solving the rational nevanlinna pick problem for n 1 interpolating conditions and the degree of interpolants bounded by n the primal problem of maximizing this entropy gain has a very well behaved dual problem this dual is a convex optimization problem in a finite dimensional space and gives rise to an algorithm for finding all interpolants which are positive real and rational of degree at most n the criterion requires a selection of a monic schur polynomial of degree n it follows that this class of monic polynomials completely parameterizes all such rational interpolants and it therefore provides a set of design parameters for specifying such interpolants the algorithm is implemented in a state space form and applied to several illustrative problems in systems and control namely sensitivity minimization maximal power transfer and spectral estimation

on the frequency domain accuracy of closed loop estimates it has been argued that the frequency domain accuracy of high model order estimates obtained on the basis of closed loop data is largely invariant to whether direct or indirect approaches are used the analysis underlying this conclusion has employed variance expressions that are asymptotic both in the data length and the model order and hence are approximations when either of these are finite however recent work has provided variance expressions that are exact for finite possibly low model order and hence can potentially deliver more accurate quantification of estimation accuracy this paper and a companion one revisits the study of identification from closed loop data in light of these new quantifications and establishes that under certain assumptions there can be significant differences in the accuracy of frequency response estimates these discrepencies are established here and in the companion paper to be dependent on what type of direct indirect or joint input output identification strategy is pursued

judgment extremity and accuracy under epistemic vs aleatory uncertainty people view uncertain events as knowable in principle epistemic uncertainty as fundamentally random aleatory uncertainty or as some mixture of the two we show that people make more extreme probability judgments i e closer to 0 or 1 for events they view as entailing more epistemic uncertainty and less aleatory uncertainty we demonstrate this pattern in a domain where there is agreement concerning the balance of evidence pairings of teams according to their seed in a basketball tournament but individual differences in the perception of the epistemicness aleatoriness of that domain study 1 across a range of domains that vary in their perceived epistemicness aleatoriness study 2 in a single judgment task for which we only vary the degree of randomness with which events are selected study 3 and when we prime participants to see events as more epistemic or aleatory study 4 decomposition of accuracy scores suggests that the greater judgment extremity of more epistemic events can manifes

prony s method in several variables the paper gives an extension of prony s method to the multivariate case which is based on the relationship between polynomial interpolation normal forms modulo ideals and h bases though the approach is mainly of algebraic nature we also give an algorithm using techniques from numerical linear algebra to solve the problem in a fast and efficient way

a convex optimization approach to arma modeling we formulate a convex optimization problem for approximating any given spectral density with a rational one having a prescribed number of poles and zeros n poles and m zeros inside the unit disc and their conjugates the approximation utilizes the kullback leibler divergence as a distance measure the stationarity condition for optimality requires that the approximant matches n 1 covariance moments of the given power spectrum and m cepstral moments of the corresponding logarithm although the latter with possible slack the solution coincides with one derived by byrnes enqvist and lindquist who addressed directly the question of covariance and cepstral matching thus the present paper provides an approximation theoretic justification of such a problem since the approximation requires only moments of spectral densities and of their logarithms it can also be used for system identification

spectral estimation via selective harmonic amplification the state covariance of a linear filter is characterized by a certain algebraic commutativity property with the state matrix of the filter and also imposes a generalized interpolation constraint on the power spectrum of the input process this algebraic property and the relationship between state covariance and the power spectrum of the input allow the use of matrix pencils and analytic interpolation theory for spectral analysis several algorithms for spectral estimation are developed with resolution higher than state of the art

matrix pencil method for estimating parameters of exponentially damped undamped sinusoids in noise a study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and or undamped sinusoids in noise is presented comparison of this method to a polynomial method svd prony method shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes it is found through perturbation analysis and simulation that for signals with unknown damping factors the pencil method is less sensitive to noise than the polynomial method an expression of the cramer rao bound for the exponential signals is presented

on the convergence of an efficient algorithm for kullback leibler approximation of spectral densities this paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a la byrnes georgiou lindquist the approximation is pursued with respect to the kullback leibler pseudo distance which gives rise to a convex optimization problem after developing the variational analysis we discuss the properties of an efficient algorithm for the solution of the corresponding dual problem based on the iteration of a nonlinear map in a bounded subset of the dual space our main result is the proof of local convergence of the latter established as a consequence of the central manifold theorem supported by numerical evidence we conjecture that in the mentioned bounded set the convergence is actually global

a performance analysis of subspace based methods in the presence of model error ii multidimensional algorithms for pt i see ibid vol 40 no 7 p 1758 74 1992 in pt i the performance of the music algorithms for narrowband direction of arrival doa estimation when the array manifold and noise covariance are not correctly modeled was investigated this analysis is extended to multidimensional subspace based algorithms including deterministic or conditional maximum likelihood md music weighted subspace fitting wsf mode and esprit a general expression for the variance of the doa estimates that can be applied to any of the above algorithms and to any of a wide variety of scenarios is presented optimally weighted subspace fitting algorithms are presented for special cases involving random unstructured errors of the array manifold and noise covariance it is shown that one dimensional music outperforms all of the above multidimensional algorithms for random angle independent array perturbations

stability results for scattered data interpolation by trigonometric polynomials a fast and reliable algorithm for the optimal interpolation of scattered data on the torus mathbb t d by multivariate trigonometric polynomials is presented the algorithm is based on a variant of the conjugate gradient method in combination with the fast fourier transforms for nonequispaced nodes the main result is that under mild assumptions the total complexity for solving the interpolation problem at m arbitrary nodes is of order cal o m log m this result is obtained by the use of localized trigonometric kernels where the localization is chosen in accordance with the spatial dimension d numerical examples show the efficiency of the new algorithm

the structure of state covariances and its relation to the power spectrum of the input we study the relationship between power spectra of stationary stochastic inputs to a linear filter and the corresponding state covariances and identify the structure of positive semidefinite matrices that qualify as state covariances of the filter this structure is best revealed by a rank condition pertaining to the solvability of a linear equation involving the state covariance and the system matrices we then characterize all input power spectra consistent with any specific state covariance the parametrization of input spectra is achieved through a relation to solutions of an analytic interpolation problem which is analogous but not equivalent to a matricial nehari problem

the interpolation problem with a degree constraint the author previously 1983 1987 showed that there is a correspondence between nonnegative hermitian trigonometric polynomials of degree spl les n and solutions to the standard nevanlinna pick caratheodory interpolation problem with n 1 constraints which are rational and also of degree spl les n it was conjectured that the correspondence under suitable normalization is bijective and thereby that it results in a complete parametrization of rational solutions of degree spl les n the conjecture was proven by byrnes et al 1995 along with a detailed study of this parametrization however byrnes et al used a slightly restrictive assumption that the trigonometric polynomials are positive and accordingly the corresponding solutions have positive real part the purpose of the present note is to extend the result to the case of nonnegative trigonometric polynomials as well we present the arguments in the context of the general nevanlinna pick caratheodory fejer interpolation

estimating two dimensional frequencies by matrix enhancement and matrix pencil a new method called the matrix enhancement and matrix pencil memp method is presented for estimating two dimensional 2 d frequencies in the memp method an enhanced matrix is constructed from the data samples and then the matrix pencil approach is used to extract out the 2 d sinusoids from the principal eigenvectors of the enhanced matrix the memp method yields the estimates of the 2 d frequencies efficiently without solving the roots of a 2 d polynomial or searching in a 2 d space it is shown that the memp method can be faster than a 2 d fft method if the number of the 2 d sinusoids is much smaller than the data set simulation results are provided to show that the accuracy of the memp method can be very close to the cramer rao lower bound

input design via lmis admitting frequency wise model specifications in confidence regions a framework for reformulating input design problems in prediction error identification as convex optimization problems is presented for linear time invariant single input single output systems this framework unifies and extends existing results on open loop input design that are based on the finite dimensional asymptotic covariance matrix of the parameter estimates basic methods for parametrizing the input spectrum are provided and conditions on these parametrizations that guarantee that all possible covariance matrices for the asymptotic distribution of the parameter estimates can be generated are provided a wide range of model quality constraints can be handled in particular different frequency by frequency constraints can be used this opens up new applications of input design in areas such as robust control furthermore quality specifications can be imposed on all models in a confidence region thus allowing for statements such as with at least 99 probability the model quality specifications will be satisfied

asymptotic variance expressions for estimated frequency functions expressions for the variance of an estimated frequency function are necessary for many issues in model validation and experiment design a general result is that a simple expression for this variance can be obtained asymptotically as the model order tends to infinity this expression shows that the variance is inversely proportional to the signal to noise ratio frequency by frequency still for low order models the actual variance may be quite different we derive an exact expression for the variance which is not asymptotic in the model order this expression applies to a restricted class of models ar models as well as fixed pole models with a polynomial noise model it brings out the character of the simple approximation and the convergence rate to the limit as the model order increases it also provides nonasymptotic lower bounds for the general case the calculations are illustrated by numerical examples

a belief based account of decision under uncertainty we develop a belief based account of decision under uncertainty this model predicts decisions under uncertainty from i judgments of probability which are assumed to satisfy support theory and ii decisions under risk which are assumed to satisfy prospect theory in two experiments subjects evaluated uncertain prospects and assessed the probability of the respective events study 1 involved the 1995 professional basketball playoffs study 2 involved the movement of economic indicators in a simulated economy the results of both studies are consistent with the belief based account but violate the partition inequality implied by the classical theory of decision under uncertainty

variance error interpolation and experiment design we investigate how the variance error associated with the prediction error identification is related to the power spectral densities of the input and the additive noise at the output let f e i w be the ratio of the input power spectral density psd to the output noise psd we characterize the set of all functions f for which the variance error remains constant this analysis results a minimal finite dimensional affine parameterization of the variance error this parameterization connects our analysis with the theory of nevanlinna pick interpolation it is shown that the set of all f for which the variance error remains constant can be characterized by the solutions of a nevanlinna pick interpolation problem this insight has interesting consequences in optimal input design where it is possible to use some recent tools in analytic interpolation theory to tune shape of the input psd to suit certain needs

almost sure identifiability of multidimensional harmonic retrieval two dimensional 2 d and more generally multidimensional harmonic retrieval is of interest in a variety of applications including transmitter localization and joint time and frequency offset estimation in wireless communications the associated identifiability problem is key in understanding the fundamental limitations of parametric methods in terms of the number of harmonics that can be resolved for a given sample size consider a mixture of 2 d exponentials each parameterized by amplitude phase and decay rate plus frequency in each dimension suppose that i equispaced samples are taken along one dimension and likewise j along the other dimension we prove that if the number of exponentials is less than or equal to roughly ij 4 then assuming sampling at the nyquist rate or above the parameterization is almost surely identifiable this is significant because the best previously known achievable bound was roughly i j 2 for example consider i j 32 our result yields 256 versus 32 identifiable exponentials we also generalize the result to n dimensions proving that the number of exponentials that can be resolved is proportional to total sample size

towards a mathematical theory of super resolution this paper develops a mathematical theory of super resolution broadly speaking super resolution is the problem of recovering the fine details of an object the high end of its spectrum from coarse scale information only from samples at the low end of the spectrum suppose we have many point sources at unknown locations in 0 1 and with unknown complex valued amplitudes we only observe fourier samples of this object up to a frequency cutoff fc we show that one can super resolve these point sources with infinite precision i e recover the exact locations and amplitudes by solving a simple convex optimization problem which can essentially be reformulated as a semidefinite program this holds provided that the distance between sources is at least 2 fc this result extends to higher dimensions and other models in one dimension for instance it is possible to recover a piecewise smooth function by resolving the discontinuity points with infinite precision as well we also show that the theory and methods are robust to noise in particular in the discrete setting we develop some theoretical results explaining how the accuracy of the super resolved signal is expected to degrade when both the noise level and the super resolution factor vary 2014 wiley periodicals inc

asymptotic variance expressions for identified black box transfer function models identification of black box transfer function models is considered it is assumed that the transfer function models possess a certain shift property which is satisfied for example by all polynomial type models expressions for the variances of the transfer function estimates are derived that are asymptotic both in the number of observed data and in the model orders the result is that the joint covariance matrix of the transfer functions from input to output and from driving white noise source to the additive output disturbance respectively is proportional to the inverse of the joint spectrum matrix for the input and driving noise multiplied by the spectrum of the additive output noise the factor of proportionality is the ratio of model order to number of data this result is independent of the particular model structure used the result is applied to evaluate the performance degradation due to variance for a number of typical model uses some consequences for input design are also drawn