computational methods for risk averse undiscounted transient markov models the total cost problem for discrete time controlled transient markov models is considered the objective functional is a markov dynamic risk measure of the total cost two solution methods value and policy iteration are proposed and their convergence is analyzed in the policy iteration method we propose two algorithms for policy evaluation the nonsmooth newton method and convex programming and we prove their convergence the results are illustrated on a credit limit control problem

modified subspace algorithms for doa estimation with large arrays this paper proposes the use of a new generalized asymptotic paradigm in order to analyze the performance of subspace based direction of arrival doa estimation in array signal processing applications instead of assuming that the number of samples is high whereas the number of sensors antennas remains fixed the asymptotic situation analyzed herein assumes that both quantities tend to infinity at the same rate this asymptotic situation provides a more accurate description of a potential situation where these two quantities are finite and hence comparable in magnitude it is first shown that both music and ssmusic are inconsistent when the number of antennas sensors increases without bound at the same rate as the sample size this is done by analyzing and deriving closed form expressions for the two corresponding asymptotic cost functions by examining these asymptotic cost functions one can establish the minimum number of samples per antenna needed to resolve closely spaced sources in this asymptotic regime next two alternative estimators are constructed that are strongly consistent in the new asymptotic situation i e they provide consistent doa estimates not only when the number of snapshots goes to infinity but also when the number of sensors antennas increases without bound at the same rate these estimators are inspired by the theory of g estimation and are therefore referred to as g music and g ssmusic respectively simulations show that the proposed algorithms outperform their traditional counterparts in finite sample size situations although they still present certain limitations

indirect dominant mode rejection a solution to low sample support beamforming under conditions of low sample support a low rank solution of the minimum variance distortionless response mvdr equations can yield a higher output signal to interference plus noise ratio sinr than the full rank mvdr beamformer in this paper we investigate several low rank beam forming techniques and we also propose a new beamformer that we refer to as the indirect dominant mode rejection idmr we analyze the degradation in the output sinr caused by residual cross correlations embedded in the sampled covariance matrix due to low sample support the idmr beamformer is based on a parametric estimate of the covariance matrix in which any cross correlation is canceled out simulations reveal that the idmr beamformer yields a dramatic improvement in output sinr relative to the conjugate gradient cg principal component inverse pci and dominant mode rejection dmr beamformers in our investigation of the low rank cg beamformer we address the issue of whether the unity gain constraint in the look direction should be enforced a priori via the use of a blocking matrix or effected a posteriori through simple scaling of the beamforming vector remarkably it is proven that the two methods yield exactly the same low rank beamformer at each and every rank

on the virtual array concept for higher order array processing for about two decades many fourth order fo array processing methods have been developed for both direction finding and blind identification of non gaussian signals one of the main interests in using fo cumulants only instead of second order so ones in array processing applications relies on the increase of both the effective aperture and the number of sensors of the considered array which eventually introduces the fo virtual array concept presented elsewhere and allows in particular a better resolution and the processing of more sources than sensors to still increase the resolution and the number of sources to be processed from a given array of sensors new families of blind identification source separation and direction finding methods at an order m 2q q spl ges 2 only have been developed recently in this context the purpose of this paper is to provide some important insights into the mechanisms and more particularly to both the resolution and the maximal processing capacity of numerous 2qth order array processing methods whose previous methods are part of by extending the virtual array concept to an arbitrary even order for several arrangements of the data statistics and for arrays with space angular and or polarization diversity

direction finding with partly calibrated uniform linear arrays a new method for direction finding with partly calibrated uniform linear arrays ulas is presented it is based on the conventional estimation of signal parameters via rotational invariance techniques esprit by modeling the imperfections of the ulas as gain and phase uncertainties for a fully calibrated array it reduces to the conventional esprit algorithm moreover the direction of arrivals doas unknown gains and phases of the uncalibrated sensors can be estimated in closed form without performing a spectral search hence it is computationally very attractive the cramer rao bounds crbs of the partly calibrated ulas are also given simulation results show that the root mean squared error rmse performance of the proposed algorithm is better than the conventional methods when the number of uncalibrated sensors is large it also achieves satisfactory performance even at low signal to noise ratios snrs

singularity formation in chemotaxis a conjecture of nagai consider the initial boundary value problem for the system s ut uxx uvx x vt u av on an interval 0 1 for t 0 where a 0 with ux 0 t ux 1 t 0 suppose mu v0 are positive constants the corresponding spatially homogeneous global solution u t mu v t mu a v0 mu a exp at is stable in the sense that if mu v0 are positive constants the corresponding spatially homogeneous solution will be uniformly close to u cdot v cdot we consider in sequence space an approximate system s which is related to s in the following sense the chemotactic term uvx x is replaced by the inverse fourier transform of the finite part of the convolution integral for the fourier transform of uvx x here the finite part of the convolution on the line at a point x of two functions f g is defined as int 0 x f y g y x dy we prove the following if mu a then in every neighborhood of mu v0 there are spatially nonconstant initial data for which the solution of proble

complex elliptically symmetric distributions survey new results and applications complex elliptically symmetric ces distributions have been widely used in various engineering applications for which non gaussian models are needed in this overview circular ces distributions are surveyed some new results are derived and their applications e g in radar and array signal processing are discussed and illustrated with theoretical examples simulations and analysis of real radar data the maximum likelihood ml estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness and for convergence of the iterative fixed point algorithm are established specific ml estimators for several ces distributions that are widely used in the signal processing literature are discussed in depth including the complex t distribution k distribution the generalized gaussian distribution and the closely related angular central gaussian distribution a generalization of ml estimators the m estimators of the scatter matrix are also discussed and asymptotic analysis is provided applications of ces distributions and the adaptive signal processors based on ml and m estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for direction of arrival doa estimation and beamforming furthermore experimental validation of the usefulness of ces distributions for modelling real radar data is given

risk sensitive control of finite state machines on an infinite horizon i in this paper we consider robust and risk sensitive control of discrete time finite state systems on an infinite horizon the solution of the state feedback robust control problem is characterized in terms of the value of an average cost dynamic game the risk sensitive stochastic optimal control problem is solved using the policy iteration algorithm and the optimal rate is expressed in terms of the value of a stochastic dynamic game with average cost per unit time criterion by taking a small noise limit a deterministic dynamic game which is closely related to the robust control problem is obtained

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

steady state analysis of the multistage constant modulus array the multistage constant modulus cm array is a cascade adaptive beamforming system that can recover several narrowband cochannel signals without training we examine its steady state properties at convergence using a stochastic analysis and computer simulations based on a wiener model of convergence for the gradient adaptive algorithms closed form expressions are derived for the cm array and canceller weight vectors as well as the effective source direction vectors at all stages along the cascade system the signal capture and direction finding capabilities of the system are also discussed computer simulations for stationary and fading sources are presented to confirm the theoretical results and to illustrate the rapid convergence behavior of the adaptive algorithms

theoretical analyses of gain and phase error calibration with optimal implementation for linear equispaced array in array signal processing high resolution direction of arrival doa estimation algorithms are known to be sensitive to system errors in practice the system should be properly calibrated before doa estimation in this paper a calibration method of gain and phase errors of linear equispaced arrays leas is considered a class of simplified calibration algorithms based on different diagonal lines of the covariance matrix is proposed the statistical performance analyses of the calibration algorithms due to finite data perturbations are presented expressions for average bias abias and square root of average variance srav of the calibration algorithms are derived using first order approximation these statistical and computer simulation results reveal and explain why the more diagonal lines that are used for gain and phase error estimations the more inferior performance that may be obtained based on this conclusion the simple and optimal gain and phase error calibration algorithms for such model are obtained

analysis of a risk sensitive control problem for hidden markov chains in this paper the risk sensitive control of partially observed markov decision processes is considered the replacement problem is analyzed in this context and the structure of risk sensitive optimal controllers is given

doa estimation by exploiting the symmetric configuration of uniform linear array a new direction of arrival doa estimation method is proposed for uniform linear array in this paper when both uncorrelated and coherent sources are present the uncorrelated and coherent sources are estimated at two different stages the uncorrelated sources are first estimated using conventional subspace methods and then they are eliminated by exploiting the symmetric configuration of the array finally the remaining coherent sources are estimated by reconstructing a non toeplitz matrix the number of sources resolved by our method can exceed the number of array elements simulation results demonstrate the effectiveness and efficiency of our proposed method

risk sensitive optimal control of hidden markov models structural results the authors consider a risk sensitive optimal control problem for finite state and action spaces hidden markov models hmm they present results of an investigation on the nature and structure of risk sensitive controllers for hmm several general structural results are presented as well as a particular case study of a popular benchmark problem for the latter they obtain structural results for the optimal risk sensitive controller and compare it to that of the risk neutral controller furthermore they show that indeed the risk sensitive controller and its corresponding information state converge to the known solutions for the risk neutral situation as the risk factor goes to zero they also study the infinite and general risk aversion cases

risk sensitive control of markov processes in countable state space in this paper we consider infinite horizon risk sensitive control of markov processes with discrete time and denumerable state space this problem is solved by proving under suitable conditions that there exists a bounded solution to the dynamic programming equation the dynamic programming equation is transformed into an isaacs equation for a stochastic game and the vanishing discount method is used to study its solution in addition we prove that the existence conditions are also necessary

a novel online mutual coupling compensation algorithm for uniform and linear arrays in this paper a novel online mutual coupling compensation algorithm especially tailored to uniform and linear arrays is presented it is conceived to simultaneously compensate for mutual coupling and estimate the direction of arrivals doas of signals impinging on the array since the estimated calibration matrix can be embedded within any classical super resolution direction finding method an alternating minimization procedure based on closed form solutions is performed to estimate the mutual coupling matrix in the field of complex symmetric toeplitz matrices unlike many existing array calibration methods it requires neither the presence of calibration sources nor previous calibration information as initialization computer simulations show the effectiveness of the proposed technique and prove that the nice statistical properties of classical super resolution doa estimation algorithms can be restored despite the presence of mutual coupling

coprime sensing via chinese remaindering over quadratic fields part i array designs a coprime antenna array consists of two or more sparse subarrays featuring enhanced degrees of freedom dof and reduced mutual coupling this paper introduces a new class of planar coprime arrays based on the theory of ideal lattices in quadratic number fields a splitting prime p can be decomposed into the product of two distinct prime ideals which give rise to the two sparse subarrays their virtual difference coarray enjoys a quadratic gain in dof thanks to the generalized chinese remainder theorem crt to enlarge the contiguous aperture of the coarray we present hole free symmetric crt arrays with simple closed form expressions the ring of gaussian integers and the ring of eisenstein integers are considered as examples to demonstrate the procedure of designing coprime arrays with eisenstein integers our design yields a difference coarray that is a subset of the hexagonal lattice offering a significant gain in dof over the rectangular lattice given the same physical areas maximization of crt arrays in the aspect of essentialness and the superior performance in the context of angle estimation will be presented in the companion paper part ii

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

consistency and mse performance of music based doa of a single source in white noise with randomly missing data music is a popular algorithm for estimating the direction of arrival doa in array signal processing applications in this paper we analyze the performance of the music algorithm for a single source system in the presence of noisy and missing data when only a random subset of the entries in the data matrix are observed we prove consistency of the doa estimate when signal from a single source is impinging on low coherence arrays and derive an analytic expression for the mean squared error mse performance of music for the case of uniform linear arrays in the large array and relatively large sample setting our analysis is mathematically justified in both the sample rich and deficient regimes the expression for the mse is a simple function of array geometry signal to noise ratio snr the fraction of entries observed and the ratio of the number of sensors to number of snapshots we derive a phase transition threshold which separates a regime where music is consistent from a regime where music is inconsistent this threshold depends upon the snr the probability of observing entries in the data matrix and number of sensors and snapshots in a simple manner which we make explicit

a two stage method for inverse medium scattering we present a novel numerical method to the time harmonic inverse medium scattering problem of recovering the refractive index from noisy near field scattered data the approach consists of two stages one pruning step of detecting the scatterer support and one resolution enhancing step with nonsmooth mixed regularization the first step is strictly direct and of sampling type and it faithfully detects the scatterer support the second step is an innovative application of nonsmooth mixed regularization and it accurately resolves the scatterer size as well as intensities the nonsmooth model can be efficiently solved by a semi smooth newton type method numerical results for two and three dimensional examples indicate that the new approach is accurate computationally efficient and robust with respect to data noise

optimal control of partially observable stochastic systems with an exponential of integral performance index the stochastic control problem with linear stochastic differential equations driven by brownian motion processes and as cost functional the exponential of a quadratic form is considered the soluti

discounted mdp s distribution functions and exponential utility maximization the present value of the rewards associated with a discrete time markov process has a probability distribution which depends on the initial state the first part of the paper applies fixed point theory to a system of equations for the distribution functions of the present value the second part of the paper expands the model to a markov decision process mdp and considers the maximization of the expected utility of the present value when the utility function is exponential

performance analysis of spatial smoothing with interpolated arrays the interpolated spatial smoothing algorithm is a computationally efficient method for estimating the directions of arrival doas of signals some of which may be perfectly correlated it extends the spatial smoothing method to arbitrary array geometries a statistical performance analysis of the algorithm is presented closed form expressions for the covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluating these expressions for specific cases and comparing them to the cramer rao lower bound for the doa estimates provides insight into the statistical efficiency of this algorithm the formulas for the error covariance are quite general and can be specialized to provide results for other doa estimation algorithms as well

brief risk sensitive and minimax control of discrete time finite state markov decision processes this paper analyzes a connection between risk sensitive and minimax criteria for discrete time finite state markov decision processes mdps we synthesize optimal policies with respect to both criteria both for the finite horizon and the discounted infinite horizon problem a generalized decision making framework is introduced which includes as special cases a number of approaches that have been considered in the literature the framework allows for discounted risk sensitive and minimax formulations leading to stationary optimal policies on the infinite horizon we illustrate our results with a simple machine replacement problem

erratum singularity formation in chemotaxis a conjecture of nagai in h a levine and j renc l awowicz em siam j appl math 65 2004 pp 336 360 we considered the problem u t u xx uv x x v t u av on the interval i 0 1 where u x v x 0 at the end points u x 0 v x 0 are prescribed and a 0 it was claimed in that article that there were solutions that blow up in finite time in every neighborhood of the spatially homogeneous steady state u v mu mu a if mu a here we correct an estimate and reduce nagai s conjecture to the following statement let sigma a mu a rho 1 1 if lim n to infty rho n exists where for n ge 2 rho n n equiv 1 n 1 sum j 1 n 1 1 sigma j rho j j rho n j n j then the blow up assertion holds

process based risk measures and risk averse control of discrete time systems for controlled discrete time stochastic processes we introduce a new class of dynamic risk measures which we call process based their main feature is that they measure risk of processes that are functions of the history of a base process we introduce a new concept of conditional stochastic time consistency and we derive the structure of process based risk measures enjoying this property we show that they can be equivalently represented by a collection of static law invariant risk measures on the space of functions of the state of the base process we apply this result to controlled markov processes and we derive dynamic programming equations we also derive dynamic programming equations for multistage stochastic programming with decision dependent distributions

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

performance analysis of the enhanced minimum variance spatial spectrum estimator the performance of the enhanced minimum variance emv spatial spectrum estimator is studied expressions are presented fur the variance and bias of direction of arrival estimators based on general functions of the covariance matrix and these expressions are then used to study the emv estimator finite data effects and random perturbations on the ideal modeling assumptions are studied separately

discounted linear exponential quadratic gaussian control in this note we describe a recursive formulation of discounted costs for a linear quadratic exponential gaussian linear regulator problem which implies time invariant linear decision rules in the infinite horizon case time invariance in the discounted case is attained by surrendering state separability of the risk adjusted costs

a critical study of a self calibrating direction finding method for arrays the self calibrating direction finding method was developed by friedlander and weiss 1988 it refines the estimates of the array element gains and phases while it estimates the signal directions this study shows that the outputs of the method could be inaccurate even if noise is absent

brief on terminating markov decision processes with a risk averse objective function we consider a class of terminating markov decision processes with an exponential risk averse objective function and compact constraint sets we assume the existence of an absorbing cost free terminal state w positive transition costs and continuity of the transition probability and cost functions without discounting future costs in the argument of the exponential utility function we establish i the existence of a real valued optimal cost function which can be achieved by a stationary policy and ii the convergence of value iteration and policy iteration to the unique solution of bellman s equation we illustrate the results with two computational examples

stability of constant steady states and existence of unbounded solutions in time to a reaction diffusion equation modelling chemotaxis abstract we consider the initial boundary value problem to a reaction diffusion equation modelling chemotaxis in one space dimension under neumann boundary conditions we study the stability of constant steady states and show that there exists an unbounded solution in time induced by the instability of constant steady states

existence of solutions to a new model of biological pattern formation abstract in this paper we study the existence of classical solutions to a new model of skeletal development in the vertebrate limb the model incorporates a general term describing adhesion interaction between cells and fibronectin an extracellular matrix molecule secreted by the cells as well as two secreted diffusible regulators of fibronectin production the positively acting differentiation factor activator tgf and a negatively acting factor inhibitor together these terms constitute a pattern forming system of equations we analyze the conditions guaranteeing that smooth solutions exist globally in time we prove that these conditions can be significantly relaxed if we add a diffusion term to the equation describing the evolution of fibronectin

kalman based estimator for doa estimations we introduce a new kalman based noise subspace estimator combined with the root music for direction of arrival doa estimation of uncorrelated narrow band plane waves impinging on an array of sensors without both a priori knowledge of the number of sources and the inflation method presented by yang and kaveh 1988 we show that the kalman based estimator can approximately estimate the complete noise subspace with small bias for high input signal to noise ratio snr scenario the proposed algorithm needs slightly more computation operations per adaptive cycle than yang and kaveh s lms based algorithm but with much more rapid convergence simulations demonstrate the effectiveness of the proposed algorithm

first order perturbation analysis of singular vectors in singular value decomposition singular value decomposition svd is an important technique in signal processing in the literature the perturbation analysis of svd has been well documented in the context of subspace decomposition the contribution of the signal subspace to the perturbation of the singular vectors that span the signal subspace is often ignored as it is treated as second and higher order terms and thus the first order perturbation is typically given as the column span of the noise subspace in this correspondence we show that not only the noise subspace but also the signal subspace contribute to the first order perturbation of the singular vectors we further show that the contribution of the signal subspace does not impact on the performance analysis of algorithms that rely on the signal subspace for parameter estimation but it affects the analysis of algorithms that depends on the individual basis vectors for the latter we also give a condition under which the contribution of the signal subspace to the perturbation of singular vectors may be ignored in the statistical sense numerical examples are provided to validate our theoretic claims

source localization in a waveguide using polynomial rooting source localization in acoustic waveguides involves a multidimensional search procedure we propose a new algorithm in which the search in the depth direction is replaced by polynomial rooting using the proposed algorithm range and depth estimation by a vertical array requires a 1 d search procedure for a 3 d localization problem i e range depth and direction of arrival doa estimation the algorithm involves a 2 d search procedure consequently the proposed algorithm requires significantly less computation than other methods that are based on a brute force search procedure over the source location parameters in order to evaluate the performance of the algorithm an error analysis is carried out and monte carlo simulations are performed the results are compared with the cramer rao bound crb and to the maximum likelihood ml simulation performance the algorithm is shown to be efficient while being computationally simpler than the ml or the bartlett processors the disadvantage of the algorithm is that its snr threshold occurs in lower snr than in the ml algorithm

analytical performance assessment of multi dimensional matrix and tensor based esprit type algorithms in this paper we present a generic framework for the asymptotic performance analysis of subspace based parameter estimation schemes it is based on earlier results on an explicit first order expansion of the estimation error in the signal subspace obtained via an svd of the noisy observation matrix we extend these results in a number of aspects firstly we demonstrate that an explicit first order expansion of the higher order svd hosvd based subspace estimate can be derived secondly we show how to obtain explicit first order expansions of the estimation error of arbitrary esprit type algorithms and provide the expressions for r d standard esprit r d unitary esprit r d standard tensor esprit as well as r d unitary tensor esprit thirdly we derive closed form expressions for the mean square error mse and show that they only depend on the second order moments of the noise hence to apply this framework we only need the noise to be zero mean and possess finite second order moments additional assumptions such as gaussianity or circular symmetry are not needed

subspace leakage analysis and improved doa estimation with small sample size classical methods of doa estimation such as the music algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix for a small number of samples such methods are exposed to performance breakdown as the sample covariance matrix can largely deviate from the true covariance matrix in this paper the problem of doa estimation performance breakdown is investigated we consider the structure of the sample covariance matrix and the dynamics of the root music algorithm the performance breakdown in the threshold region is associated with the subspace leakage where some portion of the true signal subspace resides in the estimated noise subspace in this paper the subspace leakage is theoretically derived we also propose a two step method that improves the performance by modifying the sample covariance matrix such that the amount of the subspace leakage is reduced furthermore we introduce a phenomenon named as root swap which occurs in the root music algorithm in the low sample size region and degrades the performance of the doa estimation a new method is then proposed to alleviate this problem numerical examples and simulation results are given for uncorrelated and correlated sources to illustrate the improvement achieved by the proposed methods moreover the proposed algorithms are combined with the pseudo noise resampling method to further improve the performance