convergence analysis of inexact infeasible interior point algorithms for solving linear programming problems in this paper we present a convergence analysis for some inexact polynomial variants of the infeasible interior point algorithm of kojima megiddo and mizuno for this analysis we assume that the iterates are bounded the new variants allow the use of search directions that are calculated from the defining linear system with only moderate accuracy e g via the use of krylov subspace methods like cg or qmr furthermore some numerical results for the proposed methods are given

robust matched filters the problem of designing robust matched filters for situations in which there is uncertainty in the signal structure or noise statistics is considered two general aspects of this problem are treated first maximin robust designs are characterized for a general hilbert space formulation of the matched filtering problem and explicit solutions are given for two intuitively appealing models for uncertainty these results are seen to generalize earlier results for specific matched filtering problems the second general aspect treated is the application of the theoretical maximin results to the particular problem of designing filters to combat uncertain nonlinear channel distortion channel distortion is modeled by considering an unknown received signal which may differ in l 2 norm from the transmitted or nominal signal by no more than a fixed amount the effect of the channel distortion is seen to be equivalent to that of adding a white noise to the channel whose spectral height depends on the degree of distortion general expressions are developed for the determination of the robust filter and its performance and numerical results are presented for the case of baseband detection in gauss markov noise

detection of gaussian signals in poisson modulated interference passive broadband detection of target signals by an array of hydrophones in the presence of multiple discrete interferers is analyzed under gaussian statistics and low signal to noise ratio conditions a nonhomogeneous poisson modulated interference process is used to model the ensemble of possible arrival directions of the discrete interferers closed form expressions are derived for the recognition differential of the passive sonar equation in the presence of poisson modulated interference the interference compensated recognition differential differs from the classical recognition differential by an additive positive term that depend on the interference to noise ratio the directionality of the poisson modulated interference and the array beam pattern

an experimental comparison of optimum and sub optimum filters effectiveness in the generalized correlator abstract various optimum and sub optimum filters have been added to the basic cross correlator in order to enhance its detection and estimation capabilities in the presence of noise these pre detection filters include the hannan thomson the eckart the smoothed coherence transform some least squares and two optimum filters recently derived by the authors here a quantitative comparison of all six filters has been conducted by extensive simulation for various input signal to noise ratios and signal and noise bandwidths the results define the actual enhancement in time delay detection and estimation when using the optimum filters and the amount of performance degradation from the optimum for the other filters the rank ordering of the filters is carried out histograms of the time delay estimates their mean variance and probability of detection are presented wherever available comparison of analytical predictions with the experimental results is noted

renormalization of the voter model in equilibrium we consider the d dimensional voter model for d 3 our interest is the large scale limit of the equilibrium state of the voter model where we prove the d 3 results of 1 for d 4 which turn out to be of a different nature than for d 3 for this purpose we use the historical process we establish some surprising facts about the green s function of random walks in dimension d 4 which lead to the different features in d 3 versus d 4 secondly we prove an analogous result for the voter model on the hierarchical group

different clustering regimes in systems of hierarchically interacting diffusions we study a system of interacting diffusions dx t a x t x t dt g x t dw t indexed by the hierarchical group as a genealogical two genotype model where x t denotes the frequency of say type a with hierarchically determined degrees of relationship between colonies in the case of short interaction range it is known that the system clusters that is locally one genotype dies out we focus on the description of the different regimes of cluster growth which is shown to depend on the interaction kernel a via its recurrent potential kernel one of these regimes will be further investigated by mean field methods for general interaction range we shall also relate the behavior of large finite systems indexed by finite subsets n of to that of the infinite system on the way we will establish relations between hitting times of random walks and their potentials

a crame spl acute r rao type estimation lower bound for systems with measurement faults a crame spl acute r rao type lower bound is presented for systems with measurements prone to discretely distributed faults which are a class of hybrid systems lower bounds for both the state and the markovian interruption variables fault indicators of the system are derived using the recently presented sequential version of the crame spl acute r rao lower bound crlb for general nonlinear systems because of the hybrid nature of the systems addressed the crlb cannot be directly applied due to violation of its associated regularity conditions to facilitate the calculation of the lower bound the hybrid system is first approximated by a system in which the discrete distribution of the fault indicators is replaced by an approximating continuous one the lower bound is then obtained via a limiting process applied to the approximating system the results presented herein facilitate a relatively simple calculation of a nontrivial lower bound for the state vector of systems with fault prone measurements the crlb type lower bound for the interruption process variables turns out to be trivially zero however a nontrivial non crlb type bound for these variables has been recently presented elsewhere by the authors the utility and applicability of the proposed lower bound are demonstrated via a numerical example involving a simple global positioning system gps aided navigation system where the gps measurements are fault prone due to their sensitivity to multipath errors

convergence of a class of inexact interior point algorithms for linear programs we present a convergence analysis for a class of inexact infeasible interior point methods for solving linear programs the main feature of inexact methods is that the linear systems defining the search direction at each interior point iteration need not be solved to high accuracy more precisely we allow that these linear systems are only solved to a moderate accuracy in the residual but no assumptions are made on the accuracy of the search direction in the search space in particular our analysis does not require that feasibility is maintained even if the initial iterate happened to be a feasible solution of the linear program we also present a few numerical examples to illustrate the effect of using inexact search directions on the number of interior point iterations

on achievable accuracy in edge localization edge localization occurs when an edge detector determines the location of an edge in an image the authors use statistical parameter estimation techniques to derive bounds on achievable accuracy in edge localization these bounds known as the cramer rao bounds reveal the effect on localization of factors such as signal to noise ratio snr extent of edge observed scale of smoothing filter and a priori uncertainty about edge intensity by using continuous values for both image coordinates and intensity the authors focus on the effect of these factors prior to sampling and quantization they also analyze the canny algorithm and show that for high snr its mean squared error is only a factor of two higher than the lower limit established by the cramer rao bound although this is very good the authors show that for high snr the maximum likelihood estimator which is also derived virtually achieves the lower bound

matrix crlb scaling due to measurements of uncertain origin in many estimation situations measurements are of uncertain origin this is best exemplified by the target tracking situation in which at each scan of a radar sonar or electro optical sensor a number of measurements are obtained and it is not known which if any of these is target originated the source of extraneous measurements can be false alarms especially in low snr situations that force the detector at the end of the signal processing chain to operate with a reduced threshold or spurious targets in several earlier papers the surprising observation was made that the cramer rao lower bound crlb for the estimation of a fixed parameter vector e g initial position and velocity that characterizes the target motion for the special case of multidimensional measurements in the presence of additive white gaussian noise is simply a multiple of that for the case with no uncertainty that is there is a scalar information reduction factor this is particularly useful as it allows comparison in terms of a scalar in this paper we explore this result to determine how wide the class of such problems is it turns out to include many non gaussian situations simulations corroborate the analysis

some classes of global cramer rao bounds on considere des bornes de type cramer rao pour l erreur d estimation d un parametre dans un contexte bayesien cette classe de bornes introduite par van trees s avere utile dans divers problemes de communication et de commande stochastiques

a polynomial time interior point method for conic optimization with inexact barrier evaluations we consider a primal dual short step interior point method for conic convex optimization problems for which exact evaluation of the gradient and hessian of the primal and dual barrier functions is either impossible or prohibitively expensive as our main contribution we show that if approximate gradients and hessians of the primal barrier function can be computed and the relative errors in such quantities are not too large then the method has polynomial worst case iteration complexity in particular polynomial iteration complexity ensues when the gradient and hessian are evaluated exactly in addition the algorithm requires no evaluation or even approximate evaluation of quantities related to the barrier function for the dual cone even for problems in which the underlying cone is not self dual

cluster formation in a stepping stone model with continuous hierarchically structured sites a stepping stone model with site space a continuous hierarchical group is constructed via duality with a system of delayed coalescing stable levy processes this model can be understood as a continuum limit of discrete state space two allele genetics models with hierarchically structured resampling and migration the existence of a process rescaling limit on suitably related large space and time scales is established and interpreted in terms of the dynamics of cluster formation this paper was inspired by recent work of klenke

delay estimation simulations and a normalized comparison of published results three recent publications have reported delay estimate variances from simulations using the generalized cross correlator method on both stationary random signals with noise and deterministic signals with noise further simulations with finite energy signals are reported here a method of comparing the three reported data sets is developed and a remarkable consistency is observed even though the simulation parameters have varied widely

iterative maximum likelihood displacement field estimation in quantum limited image sequences we develop an algorithm for obtaining the maximum likelihood ml estimate of the displacement vector field dvp from two consecutive image frames of an image sequence acquired under quantum limited conditions the estimation of the dvf has applications in temporal filtering object tracking stereo matching and frame registration in low light level image sequences as well as low dose clinical x ray image sequences in the latter case a controlled x ray dosage reduction may be utilized to lower the radiation exposure to the patient and the medical staff the quantum limited effect is modeled as an undesirable poisson distributed signal dependent noise artifact a fisher bayesian formulation is used to estimate the dvf and a block component search algorithm is employed in obtaining the solution several experiments involving a phantom sequence and a teleconferencing image sequence with realistic motion demonstrate the effectiveness of this estimator in obtaining the dvf under severe quantum noise conditions 20 25 events pixel

lower bounds on estimator performance for energy invariant parameters of multidimensional poisson processes using rate distortion theory lower bounds are developed for the mean square error of estimates of a random parameter of an m dimensional inhomogeneous poisson process with respect to which the energy i e the average number of points is invariant the bounds are derived without stringent assumptions on either the form of the intensity or the prior distribution of the parameter and they can handle random nuisance parameters the derivation makes use of a side information averaging principle applied to the distortion rate function and a maximum entropy property of energy constrained poisson processes under the additional assumption of conditional entropy invariance of the point process with respect to the parameter of interest an explicit bound is given which depends on the information discrimination between the inhomogeneous conditionally poisson process and a nearly homogeneous poisson process the application of the explicit bound is illustrated through a treatment of the problems of time shift estimation and relative time shift estimation for poisson streams

long step strategies in interior point primal dual methods in this paper we analyze from a unique point of view the behavior of path following and primal dual potential reduction methods on nonlinear conic problems we demonstrate that most interior point methods with o root n ln 1 epsilon efficiency estimate can be considered as different strategies of minimizing a convex primal dual potential function in an extended primal dual space their efficiency estimate is a direct consequence of large local norm of the gradient of the potential function along a central path it is shown that the neighborhood of this path is a region of the fastest decrease of the potential therefore the long step path following methods are in a sense the best potential reduction strategies we present three examples of such long step strategies we prove also an efficiency estimate for a pure primal dual potential reduction method which can be considered as an implementation of a penalty strategy based on a functional proximity measure using the convex primal dual potential we prove efficiency estimates for karmarkar type and dikin type methods as applied to a homogeneous reformulation of the initial primal dual problem

a relaxed revision of karmarkar s method a relaxed version of karmarkar s method is developed this method is proved to have the same polynomial time complexity as karmarkar s method and its efficient implementation using inexact projections is discussed computational results obtained using a preliminary implementation of the method are presented which indicate that the method is practicable

diffusive clustering in the two dimensional voter model on donne des resultats de simulation et une enquete concernant les resultats connus sur le modele du votant dans trois cas distincts trois ou plusieurs dimensions une dimension et deux dimensions

time delay estimation via cross correlation in the presence of large estimation errors the estimate of the difference in time of arrival of a common random signal received at two sensors each of which also receives uncorrelated noise is examined for both small and large estimation errors it is shown that as the post integration signal to noise ratio decreases the correlator exhibits a thresholding effect that is the probability of a large error an anomalous estimate increases rapidly approximate theoretical results for the probability of an anomaly are presented and are verified experimentally the variance of the time delay estimate is examined for both a gated mode in which the time delay corresponding to the correlation peak closest to the true time delay is used as the estimate of time delay and an ungated mode in which the time delay corresponding to the largest peak over the full range of the correlator delay times is used as the estimate the observed variance for both modes is compared with the theoretical variance based on a small error analysis for the gated modes the signal to noise ratio below which the observed variance begins to differ significantly from the small error theory can be reliably predicted from a linearity criterion it is shown however that the expected variance for the ungated mode can depart from the small error theory at a higher signal to noise ratio than for the gated modes thus the variance due to anomalies can be the most important factor in determining the region of applicability of the small error analysis

approximate maximum likelihood delay estimation via orthogonal wavelet transform a novel approximate maximum likelihood algorithm is proposed for estimating the time difference of arrival between signals received at two spatially separated sensors prior to cross correlation one of the channel outputs is optimally weighted at different frequency bands with the use of an orthogonal wavelet transform it composes an array of multirate filters and is a time domain implementation of the generalized cross correlation method however it does not suffer from the performance degradation due to the errors inherent in spectral estimation obtained from finite length data and is computationally efficient a simple decision rule is also provided to automatically determine the requisite levels of wavelet decomposition the effectiveness of the method is demonstrated by comparing with the direct cross correlator the eckart processor and the cramer rao lower bound crlb for different noise conditions and wavelet filter lengths

robust hypothesis testing for bounded classes of probability densities corresp least favorable pairs of probability density functions and robust tests are obtained for classes of density functions specified as bands with upper and lower bounds the results are shown to extend huber s solution for the epsilon contaminated classes which is contained as a special case a minimum distance property of the least favorable density pair is also made explicit

consolidation rates for two interacting systems in the plane this paper is a sequel of a paper of cox and griffeath diffusive clustering in the two dimensional voter model we continue our study of the voter model and coalescing random walks on the two dimensional integer lattice some exact asymptotics concerning the rate of clustering in the former process and the coalescence rate of the latter are derived we use these results to prove a limit law announced in that earlier paper concerning the size of the largest square centered at the origin which is of solid color at a large time t

coalescing systems of non brownian particles a well known result of arratia shows that one can make rigorous the notion of starting an independent brownian motion at every point of an arbitrary closed subset of the real line and then building a set valued process by requiring particles to coalesce when they collide arratia noted that the value of this process will be almost surely a locally finite set at all positive times and a finite set almost surely if the initial value is compact the key to both of these facts is the observation that because of the topology of the real line and the continuity of brownian sample paths at the time when two particles collide one or the other of them must have already collided with each particle that was initially between them we investigate whether such instantaneous coalescence still occurs for coalescing systems of particles where either the state space of the individual particles is not locally homeomorphic to an interval or the sample paths of the individual particles are discontinuous we give a quite general criterion for a coalescing system of particles on a compact state space to coalesce to a finite set at all positive times almost surely and show that there is almost sure instantaneous coalescence to a locally finite set for systems of brownian motions on the sierpinski gasket and stable processes on the real line with stable index greater than one

on the simulation of a class of time delay estimation algorithms the time delay between signals received at two or more sensors has proven to be a useful parameter in passive sonar for estimating the location of an acoustic source this paper presents the results of a simulation comparing the smoothed coherence transform and maximum likelihood estimation methods to the basic cross correlation technique for time delay estimation band limited random signals which are corrupted by white noise and received at two sensors are considered at various signal to noise ratios the variance of the time delay estimates are compared to the minimum variance obtainable in theory as given by the cramer rao lower bound

a subspace interior and conjugate gradient method for large scale bound constrained minimization problems a subspace adaptation of the coleman li trust region and interior method is proposed for solving large scale bound constrained minimization problems this method can be implemented with either sparse cholesky factorization or conjugate gradient computation under reasonable conditions the convergence properties of this subspace trust region method are as strong as those of its full space version computational performance on various large test problems is reported advantages of our approach are demonstrated our experience indicates that our proposed method represents an efficient way to solve large bound constrained minimization problems

continuum sites stepping stone models coalescing exchangeable partitions and random trees analogues of stepping stone models are considered where the sitespace is continuous the migration process is a general markov process and the type space is infinite such processes were defined in previous work of the second author by specifying a feller transition semigroup in terms of expectations of suitable functionals for systems of coalescing markov processes an alternative representation is obtained here in terms of a limit of interacting particle systems it is shown that under a mild condition on the migration process the continuum sites stepping stone process has continuous sample paths the case when the migration process is brownian motion on the circle is examined in detail using a duality relation between coalescing and annihilating brownian motion this duality relation is also used to show that a tree like random compact metric space that is naturally associated to an in nite family of coalescing brownian motions on the circle has hausdorff and packing dimension both almost surely equal to 1 2 and moreover this space is capacity equivalent to the middle 1 2 cantor set and hence also to the brownian zero set

robust eckart filters for time delay estimation minimax or robust filters which optimize worst case performance have been considered previously for matched and wiener filtering in this paper we show how similar ideas can be applied to obtain robust versions of one particular filter the eckart filter for time delay estimation the use of a robust filter can eliminate the requirement of estimation of the signal and noise power spectral densities psd s and cross psd s robust filters being less sensitive in their performance to variations of the input psd s within specified classes of psd s explicit solutions for specific classes of psd s are derived and several numerical examples and simulation results are given similar formulations for robust filters should also be possible for other types of filters used in time delay estimation

analysis of discrete implementation of generalized cross correlator a common discrete implementation of the cross correlator uses a parabolic fit to the peak when the delay is not an integral multiple of the sampling period this correspondence analyzes and assesses the pitfalls of this approach it is shown that this yields a biased estimate of the time delay with both the bias and variance of the estimate dependent on the location of the delay between samples snr signal and noise bandwidths and the prefilter or window used in the generalized correlator

computational results of an interior point algorithm for large scale linear programming this paper gives computational results for an efficient implementation of a variant of dual projective algorithm for linear programming the implementation uses the preconditioned conjugate gradient method for computing projections our computational experience reported in this paper indicates that this algorithm has potential as an alternative for solving very large lps in which the direct methods fail due to memory and cpu time requirements the conjugate gradient algorithm was able to find very accurate directions even when the system was ill conditioned the paper also discusses a new mathematical technique called the reciprocal estimates for estimating the primal variables we have conducted extensive computational experiments on problems representative of large classes of applications of current interest we have also chosen instances of the problems of future potential interest which could not be solved in the past due to the weakness of the prior solution methods but which represent a large class of new applications the hypergraph model is such an example comparison of our implementation with minos 5 1 shows that our implementation is orders of magnitude faster than minos 5 1 for these problems

timing estimation for a filtered poisson process in gaussian noise the problem of estimation of time shift of an inhomogeneous casually filtered poisson process in the presence of additive gaussian noise is discussed approximate expressions for the likelihood function the map estimator and the mmse estimator that becomes increasingly accurate as the per unit time density of superimposed filter responses becomes small are obtained the optimal map estimator takes the form of a cascade of linear and memoryless nonlinear components for smooth point process intensities the performance of the map estimator is studied via local bias and local variance a rate distortion type lower bound on the mse of any estimator of time delay is then derived by identification of a communications channel that accounts for the mapping from time delay to observation process results of numerical studies of estimator performance are presented based on the examples considered it is concluded 1 the small error mse of the nonlinear map estimator can be significantly better than the small error mse of the optimal linear estimator 2 the rate distortion lower bound can be significantly tighter than the poisson limited bounds determined in previous studies