fundamental limitations in passive time delay estimation part i narrow band systems time delay estimation of a noise like random signal observed at two or more spatially separated receivers is a problem of considerable practical interest in passive radar sonar applications a new method is presented to analyze the mean square error performance of delay estimation schemes based on a modified improved version of the ziv zakai lower bound zzlb this technique is shown to yield the tightest results on the attainable system performance for a wide range of signal to noise ratio snr conditions for delay estimation using narrow band ambiguity prone signals the fundamental result of this study is illustrated in fig 3 the entire domain of snr is divided into several disjoint segments indicating several distinct modes of operation if the available snr does not exceed snr 1 signal observations from the receiver outputs are completely dominated by noise thus essentially useless for the delay estimation as a result the attainable mean square error bar epsilon 2 is bounded only by the a priori parameter domain if snr 1 2 the modified zzlb coincides with the barankin bound in this regime differential delay observations are subject to ambiguities if snr snr 3 the modified zzlb coincides with the cramer rao lower bound indicating that the ambiguity in the differential delay estimation can essentially be resolved the transition from the ambiguity dominated mode of operation to the ambiguity free mode of operation starts at snr 2 and ends at snr 3 this is the threshold phenomenon in time delay estimation the various deflection points snr i and the various segments of the bound fig 3 are given as functions of such important system parameters as time bandwidth product wt signal bandwidth to center frequency ratio w 0 and the number of half wavelengths of the signal center frequency contained in the spacing between receivers with this information the composite bound illustrated in fig 3 provides the most complete characterization of the attainable system performance under any prespecified snr conditions

bayesian hybrid generative discriminative learning based on finite liouville mixture models recently hybrid generative discriminative approaches have emerged as an efficient knowledge representation and data classification engine however little attention has been devoted to the modeling and classification of non gaussian and especially proportional vectors our main goal in this paper is to discover the true structure of this kind of data by building probabilistic kernels from generative mixture models based on liouville family from which we develop the beta liouville distribution and which includes the well known dirichlet as a special case the beta liouville has a more general covariance structure than the dirichlet which makes it more practical and useful our learning technique is based on a principled purely bayesian approach which resulted models are used to generate support vector machine svm probabilistic kernels based on information divergence in particular we show the existence of closed form expressions of the kullback leibler and renyi divergences between two beta liouville distributions and then between two dirichlet distributions as a special case through extensive simulations and a number of experiments involving synthetic data visual scenes and texture images classification we demonstrate the effectiveness of the proposed approaches

parameter bounds on estimation accuracy under model misspecification when the assumed data distribution differs from the true distribution the model is said to be misspecified or mismatched model misspecification at some level is an inevitability of engineering practice while huber s celebrated work assesses maximum likelihood ml performance under misspecification no simple theory for bounding parameter estimation exists the class of parameter bounds emerging from the covariance inequality or equivalently the minimum norm theorem is revisited the expectation operator is well known to form an inner product space flexibility in the choice of expectation integrand and measure for integration exists however to establish a class of parameter bounds under a general form of model misspecification i e distribution mismatch the cramer rao bound crb primarily and secondarily the barankin hammersley chapman robbins bhattacharyya and bobrovsky mayer wolf zakai bounds under misspecification are considered huber s sandwich covariance is readily established as a special case of the misspecified crb subject to ml constraints and generalizations of the slepian and bangs formulae under misspecification are obtained

a general class of lower bounds in parameter estimation a general class of bayesian lower bounds on moments of the error in parameter estimation is formulated and it is shown that the cramer rao the bhattacharyya the bobrovsky zakai and the weiss weinstein lower bounds are special cases in the class the bounds can be applied to the estimation of vector parameters and any given function of the parameters the extension of these bounds to multiple parameter is discussed

adaptive subspace detectors we use the theory of generalized likelihood ratio tests glrts to adapt the matched subspace detectors msds of scharf 1991 and of scharf and frielander 1994 to unknown noise covariance matrices in so doing we produce adaptive msds that may be applied to signal detection for radar sonar and data communication we call the resulting detectors adaptive subspace detectors asds these include kelly s 1987 glrt and the adaptive cosine estimator ace of kaurt and scharh see ibid vol 47 p 2538 41 1999 and of scharf and mcwhorter see proc 30th asilomar conf signals syst comput pacific grove ca 1996 for scenarios in which the scaling of the test data may deviate from that of the training data we then present a unified analysis of the statistical behavior of the entire class of asds obtaining statistically identical decompositions in which each asd is simply decomposed into the nonadaptive matched filter the nonadaptive cosine or t statistic and three other statistically independent random variables that account for the performance degrading effects of limited training data

performance of the adaptive sidelobe blanker detection algorithm in homogeneous environments the adaptive sidelobe blanker asb algorithm is a two stage detector consisting of a first stage adaptive matched filter amf detector followed by a second stage detector called the adaptive coherence or cosine estimator ace only those data test cells that survive both detection thresholdings are declared signal target bearing we provide exact novel closed form expressions for the resulting probability of detection pd and false alarm pfa for the asb algorithm and demonstrate that under homogeneous data conditions with no signal array response mismatch that i the asb is a constant false alarm rate cfar algorithm ii the asb has a higher or commensurate pd for a given pfa than both the amf and the ace and iii the asb has an overall performance that is commensurate with kelly s 1986 benchmark generalized likelihood ratio test glrt a compact statistical summary is derived providing distributions and dependencies among the glrt amf and the ace decision statistics

derived pdf of maximum likelihood signal estimator which employs an estimated noise covariance a probability density function pdf for the maximum likelihood ml signal vector estimator is derived when the estimator relies on a noise sample covariance matrix scm for evaluation by using a complex wishart probabilistic model for the distribution of the scm it is shown that the pdf of the adaptive ml aml signal estimator alias the scm based minimum variance distortionless response mvdr beamformer output and more generally the scm based linearly constrained minimum variance lcmv beamformer output is in general the confluent hypergeometric function of a complex matrix argument known as kummer s function the aml signal estimator remains unbiased but only asymptotically efficient moreover the aml signal estimator converges in distribution to the ml signal estimator known noise covariance when the sample size of the estimated noise covariance matrix is fixed it is demonstrated that there exists a dynamic tradeoff between signal to noise ratio snr and noise adaptivity as the dimensionality of the array data number of adaptive degrees of freedom is varied suggesting the existence of an optimal array data dimension that will yield the best performance

capon algorithm mean squared error threshold snr prediction and probability of resolution below a specific threshold signal to noise ratio snr the mean squared error mse performance of signal parameter estimates derived from the capon algorithm degrades swiftly prediction of this threshold snr point is of practical significance for robust system design and analysis the exact pairwise error probabilities for the capon and bartlett algorithm derived herein are given by simple finite sums involving no numerical integration include finite sample effects and hold for an arbitrary colored data covariance via an adaptation of an interval error based method these error probabilities along with the local error mse predictions of vaidyanathan and buckley facilitate accurate prediction of the capon threshold region mse performance for an arbitrary number of well separated sources circumventing the need for numerous monte carlo simulations a large sample closed form approximation for the capon threshold snr is provided for uniform linear arrays a new exact two point measure of the probability of resolution for the capon algorithm that includes the deleterious effects of signal model mismatch is a serendipitous byproduct of this analysis that predicts the snrs required for closely spaced sources to be mutually resolvable by the capon algorithm last a general strategy is provided for obtaining accurate mse predictions that account for signal model mismatch

statistics of the mle and approximate upper and lower bounds part i application to toa estimation in nonlinear deterministic parameter estimation the maximum likelihood estimator mle is unable to attain the cramer rao lower bound at low and medium signal to noise ratios snrs due the threshold and ambiguity phenomena in order to evaluate the achieved mean squared error mse at those snr levels we propose new mse approximations msea and an approximate upper bound by using the method of interval estimation mie the mean and the distribution of the mle are approximated as well the mie consists in splitting the a priori domain of the unknown parameter into intervals and computing the statistics of the estimator in each interval also we derive an approximate lower bound alb based on the taylor series expansion of noise and an alb family by employing the binary detection principle the accuracy of the proposed mseas and the tightness of the derived approximate bounds are validated by considering the example of time of arrival estimation

bayesian bounds for matched field parameter estimation matched field methods concern estimation of source locations and or ocean environmental parameters by exploiting full wave modeling of acoustic waveguide propagation because of the nonlinear parameter dependence of the signal field the estimate is subject to ambiguities and the sidelobe contribution often dominates the estimation error below a threshold signal to noise ratio snr to study the matched field performance three bayesian lower bounds on mean square error are developed the bayesian crame spl acute r rao bound bcrb the weiss weinstein bound wwb and the ziv zakai bound zzb particularly for a multiple frequency multiple snapshot random signal model a closed form minimum probability of error associated with the likelihood ratio test is derived which facilitates error analysis in a wide scope of applications analysis and example simulations demonstrate that 1 unlike the local crb the bcrb is not achieved by the maximum likelihood estimate mle even at high snr if the local performance is not uniform across the prior parameter space 2 the zzb gives the closest mle performance prediction at most snr levels of practical interest 3 the zzb can also be used to determine the necessary number of independent snapshots achieving the asymptotic performance of the mle at a given snr 4 incoherent frequency averaging which is a popular multitone processing approach reduces the peak sidelobe error but may not improve the overall performance due to the increased ambiguity baseline and finally 5 effects of adding additional parameters e g environmental uncertainty can be well predicted from the parameter coupling

on divergences and informations in statistics and information theory the paper deals with the f divergences of csiszar generalizing the discrimination information of kullback the total variation distance the hellinger divergence and the pearson divergence all basic properties of f divergences including relations to the decision errors are proved in a new manner replacing the classical jensen inequality by a new generalized taylor expansion of convex functions some new properties are proved too e g relations to the statistical sufficiency and deficiency the generalized taylor expansion also shows very easily that all f divergences are average statistical informations differences between prior and posterior bayes errors mutually differing only in the weights imposed on various prior distributions the statistical information introduced by de groot and the classical information of shannon are shown to be extremal cases corresponding to alpha 0 and alpha 1 in the class of the so called arimoto alpha informations introduced in this paper for 0 alpha 1 by means of the arimoto alpha entropies some new examples of f divergences are introduced as well namely the shannon divergences and the arimoto alpha divergences leading for alphauarr1 to the shannon divergences square roots of all these divergences are shown to be metrics satisfying the triangle inequality the last section introduces statistical tests and estimators based on the minimal f divergence with the empirical distribution achieved in the families of hypothetic distributions for the kullback divergence this leads to the classical likelihood ratio test and estimator

extended ziv zakai lower bound for vector parameter estimation the bayesian ziv zakai bound on the mean square error mse in estimating a uniformly distributed continuous random variable is extended for arbitrarily distributed continuous random vectors and for distortion functions other than mse the extended bound is evaluated for some representative problems in time delay and bearing estimation the resulting bounds have simple closed form expressions and closely predict the simulated performance of the maximum likelihood estimator in all regions of operation

doa estimation and detection in colored noise using additional noise only data in a typical array processing scenario noise acting on the array can not be assumed spatially white it is in many cases necessary to use quiet periods when only noise is received to estimate the noise covariance if estimation of the signal parameters and noise covariance is performed jointly performance can be improved this is especially true when stationarity considerations limit the amount of available valid noise only data an asymptotically valid approximative maximum likelihood method aml for the estimation problem is derived in this work the resulting criterion is when concentrated with respect to the signal parameters relatively simple in numerical experiments aml shows promising small sample performance compared to earlier methods the criterion function is also well suited for numerical optimization the new criterion function allows for the development of a novel mode like non iterative estimation procedure if the array belongs to the important class of uniform linear arrays the resulting procedure retains the asymptotic properties of maximum likelihood and numerical simulations indicate superior threshold performance when compared to an optimally weighted subspace fitting wsf formulation of mode for the detection problem no method has been presented that takes the unknown noise covariance into account here a well known detection scheme for wsf is extended to work in this scenario as well the derivations of this scheme further stress the importance of using the correct weighting in wsf when the noise covariance is unknown it is also shown that the minimum value of the criterion function associated with aml can be used for the detection purpose numerical experiments indicate very promising performance for the aml detection scheme

detection estimation of very close emitters performance breakdown ambiguity and general statistical analysis of maximum likelihood estimation we reexamine the well known problem of threshold behavior or performance breakdown in the detection estimation of very closely spaced emitters in this extreme regime we analyze the performance for maximum likelihood estimation mle of directions of arrival doa for two close gaussian sources over the range of sample volumes and signal to noise ratios snrs where the correct number of sources is reliably estimated by information theoretic criteria itc but where one of the doa estimates is severely erroneous outlier we show that random matrix theory rmt applied to the evaluation of theoretical mle performance gives a relatively simple and accurate analytical description of the threshold behavior of mle and itc in particular the introduced single cluster criterion provides accurate ambiguity bounds for the outliers

on the effect of nuisance parameters on the threshold snr value of the barankin bound the performance of nonlinear estimators of signal parameters in noise appears to exhibit a threshold phenomenon below a critical value of signal to noise ratio snr the performance of these estimators deviates significantly from the cramer rao bound in a large error ambiguity prone snr region the barankin bound has been proved to be an advantageous tool to assess the attainable performance and the threshold value obviously when the estimation problem involves additional unknown nuisance parameters the mean square error mse of the estimator does not decrease however the impact of these nuisance parameters on the threshold value is not clear in this correspondence we discuss the influence of unknown nuisance parameters on the threshold value the analysis is done for the common problem concerning estimating parameters of a gaussian process we confine our scope to a simplified problem concerning only two estimated parameters however we explain how this simplified analysis can be used to handle a more complicated problem comprising multiple nuisance parameters we derive a sufficient condition applied to the structure of the data covariance matrix when the condition is satisfied then the need to estimate additional nuisance parameters does not change the threshold value using the proposed condition we prove that the threshold snr in passive source localization does not increase when the spectral parameters of the source are unknown whereas the presence of another source at an unknown bearing may change the threshold snr

estimating 3d trajectories from 2d projections via disjunctive factored four way conditional restricted boltzmann machines estimation recognition and near future prediction of 3d trajectories based on their two dimensional projections available from one camera source is an exceptionally difficult problem due to uncertainty in the trajectories and environment high dimensionality of the specific trajectory states lack of enough labeled data and so on in this article we propose a solution to solve this problem based on a novel deep learning model dubbed disjunctive factored four way conditional restricted boltzmann machine dffw crbm our method improves state of the art deep learning techniques for high dimensional time series modeling by introducing a novel tensor factorization capable of driving forth order boltzmann machines to considerably lower energy levels at no computational costs dffw crbms are capable of accurately estimating recognizing and performing near future prediction of three dimensional trajectories from their 2d projections while requiring limited amount of labeled data we evaluate our method on both simulated and real world data showing its effectiveness in predicting and classifying complex ball trajectories and human activities

optimum array design to maximize fisher information for bearing estimation source bearing estimation is a common application of linear sensor arrays the cramer rao bound crb sets a lower bound on the achievable mean square error mse of any unbiased bearing estimate in the spatially white noise case the crb is minimized by placing half of the sensors at each end of the array however many realistic ocean environments have a mixture of both white noise and spatially correlated noise in shallow water environments the correlated ambient noise can be modeled as cylindrically isotropic this research designs a fixed aperture linear array to maximize the bearing fisher information fi under these noise conditions the fi is the inverse of the crb so maximizing the fi minimizes the crb the elements of the optimum array are located closer to the array ends than uniform spacing but are not as extreme as in the white noise case the optimum array results from a trade off between maximizing the array bearing sensitivity and minimizing output noise power variation over the bear

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

statistics of the mle and approximate upper and lower bounds part ii threshold computation and optimal pulse design for toa estimation threshold and ambiguity phenomena are studied in part i of this paper where approximations for the mean squared error mse of the maximum likelihood estimator are proposed using the method of interval estimation mie and where approximate upper and lower bounds are derived in this part we consider time of arrival estimation and we employ the mie to derive closed form expressions of the begin ambiguity end ambiguity and asymptotic signal to noise ratio snr thresholds with respect to some features of the transmitted signal both baseband and passband pulses are considered we prove that the begin ambiguity threshold depends only on the shape of the envelope of the acr whereas the end ambiguity and asymptotic thresholds only on the shape of the acr we exploit the results on the begin ambiguity and asymptotic thresholds to optimize with respect to the available snr the pulse that achieves the minimum attainable mse the results of this paper are valid for various estimation problems

the probability of a subspace swap in the svd we extend the work of tufts kot and vaccaro tkv published in 1980 to improve the analytical characterization of threshold breakdown in svd methods our results sharpen the tkv results by lower bounding the probability of a subspace swap in the svd our key theoretical result is the characteristic function for a random variable whose probability of exceeding zero bounds the probability of a threshold breakdown

effects of estimated noise covariance matrix in optimal signal detection there is loss of efficiency when an estimated noise covariance matrix is used in the place of the unknown true noise covariance matrix in the construction of the optimum filter for signal detection in the case of detecting a single signal specified by a real or a complex vector we investigate the extent of this loss by obtaining an exact confidence bound for the realized signal to noise ratio we also give an estimate of this ratio which is useful in optimum selection of features some of these results are extended to the case of discrimination between a number of given signals

performance analysis of the mvdr spatial spectrum estimator the performance of the minimum variance distortionless response spectrum estimator is analyzed finite data effects and the sensitivity of the method to random perturbations in the signal model and in the noise covariance matrix are studied the snapshots are assumed to be complex independent identically distributed gaussian vectors an expression for the exact model asymptotic bias is also derived analytical expressions for the variance and the bias of the estimator are derived and compared with simulation results these expressions are then employed to study the characteristics of the estimator

mean squared error and threshold snr prediction of maximum likelihood signal parameter estimation with estimated colored noise covariances an interval error based method mie of predicting mean squared error mse performance of maximum likelihood estimators mles is extended to the case of signal parameter estimation requiring intermediate estimation of an unknown colored noise covariance matrix an intermediate step central to adaptive array detection and parameter estimation the successful application of mie requires good approximations of two quantities 1 interval error probabilities and 2 asymptotic snrrarrinfin local mse performance of the mle exact general expressions for the pairwise error probabilities that include the effects of signal model mismatch are derived herein that in conjunction with the union bound provide accurate prediction of the required interval error probabilities the crameacuter rao bound crb often provides adequate prediction of the asymptotic local mse performance of mle the signal parameters however are decoupled from the colored noise parameters in the fisher information matrix for the deterministic signal model rendering the crb incapable of reflecting loss due to colored noise covariance estimation a new modification of the crb involving a complex central beta random variable different from but analogous to the reed mallett and brennan beta loss factor provides a working solution to this problem facilitating mse prediction well into the threshold region with remarkable accuracy

note on the calculation of the probability of detection and the generalized marcum q function a highly reliable accurate and efficient method of calculating the probability of detection p sub n x y for n incoherently integrated samples where x is the constant received signal to noise ratio of a single pulse and y is the normalized threshold level is presented the useful range of parameters easily exceeds most needs on a vax 11 computer with double precision calculations better than 13 place absolute accuracy is normally achieved there is a gradual loss of accuracy with increasing parameter values for example for n 10 sup 9 and with both nx and y near 10 sup 7 the accuracy can drop to ten places the function p sub n x y can be equated to the generalized marcum q function q sub m alpha beta the corresponding limits on alpha and beta are roughly 4500 for the 13 place accuracy and 60000 for ultimate integer 4 limit

pareto models for discriminative multiclass linear dimensionality reduction we address the class masking problem in multiclass linear discriminant analysis lda in the multiclass setting lda does not maximize each pairwise distance between classes but rather maximizes the sum of all pairwise distances this results in serious overlaps between classes that are close to each other in the input space and degrades classification performance our research proposes pareto discriminant analysis parda an approach for multiclass discriminative analysis that builds over multiobjective optimizing models parda decomposes the multiclass problem to a set of objective functions each representing the distance between every pair of classes unlike existing lda extensions that maximize the sum of all distances parda maximizes each pairwise distance to maximally separate all class means while minimizing the class overlap in the lower dimensional space experimental results on various data sets show consistent and promising performance of parda when compared with well known multiclass lda extensions highlightswe address the class masking problem cmp in multiclass lda mlda we model mlda as a set of objective functions for pairwise distances between classes we optimize the compound objective function using multiobjective optimization our models overcome the cmp and are extended to multimodal non gaussian data empirical analysis shows consistent and promising performance in favor of our models

supervised feature selection by clustering using conditional mutual information based distances in this paper a supervised feature selection approach is presented which is based on metric applied on continuous and discrete data representations this method builds a dissimilarity space using information theoretic measures in particular conditional mutual information between features with respect to a relevant variable that represents the class labels applying a hierarchical clustering the algorithm searches for a compression of the information contained in the original set of features the proposed technique is compared with other state of art methods also based on information measures eventually several experiments are presented to show the effectiveness of the features selected from the point of view of classification accuracy

a bound on mean square estimation error with background parameter mismatch in typical parameter estimation problems the signal observation is a function of the parameter set to be estimated as well as some background environmental system parameters assumed known the assumed background could differ from the true one leading to biased estimates even at high signal to noise ratio snr to analyze this background mismatch problem a ziv zakai type lower bound on the mean square error mse is developed based on the mismatched likelihood ratio test mlrt at high snr the bound incorporates the increase in mse due to estimation bias at low snr it includes the threshold effect due to estimation ambiguity the kernel of the bound s evaluation is the error probability associated with the mlrt a closed form expression for this error probability is derived under a random signal model typical of the bearing estimation passive source localization problem the mismatch is then analyzed in terms of the related ambiguity functions examples of bearing estimation with system array shape mismatch demonstrate that the developed bound describes the simulations of the maximum likelihood estimate well including the sidelobe introduced threshold behavior and the bias at high snr

global solutions for a supercritical drift diffusion equation abstract we study the global existence of solutions to a one dimensional drift diffusion equation with logistic term generalizing the classical parabolic elliptic keller segel aggregation equation arising in mathematical biology in particular we prove that there exists a global weak solution if the order of the fractional diffusion 1 c 1 2 where c 1 0 is an explicit constant depending on the physical parameters present in the problem chemosensitivity and strength of logistic damping furthermore in the range 1 c 2 2 with 0 c 2 c 1 the solution is globally smooth let us emphasize that when 1 the diffusion is in the supercritical regime

bounds for estimation of complex exponentials in unknown colored noise we consider the problem of estimating the parameters of complex exponentials in the presence of complex additive gaussian noise with unknown covariance bounds are derived for the accuracy of jointly estimating the parameters of the exponentials and the noise we first present an exact cramer rao bound crb for this problem and specialize it for the cases of circular gaussian processes and autoregressive processes we also derive an approximate expression for the crb which is related to the conditional likelihood function numerical evaluation of these bounds provides some insights on the effect of various signal and noise parameters on the achievable estimation accuracy

an efficient algorithm to find the mle of prior probabilities of a mixture in pattern recognition a number of techniques have been proposed to determine the parameters which define the unknown components of a mixture in pattern recognition the most common method is the maximum likelihood estimation mle a direct ml approach requires solution to maximize the likelihood function of the unknown prior probabilities of classes in a mixture this is a complicated multiparameter optimization problem the direct approach tends to be computationally complex and time consuming in this study we use the concave property of the kullback leibler information number to derive a simple and accurate algorithm which can find the mle of the prior probability of each class the results of a monte carlo simulation study with normal and exponential distributions are presented to demonstrate the favorable prior estimation for the algorithm

on a parabolic elliptic system with gradient dependent chemotactic coefficient abstract we consider a second order pdes system of parabolic elliptic type with chemotactic terms the system describes the evolution of a biological species u moving towards a higher concentration of a chemical stimuli v in a bounded and open domain of r n in the system considered the chemotaxis sensitivity depends on the gradient of v i e the chemotaxis term has the following expression d i v u v p 2 v where is a positive constant and p satisfies p 1 if n 1 and p 1 n n 1 if n 2 we obtain uniform bounds in l and the existence of global in time solutions for the one dimensional case we prove the existence of infinitely many non constant steady states for p 1 2 for any positive and a given positive mass

frequency domain cramer rao bound for gaussian processes an expression is derived for the asymptotic frequency domain cramer rao bound crb on the parameters of gaussian processes with information in their means the general result extends whittle s 1953 formula which is applicable to gaussian processes with information in their covariance matrices or spectra it is useful in many fields such as system identification radar and sonar examples of its application to system deconvolution and time delay estimation in colored noise are given

rate distortion bounds on passive sonar performance information theory provides a novel perspective on passive sonar performance analysis this approach begins by partitioning the search space and then considers the problem of assigning a source to the correct partition based on pressure observations from a hydrophone array prior work described necessary conditions for achieving arbitrarily small probability of error pe as a tradeoff between signal to noise ratio snr and the range accuracy of the partitions this paper presents a method to extend these results using the rate distortion function to find necessary conditions for any pe the gaussian channel bound sets an upper limit on the information rate received at the array through the rate distortion function this upper limit on the information rate implies a lower bound on pe for a given partition furthermore the current work describes a tradeoff between range accuracy pe and snr examples of this tradeoff are evaluated for both one dimensional bearing and two dimensional range depth estimation problems

maximum likelihood sequence detection for intersymbol interference channels a new upper bound on error probability maximum likelihood sequence detection of digital signaling subject to intersymbol interference and additive white gaussian noise is considered a new approach to the error probability analysis results in an upper bound which is tighter than the forney bound in addition in the case of infinite length intersymbol interference a locally convergent bound is shown to hold under fairly general assumptions on the signal autocorrelation

performance of a class of adaptive detection algorithms in nonhomogeneous environments a two dimensional 2 d adaptive sidelobe blanker asb detection algorithm was developed through experimentation as an extenuate for false alarms caused by undernulled interference encountered when applying the adaptive matched filter amf in nonhomogeneous environments the algorithm s utility has been demonstrated empirically considering theoretic performance analyses of the asb detection algorithm as well as the amf generalized likelihood ratio test glrt and the adaptive cosine estimator ace under nonideal conditions can become fairly intractable rather quickly especially in an adaptive processing context involving covariance estimation in this paper however we have developed and exploited a theoretic framework through which the performance of these algorithms under nonhomogeneous conditions can be examined theoretically it is demonstrated through theoretic analysis that in the presence of undernulled interference the asb is a pliable false alarm regulatory far detector that maintains good target sensitivity a viable method of asb threshold selection is also presented and demonstrated

a decision cognizant kullback leibler divergence in decision making systems involving multiple classifiers there is the need to assess classifier in congruence that is to gauge the degree of agreement between their outputs a commonly used measure for this purpose is the kullback leibler kl divergence we propose a variant of the kl divergence named decision cognizant kullback leibler divergence dc kl to reduce the contribution of the minority classes which obscure the true degree of classifier incongruence we investigate the properties of the novel divergence measure analytically and by simulation studies the proposed measure is demonstrated to be more robust to minority class clutter its sensitivity to estimation noise is also shown to be considerably lower than that of the classical kl divergence these properties render the dc kl divergence a much better statistic for discriminating between classifier congruence and incongruence in pattern recognition systems

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

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

a bound on mean square estimate error a lower bound on mean square estimate error is derived as an instance of the covariance inequality by concatenating the generating matrices for the bhattacharyya and barankin bounds it represents a generalization of the bhattacharyya barankin cramer rao hammersley chapman robbins kiefer and mcaulay hofstetter bounds in that all of these bounds may be derived as special cases the bound is applicable to biased estimates of functions of a multidimensional parameter termed the hybrid bhattacharyya barankin bound it may be written as the sum of the mth order bhattacharyya bound and a nonnegative term similar in form to the rth order hammersley chapman robbins bound it is intended for use when small error bounds such as the cramer rao bound may not be tight unlike many large error bounds it provides a smooth transition between the small error and large error regions as an example application bounds are placed on the variance of unbiased position estimates derived from passive array measurements here the hybrid bhattacharyya barankin bound enters the large error region at a larger snr and in the large error region is noticeably greater than either the hammersley chapman robbins or the bhattacharyya bounds

on the resolution probability of conditional and unconditional maximum likelihood doa estimation after decades of research in direction of arrival doa estimation today maximum likelihood ml algorithms still provide the best performance in terms of resolution capabilities at the cost of a multidimensional search ml algorithms achieve a significant reduction of the outlier production mechanism in the threshold region where the number of snapshots per antenna and or the signal to noise ratio snr are low the objective of this paper is to characterize the resolution capabilities of ml algorithms in the threshold region both conditional and unconditional versions of the ml algorithms are investigated in the asymptotic regime where both the number of antennas and the number of snapshots are large but comparable in magnitude by using random matrix theory techniques the finite dimensional distributions of both cost functions are shown to be gaussian distributed in this asymptotic regime and a closed form expression of the corresponding asymptotic covariance matrices is provided these results allow to characterize the asymptotic behavior of the resolution probability which is defined as the probability that the cost function evaluated at the true doas is smaller than the values that it takes at the positions of the other asymptotic local minima

performance study of conditional and unconditional direction of arrival estimation a numerical and analytical study of conditional and unconditional direction of arrival doa estimation is presented explicit expressions for the unconditional cramer rao bounds on the doa estimation accuracy and the covariance matrix of the conditional maximum likelihood method are given it is shown that many doa estimation methods have the same asymptotic statistical properties under conditional and unconditional models the situation of two narrowband plane signals impinging on a uniformly spaced linear array is discussed

mean squared error prediction for bayesian direction of arrival estimation in this article we study the mean squared error performance of bayesian direction of arrival doa estimation in which prior belief about the target location is incorporated into the estimation process our primary result is an extension of the method of interval errors mie to the case of maximum a posteriori map direction of arrival estimation we work in a general framework in which the prior information used in the map estimation may not match the actual target distribution in particular when the prior is incorrect the map estimator degrades relative to the performance of a map estimator with the correct prior our methods are able to accurately predict the performance of a map estimator in this more general situation we apply our methods to investigate the sensitivity of map direction of arrival estimation to mismatches between the chosen prior and the actual angular distribution of the target