sensitivity analysis for antenna near field imaging although imaging and inverse scattering problems have been thoroughly studied during the last century there is only a partial understanding of these complex problems most of the efforts have been placed on the development of efficient inversion algorithms and mathematical uniqueness results in comparison there are very few results and a limited knowledge about the information content in the inversion data in this paper we provide a mathematical framework for sensitivity analysis of antenna near field imaging problems based on the multipole expansion of the electromagnetic field and the fisher information to quantify the quality of data by exploiting this framework a fundamental relation for accuracy and resolution is formulated based on the crameacuter rao bound crb the sensitivity analysis is illustrated using a relevant example with cylindrical measurement data

the beta model maximum likelihood cramer rao bounds and hypothesis testing we study the maximum likelihood estimator in a setting where the dependent variable is a random graph and covariates are available on a graph level the model generalizes the well known beta model for random graphs by replacing the constant model parameters with regression functions cramer rao bounds are derived for special cases of the undirected beta model the directed beta model and the covariate based beta model the corresponding maximum likelihood estimators are compared with the bounds by means of simulations moreover examples are given on how to use the presented maximum likelihood estimators to test for directionality and significance finally the applicability of the model is demonstrated using temporal social network data describing communication among healthcare workers

joint estimation of porosity and saturation using stochastic rock physics modeling sediment porosity and saturation affect bulk modulus shearmodulus anddensity consequently estimatinghydrocarbon saturation and reservoir porosity from seismic data is a joint estimation problem uncertainty in porosity will lead toerrorsinsaturationprediction andviceversa porosityand saturation can be jointly estimated using stochastic rockphysicsmodelingandformalbayesianestimationmethodology knowledge of shear impedance reduces the uncertainty inporosityandthusalsoreducesuncertaintyinsaturationestimation this study investigates joint estimation of porosity and saturation by using rock physics stochastic modeling and bayesian estimation theory to derive saturation and porosity maps of expected pay sands in the field example the uncertainty in porosity quantified by the standard deviation stdassociatedwiththeposteriorprobabilitydensityfunctionpdf derivedfrominversionofseismicdataismuchless than the uncertainty in the derived saturation for a typical case the std associated with saturation is 24 while porositystdisabout1 34porosityunitsgivenseismic derived inversionattributeswithreasonableaccuracy comparisonof these numbers with prior estimates showed that inversion of seismic data decreased the uncertainty in porosity to 15 of the prior uncertainty while saturation uncertainty was only reduced to 92 of the prior uncertainty although these resultsmayvaryfromonelocationtoanother themethodology isgeneralandcanbeappliedtootherlocations

limits of sensing temporal concentration changes by single cells berg and purcell biophys j 20 193 1977 calculated how the accuracy of concentration sensing by single celled organisms is limited by noise from the small number of counted molecules here we generalize their results to the sensing of concentration ramps which is often the biologically relevant situation e g during bacterial chemotaxis we calculate lower bounds on the uncertainty of ramp sensing by three measurement devices a single receptor an absorbing sphere and a monitoring sphere we contrast two strategies simple linear regression of the input signal versus maximum likelihood estimation and show that the latter can be twice as accurate as the former finally we consider biological implementations of these two strategies and identify possible signatures that maximum likelihood estimation is implemented by real biological systems

performance of two methods for solving separable hamiltonian systems abstract we make qualitative comparisons of fixed step symplectic and variable step nonsymplectic integrations of the separable henon heiles hamiltonian system emphasis is given to interesting numerical phenomena particularly we observe the relationship of the error in the computed hamiltonian to the presence and absence of chaos when computing with a symplectic fixed step method qualitative phenomena in the hamiltonian error for a variable step method and the sensitivity of the chaotic behavior and of the computation of features in poincare sections to very small changes in initial conditions step sizes and error tolerances

pure adaptive search in global optimization pure adaptive seach iteratively constructs a sequence of interior points uniformly distributed within the corresponding sequence of nested improving regions of the feasible space that is at any iteration the next point in the sequence is uniformly distributed over the region of feasible space containing all points that are strictly superior in value to the previous points in the sequence the complexity of this algorithm is measured by the expected number of iterations required to achieve a given accuracy of solution we show that for global mathematical programs satisfying the lipschitz condition its complexity increases at mostlinearly in the dimension of the problem

robust linear channel estimation methods for per subcarrier transmit antenna selection the linear minimum mean squared error mse channel estimator for systems employing per subcarrier transmit antenna selection is developed frequency domain correlations after the selection process are shown to be approximated well using a simple function which makes near optimal channel estimation practically possible however the resultant estimators are not robust to errors in the assumed model in terms of the antenna to subcarrier assignment used at transmission as we motivate both analytically and via simulations this is an issue when the channels for conveying this information to the receiver are severely constrained we present windowed channel estimations and new robust estimation algorithms either individually or in combination as solutions to counter this sensitivity the robust estimators are developed based on the principles of 1 minimising the worst case mse over the set of possible models and 2 minimising the expected mse over the set of possible models the latter estimator is preferred due to the lower implementation complexity and better mse performance we also prove theoretical asymptotic in signal to noise ratio performances of the two estimators used with the proposed correlation model simulation results illustrate the performance gains and improved robustness offered by the developed estimators

invariance of distribution of coherence estimate to second channel statistics when one of the two channels used in a coherence estimator contains only zero mean stationary gaussian noise the probability distribution of the magnitude squared coherence estimate is utterly independent of the distribution in the other channel when the random variables in the two channels are statistically independent of each other thus proper threshold settings for specified false alarm probabilities in a coherence detector can be realized under complete ignorance of the statistics of the non gaussian channel

active learning applied to rcs computations with nonuniform sampling using different objective functions an active learning framework is introduced to reduce the number of frequencies and angles one must consider for wideband monostatic scattering computations or measurements this method is used to optimally select those frequencies and angles that would be most informative resulting in nonuniform sampling and often a reduced number of points vis agrave vis uniform sampling in this paper we focus on jointly two dimensional optimal sampling in frequency and incident angle thetas for monostatic scattering the method consists of two basic steps one step involves estimation of model parameters using a least square ls algorithm the next step is to optimally choose the next point frequency and thetas for analysis by the computational model or experiment this new point is selected with the goal of reducing uncertainty in the parametric model quantified via the fisher information matrix iterating these two steps a sequence of numerical computations or measurements are performed each at the most informative point for learning the parameters of the associated simpler parametric model this idea is demonstrated here in the context of reducing the number of points frequencies and orientations at which a computational model must be employed and in order to avoid repeatedly gathering samplings at the edge of the input space an alternative objective function is applied which makes the actively selected points closer to a region of interest

a direct stochastic algorithm for global search this paper presents a new algorithm called probabilistic global search lausanne pgsl pgsl is founded on the assumption that optimal solutions can be identified through focusing search around sets of good solutions tests on benchmark problems having multi parameter non linear objective functions revealed that pgsl performs better than genetic algorithms and advanced algorithms for simulated annealing in 19 out of 23 cases studied furthermore as problem sizes increase pgsl performs increasingly better than these other approaches empirical evidence of the convergence of pgsl is provided through its application to lennard jones cluster optimisation problem finally pgsl has already proved to be valuable for engineering tasks in areas of design diagnosis and control

invariance of the magnitude squared coherence estimate with respect to second channel statistics properties of the magnitude squared coherence msc estimate in the presence of spherically symmetric noise are examined from a geometric point of view invariance to second channel statistics is shown and the distribution function of the estimate is derived a relationship between spherically symmetric and gaussian sequences is also given

a symplectic integration algorithm for separable hamiltonian functions abstract we derive an algorithm to numerically integrate differential equations derivable from a separable hamiltonian function this symplectic algorithm is accurate to fourth order in the time step and preserves exactly the poincare cartan integral invariants associated with the topology of the phase flow we compare the efficiency and accuracy of this method to that of existing integrators both symplectic and non symplectic by integrating the equations of motion corresponding to a nonlinear pendulum a particle in the field of a standing wave and a harmonic oscillator perturbed by a plane wave

a new hybrid method for solving global optimization problem abstract in this paper we present a new hybrid method called the sasp method the purpose of this method is the hybridization of the simulated annealing sa with the descent method where we estimate the gradient using simultaneous perturbation firstly the new hybrid method finds a local minimum using the descent method then sa is executed in order to escape from the currently discovered local minimum to a better one from which the descent method restarts a new local search and so on until convergence the new hybrid method can be widely applied to a class of global optimization problems for continuous functions with constraints experiments on 30 benchmark functions including high dimensional functions show that the new method is able to find near optimal solutions efficiently in addition its performance as a viable optimization method is demonstrated by comparing it with other existing algorithms numerical results improve the robustness and efficiency of the method presented

retinal vessel centerline extraction using multiscale matched filters confidence and edge measures motivated by the goals of improving detection of low contrast and narrow vessels and eliminating false detections at nonvascular structures a new technique is presented for extracting vessels in retinal images the core of the technique is a new likelihood ratio test that combines matched filter responses confidence measures and vessel boundary measures matched filter responses are derived in scale space to extract vessels of widely varying widths a vessel confidence measure is defined as a projection of a vector formed from a normalized pixel neighborhood onto a normalized ideal vessel profile vessel boundary measures and associated confidences are computed at potential vessel boundaries combined these responses form a six dimensional measurement vector at each pixel a training technique is used to develop a mapping of this vector to a likelihood ratio that measures the vesselness at each pixel results comparing this vesselness measure to matched filters alone and to measures based on the hessian of intensities show substantial improvements both qualitatively and quantitatively the hessian can be used in place of the matched filter to obtain similar but less substantial improvements or to steer the matched filter by preselecting kernel orientations finally the new vesselness likelihood ratio is embedded into a vessel tracing framework resulting in an efficient and effective vessel centerline extraction algorithm

iterative cdma multiuser receiver with soft decision directed channel estimation we develop an iterative code division multiple access cdma receiver for multipath block fading channels in the uplink the mean square error mse of the channel estimates is reduced iteratively by using soft data estimates as additional pilots the multiuser detector performs parallel interference cancellation pic with subsequent linear filtering we consider a single user matched filter sumf and develop a low complexity linear minimum mse lmmse filter for intersymbol interference isi channels that allows for 33 more users than the sumf we investigate two choices of training sequences for initial channel estimation the first is a random pilot symbol sequence modulated by a short spreading sequence rand and the second is a perfect root of unity sequence prus used as long sounding chip sequence we observe that the rand scheme approaches the single user bound up to 2 db and in case of prus up to 1 db at a target bit error rate ber of 10 3 further several channel estimators are developed that use various combinations of soft decision symbols and statistical a priori knowledge about the channel these are the approximated least squares als approximated linear mmse almmse and linear mmse lmmse estimators the iterative estimators show an improvement of 2 5 and 5 db with prus and rand pilots respectively over estimators that do not exploit soft feedback symbols at a ber of 10 3 the als is sacrificing less than 0 6 db to obtain a ber of 10 3 in a system at load 1 5 when compared with the almmse and lmmse schemes the load is understood as the ratio of the number of users to the spreading factor this paper shows that significant improvements in system capacity can be achieved in multipath scenarios with low complexity choices of multiuser detectors and channel estimators

on minimum variance unbiased estimation of clock offset in a two way message exchange mechanism for many applications distributed networks require the local clocks of the constituent nodes to run close to an agreed upon notion of time most of the widely used clock synchronization algorithms in such systems employ the sender receiver protocol based on a two way timing message exchange paradigm maximum likelihood estimator mle of the clock offset based on the timing message exchanges between two clocks was derived in d r jeske on maximum likelihood estimation of clock offset ieee trans commun vol 53 pp 53 54 jan 2005 when the fixed delays are symmetric and the variable delays in each direction assume an exponential distribution with an unknown mean herein the best linear unbiased estimate using order statistics blue os of the clock offset between two nodes is derived assuming both symmetric and asymmetric exponential network delays respectively the rao blackwell lehmann scheffe theorem is then exploited to obtain the minimum variance unbiased estimate mvue for the clock offset which it is shown to coincide with the blue os in addition it is found that the mvue of the clock offset in the presence of symmetric network delays also coincides with the mle finally in the presence of asymmetric network delays although the mle is biased it is shown to achieve lesser mean square error mse than the mvue in the region around the point where the bidirectional network link delays are symmetric and hence its merit as the most versatile estimator is fairly justified

asymptotic analysis of the generalized coherence estimate the generalized coherence gc estimate has shown promise as a multiple channel detection statistic but analysis of its performance in this role has been hampered because its probability density function is difficult to evaluate under signal absent hypotheses and is unknown under signal present hypotheses this paper presents an as asymptotic analysis of the gc estimate that provides tractable closed form expressions for the density of the cc estimate under useful signal absent and signal present hypotheses these expressions are valid as the number of data samples employed in the estimate approaches infinity theoretical predictions of the detection performance based on these expressions are shown to match closely results obtained by monte carlo simulation even when relatively small numbers of samples are used in the gc estimate these results are used to further examine the merits of the cc estimate as a multiple channel detection statistic

representation of mutual information via input estimates a relationship between information theory and estimation theory was recently shown for the gaussian channel relating the derivative of mutual information with the minimum mean square error this paper generalizes the link between information theory and estimation theory to arbitrary channels giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs we illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

improvement of tdoa position fixing using the likelihood curvature a conventional multilateration is a two step process where in the first step the time difference of arrivals tdoa of a signal at multiple sensors are estimated and in the second step these tdoas are used in some position fixing technique to estimate the location of an emitter several estimators have been proposed over the years for the estimation of the tdoas many techniques have been proposed for position fixing as well much of the research on position fixing has been focused on obtaining a simplified closed form solution for the unknown deterministic signal model stein had derived the maximum likelihood estimator mle for the tdoa between two sensors which is the peak location of the cross correlation function since the asymptotic variance of an mle approaches the cramer rao lower bound crlb which is the inverse of the negative of the expected value of the curvature of the log likelihood function using this as a motivation we propose a weighted least squares type position fixing technique where the weights are computed from the curvature of the log likelihood function

the risk unbiased cramer rao bound for non bayesian multivariate parameter estimation how accurately can one estimate a deterministic parameter subject to other unknown deterministic model nuisance parameters the most popular answer to this question is given by the cramer rao bound crb the main assumption behind the derivation of the crb is local unbiased estimation of all model parameters the foundations of this paper rely on doubting this assumption generally in multivariate parameter estimation each parameter in its turn can be treated as a single parameter of interest whereas the other model parameters are treated as nuisance as their misknowledge interferes with the estimation of the parameter of interest this approach is utilized in this paper to provide a fresh look at deterministic parameter estimation a new cramer rao cr type bound is derived without assuming unbiased estimation of the nuisance parameters rather than that we apply lehmann s concept of unbiasedness for a risk that measures the distance between the estimator and the locally best unbiased estimator which assumes perfect knowledge of the nuisance parameters the proposed risk unbiased crb rucrb is proven to be asymptotically attainable by the maximum likelihood estimator while being tighter than the conventional crb furthermore simulations verify the asymptotic achievability of the rucrb by the maximum likelihood estimator for an array processing problem

fourth order symplectic integration abstract in this paper we present an explicit fourth order method for the integration of hamilton s equations this method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state that is the integration step is an explicit symplectic map although the result is first derived for a specific type of hamiltonian it is shown to be quite general in particular the results can be applied to any lie group

hesitant adaptive search for global optimisation pure adaptive search is a stochastic algorithm which has been analysed in distinct ways for finite and continuous global optimisation in this paper motivated by the behaviour of practical algorithms such as simulated annealing we extend these ideas we present a unified theory which yields both the finite and continuous results for pure adaptive search at the same time we allow our extended algorithm to hesitate before improvement continues results are obtained for the expected number of iterations to convergence for such an algorithm 1998 the mathematical programming society inc published by elsevier science b v

robust rls in the presence of correlated noise using outlier sparsity relative to batch alternatives the recursive least squares rls algorithm has well appreciated merits of reduced complexity and storage requirements for online processing of stationary signals and also for tracking slowly varying nonstationary signals however rls is challenged when in addition to noise outliers are also present in the data due to e g impulsive disturbances existing robust rls approaches are resilient to outliers but require the nominal noise to be white an assumption that may not hold in e g sensor networks where neighboring sensors are affected by correlated ambient noise prewhitening with the known noise covariance is not a viable option because it spreads the outliers to noncontaminated measurements which leads to inefficient utilization of the available data and unsatisfactory performance in this correspondence a robust rls algorithm is developed capable of handling outliers and correlated noise simultaneously in the proposed method outliers are treated as nuisance variables and estimated jointly with the wanted parameters identifiability is ensured by exploiting the sparsity of outliers which is effected via regularizing the least squares ls criterion with the l1 norm of the outlier vectors this leads to an optimization problem whose solution yields the robust rls estimates for low complexity real time operation a suboptimal online algorithm is proposed which entails closed form updates per time step in the spirit of rls simulations demonstrate the effectiveness and improved performance of the proposed method in comparison with the nonrobust rls and its state of the art robust renditions

seeker optimization algorithm for parameter estimation of time delay chaotic systems time delay chaotic systems have some very interesting properties and their parameter estimation has received increasing interest in the recent years it is well known that parameter estimation of a chaotic system is a nonlinear multivariable and multimodal optimization problem for which global optimization techniques are required in order to avoid local minima in this work a seeker optimization algorithm soa based method is proposed to address this issue in the soa search direction is based on the empirical gradients by evaluating the response to the position changes and step length is based on uncertainty reasoning by using a simple fuzzy rule the performance of the algorithm is evaluated on two typical test systems moreover two state of the art algorithms i e particle swarm optimization and differential evolution are also considered for comparison the simulation results show that the proposed algorithm is better than or at least as good as the other two algorithms and can effectively solve the parameter estimation problem of time delay chaotic systems

matched subspace detectors we formulate a general class of problems for detecting subspace signals in subspace interference and broadband noise we derive the generalized likelihood ratio glr for each problem in the class we then establish the invariances for the glr and argue that these are the natural invariances for the problem in each case the glr is a maximal invariant statistic and the distribution of the maximal invariant statistic is monotone this means that the glr test glrt is the uniformly most powerful invariant detector we illustrate the utility of this finding by solving a number of problems for detecting subspace signals in subspace interference and broadband noise in each case we give the distribution for the detector and compute performance curves

auditory motivated level crossing approach to instantaneous frequency estimation we address the problem of estimating the instantaneous frequency if of a phase signal using its level crossing lc information based on front end auditory processing motivation we show that the problem of if estimation using lc information can be cast in the framework of estimation from irregularly sampled data the formulation has the generality of estimating different types of if without the need for a quasistationary assumption we consider two types of if polynomial and bandlimited we use polynomial interpolating functions for the former and for the latter we propose a novel line plus sum of sines model the model parameters are estimated by linear regression considering the noisy case lc data for different levels is analyzed and methods for combining different estimators from lcs are discussed theoretical and extensive simulation results show that the performance of the zero crossing zc based if estimator and the level crossing based if estimator with smaller level values is better than those obtained with higher level values or their combinations the new technique reaches the crame spl acute r rao bound crb roughly above 4 db signal to noise ratio snr and its performance does not deteriorate rapidly with mismatch in the if order compared with the other techniques in the literature

low complexity lmmse based mimo ofdm channel estimation via angle domain processing in many situations multiple input multiple output with orthogonal frequency division multiplexing mimo ofdm channels tend to be spatially correlated due for example to limited scattering prior knowledge of this channel spatial correlation and the channel frequency correlation can be exploited by using the linear minimum mean square error lmmse technique however the complexity of the 2 d lmmse technique which fully utilizes both the channel spatial and frequency correlation is quite high to solve this problem this paper presents and analyzes several low complexity suboptimal approximated lmmse channel estimation techniques in the angle domain where the channel model lends itself to a physical interpretation the choice of angle domain techniques is largely dependent on the extent of channel stochastic information e g channel correlation or power that is available to the receiver nevertheless all the proposed angle domain techniques have much lower complexity compared to the 2 d lmmse technique further all the angle domain techniques improve over the conventional least square ls technique for all the typical mimo ofdm models under consideration more importantly our simulation results show that the angle domain quasi 1 d ql d lmmse technique can achieve similar performance compared to the 2 d lmmse technique for all typical mimo ofdm models with significantly lower complexity

a geometric approach to multiple channel signal detection the paper introduces the generalized coherence gc estimate and examines its application as a statistic for detecting the presence of a common but unknown signal on several noisy channels the gc estimate is developed as a natural generalization of the magnitude squared coherence msc estimate a widely used statistic for nonparametric detection of a common signal on two noisy channels the geometrical nature of the gc estimate is exploited to derive its distribution under the h sub 0 hypothesis that the data channels contain independent white gaussian noise sequences detection thresholds corresponding to a range of false alarm probabilities are calculated from this distribution the relationship of the h sub 0 distribution of the gc estimate to that of the determinant of a complex wishart distributed matrix is noted the detection performance of the three channel gc estimate is evaluated by simulation using a white gaussian signal sequence in white gaussian noise its performance is compared with that of the multiple coherence mc estimate another nonparametric multiple channel detection statistic the gc approach is found to provide better detection performance than the mc approach in terms of the minimum signal to noise ratio on all data channels necessary to achieve desired combinations of detection and false alarm probabilities

time varying techniques for multisensor signal detection in source detection and localization the presence of a common but unknown signal can be detected from several noisy sensor measurements using the generalized coherence gc estimate we propose to improve the performance of the gc estimate for multisensor detection using noise suppressed signal estimates obtained from time varying techniques if one of the sensors has a significantly higher signal to noise ratio snr than the other sensors then it could be preprocessed prior to the gc estimate to improve detection performance for the remaining lower snr sensors we perform this processing by estimating time varying signals of interest with nonlinear phase functions using two methods a a modified matching pursuit decomposition mmpd algorithm whose dictionary is similar in time frequency structure to the signal and b an instantaneous frequency if estimation method using highly localized time frequency representations the mmpd can yield signal estimates with lower mean square errors than the if estimation technique but at the expense of higher computational cost and memory requirements using simulations we compare the performance of the gc estimate with the significantly improved performance of the gc estimate that employs the signal estimate from the high snr sensor for the two sensor detection the estimated signal is also used with a generalized likelihood ratio test statistic to further improve performance

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

fundamental limits of linear equalizers diversity capacity and complexity linear equalizers les have been widely adopted for practical systems due to their low computational complexity however it is also well known that les provide inferior performance relative to a maximum likelihood equalizer mle or other near mles because les usually cannot collect the diversity order enabled by the transmitter and at the same time they lose mutual information more importantly unlike mle or near mles the performance of les has not been well quantified this hinders more general applications of les in wireless systems in this paper we reveal a fundamental link between a channel parameter orthogonality deficiency od of the channel matrix and the diversity and capacity of les we identify that when the od of channel matrix has an upper bound strictly less than 1 the same diversity order as that of mles is collected by les and the outage capacity loss relative to mles is also a constant over signal to noise ratio snr these results can be applied to designing a framework for hybrid equalizers furthermore by studying the statistical properties of the od and comparing the complexity of different equalizers we show that hybrid equalizers can trade off between performance and complexity by tuning the channel matrix od the theoretical analysis is corroborated by computer simulations

performance of gauss implicit runge kutta methods on separable hamiltonian systems abstract we consider implementations of a variable step size and separately constant step size fourth order symplectic gauss implict runge kutta method for the solution of hamiltonian systems we test our implementations on kepler s problem with the aim of judging the algorithms qualitative behavior and efficiency in particular we introduce compensated summation as a method of controlling roundoff accumulation also we show how the variable step size gauss implicit runge kutta method performs on kepler s problem with solution orbits of high eccentricity and compare its performance with that of two runge kutta nystrom codes finally we discuss the calculation of efficient starting values for the associated iterations measure the cost in iterations of our various predictors and comment on the strategies for terminating the iteration

on posterior distributions for signals in gaussian noise with unknown covariance matrix a bayesian approach to estimate parameters of signals embedded in complex gaussian noise with unknown color is presented the study specifically focuses on a bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems by integrating out uncertainties regarding the noise color an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited several noninformative priors for the covariance matrix such as the reference prior the jeffreys prior and modifications to this are considered some of the priors result in analytical solutions whereas others demand numerical approximations in the linear signal model connections are made between the standard adaptive maximum likelihood aml estimate and a bayesian solution using the jeffreys prior with adjustments to the jeffreys prior correspondence to the regularized solution is also established this in turn enables a formal treatment of the regularization parameter simulations indicate that significant improvements compared to the aml estimator can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior the simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged

estimation of flows in flow networks abstract let g be a directed graph with an unknown flow on each edge such that the following flow conservation constraint is maintained except for sources and sinks the sum of flows into a node equals the sum of flows going out of a node given a noisy measurement of the flow on each edge the problem we address which we call the m ost p robable f low e stimation problem mpfe is to estimate the most probable assignment of flow for every edge such that the flow conservation constraint is maintained we provide an algorithm called y mpfe for solving the mpfe problem when the measurement error is gaussian g aussian mpfe the algorithm works in o e v 2 when the underlying undirected graph of g is a 2 connected planar graph and in o e v when it is a 2 connected serial parallel graph or a tree this result is applicable to any m inimum c ost f low problem for which the cost function is e x e e 2 for edge e where e and e are constants and x e is the flow on edge e we show that for all topologies the g aussian mpfe s precision for each edge is analogous to the equivalent resistance measured in series to this edge in an electrical network built by replacing every edge with a resistor reflecting the measurement s precision on that edge

hybrid fm polynomial phase signal modeling parameter estimation and cramer rao bounds parameter estimation for a class of nonstationary signal models is addressed the class contains combination of a polynomial phase signal pps and a frequency modulated fm component of the sinusoidal or hyperbolic type such signals appear in radar and sonar applications involving moving targets with vibrating or rotating components a novel approach is proposed that allows us to decouple estimation of the fm parameters from those of the pps relying on properties of the multilag high order ambiguity function ml haf the accuracy achievable by any unbiased estimator of the hybrid fm pps parameters is investigated by means of the cramer rao lower bounds crlbs both exact and large sample approximate expressions of the bounds are derived and compared with the performance of the proposed methods based on monte carlo simulations

quasi ml period estimation from incomplete timing data given a noisy sequence of possibly shifted integer multiples of a certain period it is often of interest to accurately estimate the period with known integer regressors the problem is classical linear regression in many applications however the regressors are unknown integers and only loose bounds on the period are available examples include hop period and timing estimation wherein hops may be missed at the output of the frequency discriminator or the emitter may hop out of band pulse repetition interval pri analysis and passive rotating beam radio scanning we study several pertinent period estimators our emphasis is on a quasi maximum likelihood approach developed herein and an earlier method based on the fourier transform of a dirac delta train representation of the data surprisingly both are capable of attaining the clairvoyant crame spl acute r rao bound at moderate signal to noise ratios snrs even for short e g 10 samples we carefully address parameter identifiability issues and corroborate our findings with extensive simulations

new results on deterministic cramer rao bounds for real and complex parameters the cramer rao bounds crb is a lower bound of great interest for system analysis and design in the asymptotic region high signal to noise ratio snr and or large number of snapshots as it is simple to calculate and it is usually possible to obtain closed form expressions the first part of the paper is a generalization to complex parameters of the barankin rationale for deriving mse lower bounds that is the minimization of a norm under a set of linear constraints with the norm minimization approach the study of fisher information matrix fim singularity constrained crb and regularity conditions become straightforward corollaries of the derivation the second part provides new results useful for system analysis and design a general reparameterization inequality the equivalence between reparameterization and equality constraints and an explicit relationship between parameters unidentifiability and fim singularity

an invariance property of the generalized coherence estimate the distribution of the m channel generalized coherence estimate is shown not to depend on the statistical behavior of the data on one channel provided that the other m 1 channels contain only white gaussian noise and an channels are independent this confirms a previously published conjecture and extends the utility of the gc estimate as a detection statistic to include active as well as passive scenarios