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

a simplified canonical form algorithm with application to porous metal plasticity a canonical form for the representation of material constitutive equations within standard finite element codes has been developed which is deceptive in its simplicity substitution of different equation systems is trivial and a consistent material jacobian may be obtained automatically the process is essentially numerical and does not involve the difficult algebraic manipulation associated with more traditional approaches it is nevertheless exact because partial derivatives are derived analytically and simple because calculation of these derivatives is the only algebraic manipulation required the remainder of the process is generic in this paper the algorithm is simplified further a much more detailed and transparent explanation of the key to the method is given namely calculation of the consistent jacobian a trivial modification also extends the method to plane stress the original algorithm was validated for a simple material model the new form is used to implement the significantly more difficult modified gurson model for porous metal plasticity with hydrostatic yield dependence it is tested for single element cases involving total collapse and also used to simulate necking of a notched cylindrical bar copyright 2005 john wiley sons ltd

consistent linearization and finite element implementation of an incrementally objective canonical form return mapping algorithm for large deformation inelasticity the present paper focuses on the consistent linearization and finite element implementation of an incrementally objective canonical form return mapping algorithm a general and modular algorithmic setting suited for almost any rate constitutive equations is presented where the finite deformation consistent tangent modulus is obtained as a by product of the integration algorithm numerical examples illustrate the good performance of the proposed formulation especially for large deformation increments with noteworthy superimposed rotation where the consistent formulation converges quadratically in a reasonable number of iteration

adaptive detection of point like targets in spectrally symmetric interference we address adaptive radar detection of targets embedded in ground clutter dominated environments characterized by a symmetrically structured power spectral density at the design stage we leverage on the spectrum symmetry for the interference to come up with decision schemes capable of capitalizing the a priori information on the covariance structure to this end we prove that the detection problem at hand can be formulated in terms of real variables and then we apply design procedures relying on the glrt the rao test and the wald test specifically the estimates of the unknown parameters under the target presence hypothesis are obtained through an iterative optimization algorithm whose convergence and quality guarantee is thoroughly proved the performance analysis both on simulated and on real radar data confirms the superiority of the considered architectures over their conventional counterparts which do not take advantage of the clutter spectral symmetry

extinction criteria in stage structured population models with impulsive culling we propose stage structured population models for species whose adult members are subject to culling with a view to understanding the culling regimes that are likely to result in eradication of the species a purely time dependent model is proposed in which culling occurs at particular discrete times not necessarily equally spaced then a reaction diffusion model is proposed for a situation in which the adults can diffuse in this model the culling is continuous in time but occurs only at particular discrete points in space such a model might be appropriate for pheromone trapping of insects for both models conditions are obtained that are sufficient for species eradication

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

an npz model with state dependent delay due to size structure in juvenile zooplankton the study of planktonic ecosystems is important as they make up the bottom trophic levels of aquatic food webs we study a closed nutrient phytoplankton zooplankton npz model that includes size structure in the juvenile zooplankton the closed nature of the system allows the formulation of a conservation law of biomass that governs the system the model consists of a system of a nonlinear ordinary differential equation coupled to a partial differential equation we are able to transform this system into one of delay differential equations where the delay is of threshold type and is state dependent the system of delay differential equations can be further transformed into one with fixed delay using the different forms of the model we perform a qualitative analysis of the solutions which includes studying existence and uniqueness positivity and boundedness local and global stability and conditions for extinction key parameters that are explored are the total biomass in the system and the maturity level at which the juvenile zooplankton reach maturity numerical simulations are also performed to verify our analytical results

k means clustering based data detection and symbol timing recovery for burst mode optical receiver burst mode receivers are key components of optical transmission systems including passive optical networks and have received much attention in recent years we present new efficient methods for burst optical signal detection in burst mode data transmission using a modified k means clustering technique we also develop a data aided feedforward symbol timing recovery method based on a polynomial interpolation and maximum likelihood estimation theory a performance criterion considering the error caused by the interpolation approximation is derived for this method the proposed detection and timing recovery approaches can be implemented effectively and rapidly therefore they are very suitable for burst mode receivers we also provide some numerical examples to demonstrate the performance of the proposed methods

calculation of the fisher information matrix for multidimensional data sets data sets that are acquired in many practical systems can be described as the output of a multidimensional linear separable denominator system with gaussian measurement noise an important example is nuclear magnetic resonance nmr spectroscopy in nmr spectroscopy high accuracy parameter estimation is of central importance a classical result on the crame spl acute r rao lower bound states that the inverse of the fisher information matrix fim provides a lower bound for the covariance of any unbiased estimator of the parameter vector the calculation of the fim is therefore of central importance for an assessment of the accuracy with which parameters can be estimated it is shown how the fim can be expressed using the matrices that determine the system that generates the data set for uniformly sampled data it is shown how the fim can be expressed through the solutions of lyapunov equations the novel techniques are demonstrated with an example arising from nmr spectroscopy

efficient and modular algorithms in modeling finite inelastic deformations objective integration parameter identification and sub stepping techniques this paper presents a general algorithmic formulation for constitutive equations describing inelastic material deformation the algorithmic representation focuses on the generality and modularity which is a key aspect within the development phase of constitutive equations it is shown explicitly how to solve the incremental constitutive equations by use of objective algorithms and an implicit integration scheme applying numerical as well as analytical derivatives although it is shown that using numerical gradients is significantly slower their application is easier especially in the development phase it is also demonstrated that having the constitutive equations modeled in the general context introduced the issue of parameter identification can be tackled by the same implementation using a driver algorithm besides parameter identification the general structure is also applied to two different fe simulations first the objectivity of different integration methods will be presented considering a simple shear loading superposed by a rigid rotation using a strain rate independent material model as example in the second example it is shown for a strain rate dependent material model how the simulation of the wire drawing process can be accelerated crucially by using sub stepping techniques

bounds on maximum likelihood ratio part ii application to antenna array detection estimation with imperfect wavefront coherence the multiple hypothesis testing problem of the detection estimation of an unknown number of independent gaussian point sources is adequately addressed by likelihood ratio lr maximization over the set of admissible covariance matrix models we introduce nonasymptotic lower and upper bounds for the maximum lr since lr optimization is generally a nonconvex multiextremal problem any practical solution could now be tested against these bounds enabling a high probability of recognizing nonoptimal solutions we demonstrate that in many applications the lower bound is quite tight with approximate maximum likelihood ml techniques often unable to approach this bound the introduced lower bound analysis is shown to be very efficient in determining whether or not performance breakdown has occurred for subspace based direction of arrival doa estimation techniques we also demonstrate that by proper lr maximization we can extend the range of signal to noise ratio snr values and or number of data samples wherein accurate parameter estimates are produced yet when the snr and or sample size falls below a certain limit for a given scenario we show that ml estimation suffers from a discontinuity in the parameter estimates a phenomenon that cannot be eliminated within the ml paradigm

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

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

distributed snr estimation with power constrained signaling over gaussian multiple access channels a sensor network is used for distributed signal to noise ratio snr estimation in a single time snapshot sensors observe a signal embedded in noise and each observation is phase modulated using a constant modulus scheme and transmitted over a gaussian multiple access channel to a fusion center at the fusion center the mean and variance are estimated jointly using an asymptotically minimum variance estimator it is shown that this joint estimator decouples into simple individual estimators of the mean and the variance the constant modulus phase modulation scheme ensures a fixed transmit power robust estimation across several sensing noise distributions as well as an snr estimate that requires a single set of transmissions from the sensors to the fusion center the estimators are evaluated in terms of asymptotic variance which are then used to evaluate the performance of the snr estimator with gaussian and cauchy sensing noise distributions in the cases of total transmit power constraint as well as a per sensor power constraint for each sensing noise distribution the optimal phase transmission parameters are also determined the asymptotic relative efficiency of the estimators is evaluated it is shown that among the noise distributions considered the estimators are asymptotically efficient only when the noise distribution is gaussian simulation results corroborate analytical results

on the proper forms of bic for model order selection the bayesian information criterion bic is often presented in a form that is only valid in large samples and under a certain condition on the rate at which the fisher information matrix fim increases with the sample length this form has been improperly used previously in situations in which the conditions mentioned above do not hold in this correspondence we describe the proper forms of bic in several practically relevant cases that do not satisfy the above assumptions in particular we present a new form of bic for high signal to noise ratio snr cases the conclusion of this study is that bic remains one of the most successful existing rules for model order selection if properly used

asymptotic map criteria for model selection the two most popular model selection rules in signal processing literature have been akaike s 1974 criterion aic and rissanen s 1978 principle of minimum description length mdl these rules are similar in form in that they both consist of data and penalty terms their data terms are identical but the penalties are different mdl being more stringent toward overparameterization aic penalizes for each additional model parameter with an equal incremental amount of penalty regardless of the parameter s role in the model in most of the literature on model selection mdl appears in a form that also suggests equal penalty for every unknown parameter this mdl criterion we refer to as naive mdl in this paper we show that identical penalization for every parameter is not appropriate and that the penalty has to depend on the model structure and type of model parameters the approach to showing this is bayesian and it relies on large sample theory we derive maximum a posteriori map rules for several different families of competing models and obtain forms that are similar to aic and naive mdl for some families however we find that the derived penalties are different in those cases our extensive simulations show that the map rule outperforms aic and naive mdl

model estimation and classification via model structure determination in model estimation we often face problems with unknown parameters in the candidate models this paper proposes the model structure determination msd for model estimation with unknown parameters we start with the problem of model order selection and decompose the probability density function pdf into the information provided by the data about the model parameters and that of the model structure the factor that depends on the model parameters is approximated using a minimax procedure and the msd depends on the model structure only it is shown that the msd is equivalent to the exponentially embedded family eef for model order selection under some conditions finally we apply the msd to a classification problem where we have partial knowledge about the parameters and simulation results show that it outperforms the pseudo maximum likelihood pseudo ml rule

signal detection in complex structured para normal noise in this paper we address target detection in correlated non gaussian noise we introduce a new class of multivariate complex valued distributions that allows us to specify flexible non gaussian marginals as well as correlation between the variables while preserving circular symmetry for noise belonging to this class we study the fundamental problem of signal detection under different settings and develop the needed generalized likelihood ratio tests we also consider estimation of the noise parameters and derive the maximum likelihood formulations we evaluate the merit of our approach using numerical simulations on synthetic and real data and clearly demonstrate the advantage of using both correlations and non gaussianity

the total variance of a periodogram based spectral estimate of a stochastic process with spectral uncertainty and its application to classifier design the variance of a spectral estimate of a stochastic process is essential to the formulation and performance of a spectral classifier the overall variance of a spectral estimate originates from two sources the within class spectral uncertainty and the variance introduced in the spectral estimation procedure in this paper we derive the total variance of a periodogram based spectral estimate under some assumptions using this result we formulate a linear spectral classifier based on fisher s separability metric the classifier is used to classify two oceanographic processes ocean convection versus internal waves

line search methods in general return mapping algorithms with application to porous plasticity the present paper focuses on the application of line search methods in general return mapping algorithms two inexact line search methods and an exact line search method are investigated regarding their convergence properties within an automatic time incrementation in finite element calculations as an example for the assessment of the algorithms an elastic plastic and an elastic viscoplastic version of gurson s porous plasticity model are used in simulations of the necking of a tensile bar it is shown that larger time increments are possible and therefore a smaller number of increments are required when using line search methods the exact line search method shows the best performance concerning the required number of increments but takes more cpu time to complete the simulation the application of the inexact line search methods in general lowers the number of increments along with a reduction in the cpu time as compared with the case when no line search is used copyright 2007 john wiley sons ltd

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

a stage structured mathematical model for fish stock with harvesting in this paper we propose a mathematical model for a single species fish stock with a three stage structure juveniles small adults and large adults with two harvesting strategies for mature classes maturity and size selectivities the purpose of the work is to investigate the dynamical behavior of the model and discuss the effect of harvesting we identify the adult reproduction number mathcal r a for the model obtain the local and global stability of the trivial equilibrium when mathcal r a 1 numerical simulations are provided to investigate the influence of harvesting functions discuss the optimal harvesting rates and explore the effect of periodic coefficients on the dynamical system

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

antenna geometry conditions for mimo radar with uncoupled direction estimation we mainly focus on the role played by the antenna geometry in the direction estimation performance for a direction finding df bistatic multiple input multiple output mimo radar first we introduce the signal and the noise models which satisfy the space time separability conditions then we derive an expression of the cramer rao lower bound crlb on target parameters with the antenna locations for a single point target in the far field scenario we show that under the space time separability conditions the temporal dimension parameters range and range rate and spatial dimension parameters direction of departure dod and the direction of arrival doa are uncoupled we also show that dod and doa are uncoupled because of their spatial independence in addition we derive a set of the necessary and sufficient geometrical constraints for the uncoupled direction estimation which is based on the diagonal fisher information matrix fim we present that when both the transmit and the receive antenna location parameters have equivalent auto moment of inertia tensors of x and y axes and zero cross moment of inertia tensors of x y and z axes the bistatic mimo radar system with uncoupled direction estimation can be obtained the corresponding conditions are extended to monostatic mimo radar case for their commonness of the colocated antenna geometry in numerical example section we show several representative antenna geometries to illustrate the antenna geometry conditions derived in this paper

a canonical form return mapping algorithm for rate independent plasticity a canonical form for the representation of elastic predictor radial return plasticity algorithms is presented which is deceptive in its simplicity iterative application of the corrector is in a form used universally in the solution of ordinary differential equations and substitution of different yield functions and state variable evolution equations is trivial the consistency condition is maintained by an additional constraint equation via what is in effect a lagrange multiplier a consistent material jacobian may be obtained automatically by applying partial elimination to the same set of equations the process is numerical and requires no additional algebraic manipulation to demonstrate the validity of such a simple technique existing apparently more complex formulations are derived through the simple expedient of static condensation as a practical example of the application of the method a standard von mises plasticity model is implemented and results are presented for two standard benchmarks that test quadratic convergence for large increments copyright 2001 john wiley sons ltd

on the evaluation of the polyanskiy poor verdu converse bound for finite block length coding in awgn a tight converse bound to the channel coding rate in the finite block length regime and under additive white gaussian noise conditions was recently proposed by polyanskiy poor verdu ppv the bound is a generalization of a number of other classical results and it was also claimed to be equivalent to shannon s 1959 cone packing bound in this paper we investigate methods for a reliable numerical evaluation of the bound which is troublesome even for not too large values of the block length n by compactly expressing the polyanskiy poor and verdu ppv converse bound in terms of non central chi squared distributions and by evaluating those through an integral expression and a corresponding series expansion which exploit a method proposed by temme as a result a robust evaluation method and new insights on the bound s asymptotics as well as new approximate expressions are obtained

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

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

generalization of median root prior reconstruction penalized iterative algorithms for image reconstruction in emission tomography contain conditions on which kind of images are accepted as solutions the penalty term has commonly been a function of pairwise pixel differences in the activity in a local neighborhood such that smooth images are favored attempts to ensure better edge and detail preservation involve difficult tailoring of parameter values or the penalty function itself the previously introduced median root prior mrp favors locally monotonic images mrp preserves sharp edges while reducing locally nonmonotonic noise at the same time quantitative properties of mrp are good because differences in the neighboring pixel values are not penalized as such the median is used as an estimate for a penalty reference against which the pixel value is compared when setting the penalty in order to generalize the class of mrp type of priors the standard median was replaced by other order statistic operations the l and finite impulse response median hybrid fmh filters they allow for smoother appearance as they apply linear weighting together with robust nonlinear operations the images reconstructed using the new mrp l and mrp fmh priors are visually more conventional good quantitative properties of mrp are not significantly altered by the new priors

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

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

understanding blind deconvolution algorithms blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel is unknown recent algorithms have afforded dramatic progress yet many aspects of the problem remain challenging and hard to understand the goal of this paper is to analyze and evaluate recent blind deconvolution algorithms both theoretically and experimentally we explain the previously reported failure of the naive map approach by demonstrating that it mostly favors no blur explanations we show that using reasonable image priors a naive simulations map estimation of both latent image and blur kernel is guaranteed to fail even with infinitely large images sampled from the prior on the other hand we show that since the kernel size is often smaller than the image size a map estimation of the kernel alone is well constrained and is guaranteed to succeed to recover the true blur the plethora of recent deconvolution techniques makes an experimental evaluation on ground truth data important as a first step toward this experimental evaluation we have collected blur data with ground truth and compared recent algorithms under equal settings additionally our data demonstrate that the shift invariant blur assumption made by most algorithms is often violated

twenty one ml estimators for model selection classical approaches to determine a suitable model structure from observed input output data are based on hypothesis tests and information based criteria recently the model structure has been considered as a stochastic variable and standard estimation techniques have been proposed the resulting estimators are closely related to the aforementioned methods however it turns out that there are a number of prior choices in the problem formulation which are crucial for the estimators behavior the contribution of this paper is to clarify the role of the prior choices to examine a number of possibilities and to show which estimators are consistent this is done in a linear regression framework for autoregressive models we also investigate a novel prior assumption on stability and give the estimator for the model order and the parameters themselves

conditional model order estimation a new approach to model order selection is proposed based on the theory of sufficient statistics the method does not require any prior knowledge of the model parameters it is able to discriminate between models by basing the decision on the part of the data that is independent of the model parameters this is accomplished conceptually by transforming the data into a sufficient statistic and an ancillary statistic with respect to the model parameters it is the probability density function of the ancillary statistic when adjusted for its dimensionality that is used to estimate the order furthermore the rule is directly tied to the goal of minimizing the probability of error and does not employ any asymptotic approximations the estimator can be shown to be consistent and via computer simulation is found to outperform the minimum description length estimator

rival approaches to mathematical modelling in immunology in order to formulate quantitatively correct mathematical models of the immune system one requires an understanding of immune processes and familiarity with a range of mathematical techniques selection of an appropriate model requires a number of decisions to be made including a choice of the modelling objectives strategies and techniques and the types of model considered as candidate models the authors adopt a multidisciplinary perspective

snr estimation for nonconstant modulus constellations we propose a new technique to estimate the signal to noise ratio snr over the flat fading channel this is a nondata aided envelope based estimator that can be applied to nonconstant modulus constellations which is a feature not found in existing approaches we also analyze the performance of our estimators for both phase shift keying psk and non psk constellations by deriving their asymptotic variances and comparing with the crame spl acute r rao bounds crbs moreover we discuss how the snr estimates can be used to approximate the bit error rate ber and how the accuracy of the snr estimate is related to that of the ber estimate which justifies the necessity for the accurate estimation of snr the analytical performance is shown for both psk and non psk constellations such as 8 quadrature amplitude modulation qam and 16 qam monte carlo simulation results corroborate our analysis

location estimation of a random signal source based on correlated sensor observations the problem of location estimation of a source of random signals using a network of sensors is considered a novel maximum likelihood estimation mle based approach using copula functions is proposed the measurements received at the sensors are often spatially correlated and characterized by a multivariate distribution using the theory of copulas the joint parametric density of sensor observations joint likelihood is approximated assuming only the knowledge of the marginal likelihood functions of the sensor observations the problem of selecting the best copula function to model the joint likelihood is approached as one of model selection and a model fusion strategy is used to reduce the effect of selection bias an example involving source localization of a poisson source is presented to illustrate the proposed approach and demonstrate its performance

robust precoding with limited feedback design based on precoding mse for mu miso systems for the separation of the signals in the vector broadcast channel bc some information about the channel state is necessary at the transmitter in many cases this channel state information csi must be fed back from the receivers to the transmitter we jointly design the channel estimators and the quantizers at the receivers together with the precoder at the transmitter based on a precoder centric criterion i e the minimization of a mean square error mse metric appropriate for the precoder design this is in contrast to our previous works where the quantizer design was based on a csi mse metric i e based on the minimization of the mse between the true channel and the channel recovered by the transmitter using a feedback channel interestingly the estimators resulting from this joint formulation are independent of the used codebook the codebook entries are the employed precoders therefore each receiver feeds back the index of a set of precoders and the intersection of the sets gives the appropriate precoder since the quantizers of the different receivers have to work separately the metric for the computation of the partition cells cannot be expressed as a simple squared error depending on the quantizer output the proposed system based on a joint optimization clearly outperforms previous designs with separate optimization of feedback and precoding

successive and asymptotically efficient localization of sensor nodes in closed form accurate localization of nodes in a sensor network is a crucial step before the sensor network can be utilized for various applications this paper proposes a successive estimation method to self localize the sensor nodes using time of arrival toa measurements through the aid of a few anchor nodes whose positions are known a priori the successive nature of the proposed algorithm makes it attractive for distributed computation in a resource constrained environment the proposed technique uses subsets of toas to obtain coarse sensor node estimates depending on available computation and transmission resources the node positions are refined to improve their accuracies the solution of the proposed node localization algorithm is algebraic and closed form which simplifies computation and avoids possible local convergence or divergence problems as in the traditional iterative approaches a main benefit of the proposed algorithm is that although it is closed form and performs successive estimation of the node locations it is able to reach the cramer rao lower bound crlb accuracy under white gaussian measurement noise with sufficient snr this is confirmed by the theoretical analysis and corroborated by simulations

high snr consistent linear model order selection and subset selection high snr consistency of model order selection criteria in linear regression models has attracted a lot of attention in the signal processing community recently it is now known that exponentially embedded family versions of minimum description length etc are high snr consistent however a general framework for high snr consistency in linear regression is still missing this paper fills this gap by deriving necessary and sufficient conditions nscs for model order selection criteria in both known and unknown noise variance situations to be high snr consistent many popular model order selection criteria are proved to be high snr consistent using these nscs we also provide a convergence rate analysis to discriminate between various high snr consistent model order selection criteria a direct application of model order selection techniques to the very important subset selection problem is computationally infeasible this paper establish the high snr consistency of an existing t statistics based index ordering scheme that allows the conversion of a subset selection problem into a model order selection problem combining this index ordering with high snr consistent model order selection criteria leads to a novel subset selection procedure ssp that is numerically shown to outperform existing high snr consistent ssps

detection of gaussian constellations in mimo systems under imperfect csi this paper considers the problem of gaussian symbols detection in mimo systems in the presence of channel estimation errors under this framework we develop a computationally efficient approximations of the map detector the new detectors are based on a relaxation of the discrete nature of the digital constellation and on the channel estimation error statistics this leads to a non convex program that is solved efficiently via a hidden convexity minimization approach additionally we show that using a bayesian em approach comparable ber performance to that of the map detector can be achieved next we extend the detection scheme to the case where the noise variance is unknown we present a modified bayesian em approach with annealed gibbs sampling to perform joint noise variance estimation and symbols detection simulation results in a random mimo system show that the proposed algorithm outperforms the linear mmse receiver in terms of ber

on the numerical integration of a class of pressure dependent plasticity models an unconditionally stable algorithm for the numerical integration of elastoplastic pressure dependent constitutive relations is analysed in detail in this paper the application of the method to plane stress problems in which the out of plane strain component is not defined kinematically is discussed the tangent moduli resulting from this integration algorithm are obtained by consistent linearization of the elastoplastic constitutive equations the algorithm is applied to gurson s constitutive model some one dimensional problems are solved and comparisons with exact solutions are made the paper closes with a numerical study of the necking of an axi symmetric specimen using gurson s plasticity model to describe the constitutive behaviour of the material

principal component analysis and blind separation of sources for optical imaging of intrinsic signals the analysis of data sets from optical imaging of intrinsic signals requires the separation of signals which accurately reflect stimulated neuronal activity mapping signal from signals related to background activity here we show that blind separation of sources by extended spatial decorrelation esd is a powerful method for the extraction of the mapping signal from the total recorded signal esd is based on the assumptions i that each signal component varies smoothly across space and ii that every component has zero cross correlation functions with the other components in contrast to the standard analysis of optical imaging data the proposed method i is applicable to nonorthogonal stimulus conditions ii can remove the global signal blood vessel patterns and movement artifacts iii works without ad hoc assumptions about the data structure in the frequency domain and iv provides a confidence measure for the signals z score we first demonstrate on orientation maps from cat and ferret visual cortex that principal component analysis which acts as a preprocessing step to esd can already remove global signals from image stacks as long as data stacks for at least two not necessarily orthogonal stimulus conditions are available we then show that the full esd analysis can further reduce global signal components and finally concentrate the mapping signal within a single component both for differential image stacks and for image stacks recorded during presentation of a single stimulus

class specific feature sets in classification in this correspondence we present a new approach to the design of probabilistic classifiers that circumvents the dimensionality problem rather than working with a common high dimensional feature set the classifier is written in terms of likelihood ratios with respect to a common class using sufficient statistics chosen specifically for each class

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

analytic sequential weiss weinstein bounds in this paper we explore a sequential bayesian bound for state space models focusing on hybrid continuous and discrete random states we provide an analytic recursion for the sequential weiss weinstein sww bound for linear state space models with solutions for gaussian uniform and exponential distributions as derived as well as for a combination of these we compare the sww bound for discretized states with the corresponding bound for the continuous states the sww bound is contrasted with the sequential cramer rao bound for gaussian distributions practical issues of sww bounds are discussed and numerical simulation results provide insights into their behavior

uplink synchronization in ofdma spectrum sharing systems spectrum sharing employs dynamic allocation of frequency resources for a more efficient use of the radio spectrum despite its appealing features this technology inevitably complicates the synchronization task which must be accomplished in an environment that may involve interference this paper considers the uplink of an orthogonal frequency division multiple access ofdma based spectrum sharing system and provides solutions for estimating the frequency and timing errors of multiple unsynchronized users in doing so we exploit suitably designed training blocks and apply maximum likelihood methods after modeling the interference power on each subcarrier as a random variable with an inverse gamma distribution the resulting frequency estimator turns out to be the extension to a multiuser scenario of a scheme that has previously been proposed for single user spectrum sharing systems timing recovery is more challenging and leads to a complete search over a multidimensional domain to overcome such a difficulty two alternative approaches are proposed the first one relies on a simplifying assumption about the interference distribution in the frequency domain while the second scheme operates in an iterative fashion according to the expectation maximization algorithm

some sampling properties of common phase estimators the instantaneous phase of neural rhythms is important to many neuroscience related studies in this letter we show that the statistical sampling properties of three instantaneous phase estimators commonly employed to analyze neuroscience data share common features allowing an analytical investigation into their behavior these three phase estimators the hilbert complex morlet and discrete fourier transform are each shown to maximize the likelihood of the data assuming the observation of different neural signals this connection explored with the use of a geometric argument is used to describe the bias and variance properties of each of the phase estimators their temporal dependence and the effect of model misspecification this analysis suggests how prior knowledge about a rhythmic signal can be used to improve the accuracy of phase estimates

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

a rigorous bound on error in backward difference elastoplastic time integration abstract the finite element analysis of elastoplastic structures requires in general a time stepping procedure and in most cases the integration of the constitutive law within each time step has to be carried out by numerical integration the error associated to this numerical integration depends on the degree of non linearity of the structural response and can be used as an indicator for the adaptive definition of the time step size based on martin s and ortiz theorem on minimum total work a simple estimate of the integration error associated to a backward difference scheme for elastoplastic models is derived it is shown that the proposed estimate is a rigorous upper bound on the error in the case of assigned constant strain rate finally a simple strategy for the automatic definition of the time step size is proposed the estimator and the adaptive strategy are validated by application to problems with a perfectly plastic material model

subspace partitioning for target detection and identification detection of a given target or set of targets from observed data is a problem countered in many applications regardless of the algorithm selected detection performance can be severely degraded when the subspace defined by the target data set is singular or ill conditioned high correlations between target components and their linear combinations lead to false positives and misidentifications especially for subspace based detectors in this paper we propose a subspace partitioning scheme that allows for detection to be performed in a number of better conditioned subspaces instead of the original subspace the proposed technique is applied to raman spectroscopic data analysis through both simulation and experimental results we demonstrate the improvement in the overall detection performance when using the proposed subspace partitioning scheme in conjunction with several subspace detection methods that are commonly used in practice

model order selection rules for covariance structure classification in radar the adaptive classification of the interference covariance matrix structure for radar signal processing applications is addressed in this paper this represents a key issue because many detection architectures are synthesized assuming a specific covariance structure which may not necessarily coincide with the actual one due to the joint action of the system and environment uncertainties the considered classification problem is cast in terms of a multiple hypotheses test with some nested alternatives and the theory of model order selection mos is exploited to devise suitable decision rules several mos techniques such as the akaike takeuchi and bayesian information criteria are adopted and the corresponding merits and drawbacks are discussed at the analysis stage illustrating examples for the probability of correct model selection are presented showing the effectiveness of the proposed rules

an age structured population model with state dependent delay derivation and numerical integration c and j wu abstract we present an age structured population model that accounts for complex life cycles and competition for resources limiting the transition to maturity taking all of these into account leads to a new mathematical model with a state dependent delay that cannot be analyzed using the established framework of functional differential equations or directly simulated by standard numerical schemes for age structured populations in this paper we present the derivation of the model and a numerical scheme to integrate the equations convergence of the method is proven by verifying first consistency and then stability the difficulties involved in this proof as well as in the implementation of the scheme stem from the state dependent delay term the numerical scheme is shown to be of order 2 in the given norm and at least of order 3 in the supremum norm over the mesh point values

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

an iterated graph construction and periodic orbits of hamiltonian delay equations abstract according to the arnold conjectures and floer s proofs there are non trivial lower bounds for the number of periodic solutions of hamiltonian differential equations on a closed symplectic manifold whose symplectic form vanishes on spheres we use an iterated graph construction and lagrangian floer homology to show that these lower bounds also hold for certain hamiltonian delay equations

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

periodic solutions of homogeneous equations abstract stability conditions for periodic spiral solutions of homogeneous systems in the nonautonomous and the autonomous case are derived as well as a concept of lyapunov functions and a bendixson criterion

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

multidimensional probability density function approximations for detection classification and model order selection this paper addresses the problem of calculating the multidimensional probability density functions pdfs of statistics derived from known many to one transformations of independent random variables rvs with known distributions the statistics covered in the paper include reflection coefficients autocorrelation estimates cepstral coefficients and general linear functions of independent rvs through pdf transformation these results can be used for general pdf approximation detection classification and model order selection a model order selection example that shows significantly better performance than the akaike and mdl method is included

structured population models conservation laws and delay equations abstract the general principles by which certain structured population models or renewal equations can be reduced to ordinary differential equations or delay equations are systematically investigated with particular attention to retarded and neutral delay differential equations approriate state spaces are defined and their relations are studied as well as the positivity of the resulting evolutionary systems

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

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

adaptive image denoising by targeted databases we propose a data dependent denoising procedure to restore noisy images different from existing denoising algorithms which search for patches from either the noisy image or a generic database the new algorithm finds patches from a database that contains relevant patches we formulate the denoising problem as an optimal filter design problem and make two contributions first we determine the basis function of the denoising filter by solving a group sparsity minimization problem the optimization formulation generalizes existing denoising algorithms and offers systematic analysis of the performance improvement methods are proposed to enhance the patch search process second we determine the spectral coefficients of the denoising filter by considering a localized bayesian prior the localized prior leverages the similarity of the targeted database alleviates the intensive bayesian computation and links the new method to the classical linear minimum mean squared error estimation we demonstrate applications of the proposed method in a variety of scenarios including text images multiview images and face images experimental results show the superiority of the new algorithm over existing methods

em based recursive estimation of channel parameters recursive online expectation maximization em algorithm along with stochastic approximation is employed in this paper to estimate unknown time invariant variant parameters the impulse response of a linear system channel is modeled as an unknown deterministic vector process and as a gaussian vector process with unknown stochastic characteristics using these models which are embedded in white or colored gaussian noise different types of recursive least squares rls kalman filtering and smoothing and combined rls and kalman type algorithms are derived directly from the recursive em algorithm the estimation of unknown parameters also generates new recursive algorithms for situations such as additive colored noise modeled by an autoregressive process the recursive em algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods

frequency estimation from proper sets of correlations as a complement to the periodogram low complexity frequency estimators are of interest one such estimator is based on prony s method and rely on phase information of the auto correlations without prior knowledge of the frequency e g a given frequency interval the frequency cannot be unambiguously estimated from a single correlation only we introduce a new method of phase unwrapping using an arbitrary number more than one of correlations from this arbitrary set of correlations we propose a weighted average estimator we derive the asymptotic performance and show how the correlation lags should be properly chosen from a design aspect there is often a restriction of using a fixed number of computations in addition we therefore propose a strategy to find a proper set of correlation lags subject to a given computational complexity finally simulation results that lend support to the theoretical findings are included

class of widely linear complex kalman filters recently a class of widely linear augmented complex valued kalman filters kfs that make use of augmented complex statistics have been proposed for sequential state space estimation of the generality of complex signals this was achieved in the context of neural network training and has allowed for a unified treatment of both second order circular and noncircular signals that is both those with rotation invariant and rotation dependent distributions in this paper we revisit the augmented complex kf augmented complex extended kf and augmented complex unscented kf in a more general context and analyze their performances for different degrees of noncircularity of input and the state and measurement noises for rigor a theoretical bound for the performance advantage of widely linear kfs over their strictly linear counterparts is provided the analysis also addresses the duality with bivariate real valued kfs together with several issues of implementation simulations using both synthetic and real world proper and improper signals support the analysis

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

dynamics of a neutral delay equation for an insect population with long larval and short adult phases abstract we present a global study on the stability of the equilibria in a nonlinear autonomous neutral delay differential population model formulated by bocharov and hadeler this model may be suitable for describing the intriguing dynamics of an insect population with long larval and short adult phases such as the periodical cicada we circumvent the usual difficulties associated with the study of the stability of a nonlinear neutral delay differential model by transforming it to an appropriate non neutral nonautonomous delay differential equation with unbounded delay in the case that no juveniles give birth we establish the positivity and boundedness of solutions by ad hoc methods and global stability of the extinction and positive equilibria by the method of iteration we also show that if the time adjusted instantaneous birth rate at the time of maturation is greater than 1 then the population will grow without bound regardless of the population death process

existence and nonexistence of monotone traveling waves for the delayed fisher equation abstract in this paper a new approach based on a shooting method in a half line coupled with the technique of upper lower solution pair is used to study the existence and nonexistence of monotone waves for one form of the delayed fisher equation that does not have the quasimonotonicity property a necessary and sufficient condition is provided this new method can be extended to investigate many other nonlocal and non monotone delayed reaction diffusion equations

likelihood based modulation classification for multiple antenna receiver likelihood based algorithms for the classification of linear digital modulations are systematically investigated for a multiple receive antennas configuration existing modulation classification mc algorithms are first extended to the case of multiple receive antennas and then a critical problem is identified that the overall performance of the multiple antenna systems is dominated by the worst channel estimate of a particular antenna to address the performance degradation issue we propose a new mc algorithm by optimally combining the log likelihood functions llfs furthermore to analyze the upper bound performance of the existing and the proposed mc algorithms the exact cramer rao lower bound crlb expressions of non data aided joint estimates of amplitude phase and noise variance are derived for general rectangular quadrature amplitude modulation qam numerical results demonstrate the accuracy of the crlb expressions and verify that the results reported in the literature for quadrature phase shift keying qpsk and 16 qam are special cases of our derived expressions also it is demonstrated that the probability of correct classification of the new algorithm approaches the theoretical bounds and a substantial performance improvement is achieved compared to the existing mc algorithm

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

rigid body localization using sensor networks a framework for joint position and orientation estimation of a rigid body using range measurements is proposed we consider a setup in which a few sensors are mounted on a rigid body the absolute position of the rigid body is not known however we know how the sensors are mounted on the rigid body i e the sensor topology is known the rigid body is localized using noisy range measurements between the sensors and a few anchors nodes with known absolute positions and without using any inertial measurements we propose a least squares ls and a number of constrained ls estimators where the constrained estimators solve an optimization problem on the stiefel manifold as a benchmark we derive a unitarily constrained cramer rao bound finally the known topology of the sensors can be perturbed during fabrication or if the body is not entirely rigid to take these perturbations into account constrained total least squares estimators are also proposed

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

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

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

on the minimum mean p th error in gaussian noise channels and its applications the problem of estimating an arbitrary random vector from its observation corrupted by additive white gaussian noise where the cost function is taken to be the minimum mean p th error mmpe is considered the classical minimum mean square error mmse is a special case of the mmpe several bounds properties and applications of the mmpe are derived and discussed the optimal mmpe estimator is found for gaussian and binary input distributions properties of the mmpe as a function of the input distribution signal to noise ratio snr and order p are derived the single crossing point property scpp which provides an upper bound on the mmse and which together with the mutual information mmse relationship is a powerful tool in deriving converse proofs in multi user information theory is extended to the mmpe moreover a complementary bound to the scpp is derived as a first application of the mmpe a bound on the conditional differential entropy in terms of the mmpe is provided which then yields a generalization of the ozarow wyner lower bound on the mutual information achieved by a discrete input on a gaussian noise channel as a second application the mmpe is shown to improve on previous characterizations of the phase transition phenomenon that manifests in the limit as the length of the capacity achieving code goes to infinity as a discontinuity of the mmse as a function of snr as a final application the mmpe is used to show new bounds on the second derivative of mutual information or the first derivative of the mmse

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