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

optimal spectral feature detection for spectrum sensing at very low snr spectrum sensing is one of the enabling functionalities for cognitive radio systems to operate in the spectrum white space to protect the primary incumbent users from interference the cognitive radio is required to detect incumbent signals at very low signal to noise ratio snr in this paper we study a spectrum sensing technique based on spectral correlation for detection of television tv broadcasting signals the basic strategy is to correlate the periodogram of the received signal with the a priori known spectral features of the primary signal we show that this sensing technique is asymptotically equivalent to the likelihood ratio test lrt at very low snr but with less computational complexity that is the spectral correlation based detector is asymptotically optimal according to the neyman pearson criterion from the system design perspective we analyze the effect of the spectral features on the spectrum sensing performance through the optimization analysis we obtain useful insights on how to choose effective spectral features to achieve reliable sensing simulation results show that the proposed sensing technique can reliably detect analog and digital tv signals at snr levels as low as 20 db

noncoherent detection of coherent lightwave signals corrupted by phase noise waves are treated that modulate by either on off keying ook or binary frequency shift keying fsk and are further impaired by additive gaussian noise heterodyne detection of such a waveform produces an electronic bandpass signal which to ease demodulation in the presence of phase noise is noncoherently demodulated to extract the baseband pulse stream the treatment goes beyond previous bit error rate ber analyses of optical heterodyne receivers for ook and fsk first there is full adherence to the standard brownian motion model of phase noise also the receiver structure is formulated in such a way that the probability density function of the receiver output samples can be accurately determined this permits calculations of the additive noise and phase noise tolerable when achieving bit error rates as small as 10 sup 9 finally the study is comprehensive regarding the range of parameters explored filtering at an intermediate frequency if alone as well as if filtering plus postdetection low pass filtering is considered when the receiver parameters decision threshold for ook and if filter bandwidth are optimized large amounts of phase noise can be accommodated with only minor increases in required signal to noise ratio this is especially important when the bit rate is moderate compared to the laser linewidth

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

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

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

on the khintchine constant we present rapidly converging series for the khintchine constant and for general khintchine means of continued fractions we show that each of these constants can be cast in terms of an efficient free parameter series each series involving values of the riemann zeta function rationals and logarithms of rationals we provide an alternative polylogarithm series for the khintchine constant and indicate means to accelerate such series we discuss properties of some explicit continued fractions constructing specific fractions that have limiting geometric mean equal to the khintchine constant we report numerical evaluations of such special numbers and of various khintchine means in particular we used an optimized series and a collection of fast algorithms to evaluate the khintchine constant to more than 7000 decimal places k 1

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

preconditioned iterative methods for sparse linear algebra problems arising in circuit simulation the dc operating point of a circuit may be computed by tracking the zero curve of an associated artificial parameter homotopy homotopy algorithms exist that are globally convergent with probability one for the dc operating point problem these algorithms require computing the one dimensional kernel of the jacobian matrix of the homotopy mapping at each step along the zero curve and hence the solution of a linear system of equations at each step these linear systems are typically large highly sparse non symmetric and indefinite several iterative methods which are applicable to such problems including craig s method gmres k bicgstab qmr kacz and lsqr are applied to a suite of test problems derived from simulations of actual bipolar circuits preconditioning techniques considered include incomplete lu factorization ilu sparse submatrix ilu and ilu allowing restricted fill in bands or blocks timings and convergence statistics are given for each iterative method and preconditioner

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 superlinear convergence behaviour of gmres abstract gmres is a rather popular iterative method for the solution of nonsingular nonsymmetric linear systems it is well known that gmres often has a so called superlinear convergence behaviour i e the rate of convergence seems to improve as the iteration proceeds for the conjugate gradients method this phenomenon has been related to a modest degree of convergence of the ritz values it has been observed in experiments that for gmres too changes in the convergence behaviour seem to be related to the convergence of ritz values in this paper we prove that as soon as eigenvalues of the original operator are sufficiently well approximated by ritz values gmres from then on converges at least as fast as for a related system in which these eigenvalues and their eigenvector components are missing

reconstruction of multidimensional signals from irregular noisy samples we focus on a multidimensional field with uncorrelated spectrum and study the quality of the reconstructed signal when the field samples are irregularly spaced and affected by independent and identically distributed noise more specifically we apply linear reconstruction techniques and take the mean square error mse of the field estimate as a metric to evaluate the signal reconstruction quality we find that the mse analysis could be carried out by using the closed form expression of the eigenvalue distribution of the matrix representing the sampling system unfortunately such distribution is still unknown thus we first derive a closed form expression of the distribution moments and we find that the eigenvalue distribution tends to the marcenko pastur distribution as the field dimension goes to infinity finally by using our approach we derive a tight approximation to the mse of the reconstructed field

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

formulas for higher derivatives of the riemann zeta function the functional equation for c s is used to obtain formulas for all derivatives t k s a closed form evaluation of t k 0 is given and numerical values are computed to

sequential detection of targets in multichannel systems it is supposed that there is a multichannel sensor system which performs sequential detection of a target sequential detection is done by implementing a generalized wald s sequential probability ratio test which is based on the maximum likelihood ratio statistic and allows one to fix the false alarm rate and the rate of missed detections at specified levels we present the asymptotic performance of this sequential detection procedure and show that it is asymptotically optimal in the sense of minimizing the expected sample size when the probabilities of erroneous decisions are small we do not assume that the observations are independent and identically distributed i i d the first order asymptotic optimality result holds for general statistical models that are not confined to the restrictive i i d assumption however for i i d and quasi i i d cases where the log likelihood ratios can be represented in the form of sums of random walks and slowly changing sequences we obtain much stronger results specifically using the nonlinear renewal theory we are able to obtain both tight expressions for the error probabilities and higher order approximations for the average sample size up to a vanishing term the performance of the multichannel sequential detection algorithm is illustrated by an example of detection of a deterministic signal in correlated colored gaussian noise in this example we provide both the results of theoretical analysis and the results of a monte carlo experiment these results allow us to conclude that the use of the sequential detection algorithm substantially reduces the required resources of the system compared to the best nonsequential algorithm

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

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

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 cramer rao bound for estimating a sparse parameter vector the goal of this contribution is to characterize the best achievable mean squared error mse in estimating a sparse deterministic parameter from measurements corrupted by gaussian noise to this end an appropriate definition of bias in the sparse setting is developed and the constrained cramer rao bound crb is obtained this bound is shown to equal the crb of an estimator with knowledge of the support set for almost all feasible parameter values consequently in the unbiased case our bound is identical to the mse of the oracle estimator combined with the fact that the crb is achieved at high signal to noise ratios signal to noise ratio snrs by the maximum likelihood technique our result provides a new interpretation for the common practice of using the oracle estimator as a gold standard against which practical approaches are compared

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

sequential testing of sorted and transformed data as an efficient way to implement long glrts it is often required to detect a long weak signal in gaussian noise and frequently the exact form of that signal is parameterized but not known a bank of matched filters provides an appropriate detector however in some practical applications there are very many matched filters and most are quite long the consequent computational needs may render the classical bank of filters approach infeasibly expensive one example and our original motivation is the detection of chirp gravitational waves by an earth based interferometer in this paper we provide a computational approach to this problem via sequential testing since the sequential tests to be used are not for constant signals we develop the theory in terms of average sample number asn for this case specifically we propose two easily calculable expressions for the asn one a bound and the other an approximation the sequential approach does yield moderate computational savings but we find that by preprocessing the data using short medium fast fourier transforms ffts and an appropriate sorting of these fft outputs such that the most informative samples are entered to a sequential test first quite high numerical efficiency can be realized the idea is simple but appears to be quite successful examples are presented in which the computational load is reduced by several orders of magnitude the fft is an example of an energy agglomerating transform but of course there are many others the point here is that the transform need not match the sought signal exactly in the sense that all energy becomes confined to a single sample it is enough that the energy becomes concentrated and the more concentrated the better

special values of multiple polylogarithms historically the polylogarithm has attracted specialists and non specialists alike with its lovely evaluations much the same can be said for euler sums or multiple harmonic sums which within the past decade have arisen in combinatorics knot theory and high energy physics more recently we have been forced to consider multidimensional extensions encompassing the classical polylogarithm euler sums and the riemann zeta function here we provide a general framework within which previously isolated results can now be properly understood applying the theory developed herein we prove several previously conjectured evaluations including an intriguing conjecture of don zagier

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

numerical linear algebra aspects of globally convergent homotopy methods probability one homotopy algorithms are a class of methods for solving nonlinear systems of equations that are globally convergent with probability one these methods are theoretically powerful and if constructed and implemented properly are robust numerically stable accurate and practical the concomitant numerical linear algebra problems deal with rectangular matrices and good algorithms require a delicate balance not always achieved of accuracy robustness and efficiency in both space and time the author s experience with globally convergent homotopy algorithms is surveyed here and some of the linear algebra difficulties for dense and sparse problems are discussed

generalized log sine integrals and the mordell tornheim zeta values we introduce certain integrals of a product of the bernoulli polynomials and logarithms of milnor s multiple sine functions it is shown that all the integrals are expressed by the mordell tornheim zeta values at positive integers and that the converse is also true moreover we apply the theory of the integral to obtain various new results for the mordell tornheim zeta values

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

crandall s computation of the incomplete gamma function and the hurwitz zeta function with applications to dirichlet l series this paper extends tools developed by crandall 2012 16 to provide robust high precision methods for computation of the incomplete gamma function and the lerch transcendent we then apply these to the corresponding computation of the hurwitz zeta function and so of dirichlet l series and character polylogarithms

computational strategies for the riemann zeta function we provide a compendium of evaluation methods for the riemann zeta function presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new we concentrate primarily on practical computational issues such issues depending on the domain of the argument the desired speed of computation and the incidence of what we call value recycling c 2000 elsevier science b v all rights reserved

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

on the end performance metric estimator selection it is well known that appropriately biasing an estimator can potentially lead to a lower mean square error mse than the achievable mse within the class of unbiased estimators nevertheless the choice of an appropriate bias is generally unclear and only recently there have been attempts to systematize such a selection these systematic approaches aim at introducing mse bounds that are lower than the unbiased cramer rao bound crb for all values of the unknown parameters and at choosing biased estimators that beat the standard maximum likelihood ml and or least squares ls estimators in the finite sample case in this paper we take these approaches one step further and investigate the same problem from the aspect of an end performance metric different than the classical mse this study is motivated by recent advances in the area of system identification indicating that the optimal experiment design should be done by taking into account the end performance metric of interest and not by quantifying a quadratic distance of the unknown model from the true one

operating characteristic and average sample number of binary and multi hypothesis sequential probability ratio test the operating characteristic oc and average sample number asn of the sequential probability ratio test sprt and multi hypothesis sprt msprt are studied we consider the case where the observation sequence is independent but not necessarily identically distributed also the thresholds for the test can be time varying based on the governing equations for oc and asn of the sprt developed in our previous work a solution for the general case is proposed the governing equations for oc and asn of the msprt are also obtained numerical solutions for msprt are developed basically the solutions rely on approximating the original test by truncation that is truncating the test at some finite time k we show that under some mild conditions the approximation error diminishes as k increases at the cost of increased computation numerical examples are provided to demonstrate our solutions by comparing with monte carlo simulations simon s lower bound and dragalin s method if available for asn

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

large sparse continuation problems we study and develop efficient and versatile predictor corrector continuation methods for large sparse problems the first object is to show how special solving methods for a large sparse linear systems can be incorporated into the basic steps of a continuation method next we describe how to use a special nonlinear conjugate gradient method to perform the corrector phase it is shown how such methods can be used to detect bifurcation points and how to trace bifurcating solution branches by using local perturbations finally a numerical example involving bifurcating branches of a nonlinear eigenvalue problem is given

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

experiments with conjugate gradient algorithms for homotopy curvetracking there are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points i e with probability one the essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map hompack is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve and has separate routines for dense and sparse jacobian matrices the hompack algorithms for sparse jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernal of the homotopy jacobian matrix a required linear algebra step for homotopy curve tracking here variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with craig s preconditioned conjugate gradient method used in hompack the test problems used include actual large scale sparse structural mechanics problems

parallel adaptive gmres implementations for homotopy methods the success of probability one homotopy methods in solving large scale optimization problems and nonlinear systems of equations on parallel architectures may be significantly enhanced by the accurate parallel solution of large sparse nonsymmetric linear systems iterative solution techniques such as gmres k favor parallel implementations however their straightforward parallelization usually leads to a poor parallel performance because of global communication incurred by processors one variation of gmres k considered here is to adapt the restart value k for any given problem and use householder reflections in the orthogonalization phase coupled with graph based matrix partitioning to achieve high accuracy and reduce the communication overhead this particular gmres implementation is tailored to the uniquely stringent requirements imposed on a linear system solver by probability one homotopy algorithms occasionally unusually high accuracy ability to adapt to problems of widely varying difficulty and parallelism

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

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

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

quadratic detection of signals with drifting phase the problem of detecting a sinusoid with drifting phase in the presence of additive white gaussian noise is considered a lorentzian signal model is used in which the signal to be detected is modeled as a sinusoid whose phase is drifting with brownian motion a class of quadratic detectors that trade off coherent and noncoherent averaging of the received waveform is studied the deflection ratio is used as a performance criterion and the optimum quadratic detector structure as parametrized by the phase bandwidth is derived then the performance relative to the optimum of a class of suboptical detectors called m order noncoherent detectors is considered it is shown that the best detector in this class performs nearly as well as the optimum quadratic detector this is in sharp contrast with standard envelope detection whose performance is shown to degrade severely in the presence of phase drift simulated detection probabilities that verify this performance disparity are also presented

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

sequential detection of almost harmonic signals to detect a purely harmonic signal it is difficult to beat a fast fourier transform fft however when the signal is very long and weak parker and white 1999 have shown that a sequential probability ratio test sprt operating on magnitude square fft data is far more efficient indeed both from a numerical error perspective and in terms of robustness against a deviation from a precisely tonal signal the block fft sprt idea is very appealing here the approach is extended to the case that the frequency is unknown and expressions are developed for performance both in terms of detection and of sample number the approach is applicable to a large number of practical problems but particular attention is paid to the continuous gravitational wave gw example the computational savings as compared with a fixed test vary as a function of signal strength block length bandwidth and operating point however gains of a factor of two are easy that these gains are not more exciting relates mostly to the underlying fft structure although many sprts end early it is difficult to take advantage of that with an efficient fft algorithm however the progressive reduction of the number of working sprts implies a substantial reduction of the ensemble of the candidate frequencies with time which is an appealing feature particularly in the gw case

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

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

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

quadratic and cubic harmonic number sums abstract this paper develops an approach to evaluation of euler related sums the approach is based on simple integral computations by the approach we can obtain some closed form representations of sums of quadratic and cubic harmonic numbers and reciprocal binomial coefficients the given representations are new

sequential detection of markov targets with trajectory estimation the problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered assuming a markov evolution of the system in particular the pair signal observation forms a hidden markov model hmm a sequential procedure is proposed wherein the detection part is a sequential probability ratio test sprt and the estimation part relies upon a maximum a posteriori probability map criterion gated by the detection stage the parameter to be estimated is the trajectory of the state evolution of the system itself a thorough analysis of the asymptotic behavior of the test in this new scenario is given and sufficient conditions for its asymptotic optimality are stated i e for almost sure minimization of the stopping time and for first order minimization of any moment of its distribution an application to radar surveillance problems is also examined

lattice sums arising from the poisson equation in recent times attention has been directed to the problem of solving the poisson equation either in engineering scenarios computational or in regard to crystal structure theoretical herein we study a class of lattice sums that amount to poisson solutions namely the n dimensional forms by virtue of striking connections with jacobi function values we are able to develop new closed forms for certain values of the coordinates rk and extend such analysis to similar lattice sums a primary result is that for rational x y the natural potential 2 x y is where a is an algebraic number various extensions and explicit evaluations are given such work is made possible by number theoretical analysis symbolic computation and experimental mathematics including extensive numerical computations using up to 20 000 digit arithmetic

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

parallel integer relation detection techniques and applications let x1 x2 xn be a vector of real numbers an integer relation algorithm is a computational scheme to find the n integers ak if they exist such that a1x1 a2x2 anxn 0 in the past few years integer relation algorithms have been utilized to discover new results in mathematics and physics existing programs for this purpose require very large amounts of computer time due in part to the requirement for multiprecision arithmetic yet are poorly suited for parallel processing this paper presents a new integer relation algorithm designed for parallel computer systems but as a bonus it also gives superior results on single processor systems single and multi level implementations of this algorithm are described together with performance results on a parallel computer system several applications of these programs are discussed including some new results in number theory quantum field theory and chaos theory

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

computation and theory of extended mordell tornheim witten sums we consider some fundamental generalized mordell tornheim witten mtw zeta function values along with their derivatives and explore connections with multiple zeta values mzvs to achieve this we make use of symbolic integration high precision numerical integration and some interesting combinatorics and special function theory our original motivation was to represent unresolved constructs such as eulerian log gamma integrals we are able to resolve all such integrals in terms of a mtw basis we also present for a substantial subset of mtw values explicit closed form expressions in the process we signicantly extend methods for high precision numerical computation of polylogarithms and their derivatives with respect to order

the riemann zeta function and its derivatives formulas for higher derivatives of the riemann zeta function are developed from ramanujan s theory of the constant of series by using the euler maclaurin summation methods formulas for zeta n s zeta n 1 s and zeta n 0 are obtained additional formulas involving the stieltjes constants are also derived analytical expression for error bounds is given in each case the formulas permit accurate derivative evaluation and the error bounds are shown to be realistic a table of zeta prime s is presented to 20 significant figures for s 20 0 1 20 for rational arguments zeta 1 k zeta prime 1 k are given for k 10 1 10 the first ten zeros of zeta prime s are also tabulated because the stieltjes constants appear in many formulas the constants were evaluated freshly for this work formulas for the gamma n are derived with new error bounds and a tabulation of the constants is given from n 0 to 100

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