analysis of subspace fitting and ml techniques for parameter estimation from sensor array data it is shown that the multidimensional signal subspace method termed weighted subspace fitting wsf is asymptotically efficient this results in a novel compact matrix expression for the cramer rao bound crb on the estimation error variance the asymptotic analysis of the maximum likelihood ml and wsf methods is extended to deterministic emitter signals the asymptotic properties of the estimates for this case are shown to be identical to the gaussian emitter signal case i e independent of the actual signal waveforms conclusions concerning the modeling aspect of the sensor array problem are drawn

concentrated cramer rao bound expressions we present a method to simplify the analytical computation of the cramer rao bound the method circumvents bound calculations for so called nuisance parameters under mild regularity conditions the technique which replaces expectations with almost sure limits can significantly lower the analytical complexity as compared to traditional methods the dimension of a matrix that requires computation and inversion is reduced to the length of the parameter vector of interest we give applications to random variables having densities in the exponential family for normal distributions the resulting expressions take on particularly simple closed forms

subspace fitting approaches for frequency estimation using real valued data a novel data covariance model has recently been proposed for the subspace based estimation of multiple real valued sine wave frequencies in this paper we develop weighted subspace fitting approaches using this new data model a new parameterization of the noise subspace is proposed this parameterization is used to solve the subspace fitting problem analytically an expression for the residual covariance matrix is derived this covariance matrix is further used to obtain an optimally weighted gauss markov estimator a computationally efficient suboptimal weighting is also proposed and the associated estimator is close to the gauss markov estimator in performance the suboptimal weighting strategy is quite general and can be used in other related applications the performance of the algorithms are illustrated using numerical simulations the proposed subspace fitting approach shows improved resolution performance it is also robust to additive noise

semiparametric crb and slepian bangs formulas for complex elliptically symmetric distributions the main aim of this paper is to extend the semiparametric inference methodology recently investigated for real elliptically symmetric res distributions to complex elliptically symmetric ces distributions the generalization to the complex field is of fundamental importance in all practical applications that exploit the complex representation of the acquired data moreover the ces distributions has been widely recognized as a valuable and general model to statistically describe the non gaussian behaviour of datasets originated from a wide variety of physical measurement processes the paper is divided in two parts in the first part a closed form expression of the constrained semiparametric cramer rao bound cscrb for the joint estimation of complex mean vector and complex scatter matrix of a set of ces distributed random vectors is obtained by exploiting the so called wirtinger or mathbb c mathbb r calculus the second part deals with the derivation of the semiparametric version of the slepian bangs formula in the context of the ces model specifically the proposed semiparametric slepian bangs ssb formula provides us with a useful and ready to use expression of the semiparametric fisher information matrix sfim for the estimation of a parameter vector parametrizing the complex mean and the complex scatter matrix of a ces distributed vector in the presence of unknown nuisance density generator furthermore we show how to exploit the derived ssb formula to obtain the semiparametric counterpart of the stochastic crb for direction of arrival doa estimation under a random signal model assumption simulation results are also provided to clarify the theoretical findings and to demonstrate their usefulness in common array processing applications

conditional maximum likelihood timing recovery estimators and bounds this paper is concerned with the derivation of new estimators and performance bounds for the problem of timing estimation of linearly digitally modulated signals the conditional maximum likelihood cml method is adopted in contrast to the classical low snr unconditional ml uml formulation that is systematically applied in the literature for the derivation of non data aided nda timing error detectors teds a new cml ted is derived and proved to be self noise free in contrast to the conventional low snr uml ted in addition the paper provides a derivation of the conditional cramer rao bound crb sub c which is higher less optimistic than the modified crb mcrb which is only reached by decision directed dd methods it is shown that the crb is a lower bound on the asymptotic statistical accuracy of the set of consistent estimators that are quadratic with respect to the received signal although the obtained bound is not general it applies to most nda synchronizers proposed in the literature a closed form expression of the conditional crb is obtained and numerical results confirm that the cml ted attains the new bound for moderate to high e sub s n sub o

generalized hamiltonian dynamics i formulation on t q tq the dirac bergmann generalized hamiltonian dynamics for a degenerate lagrangian system is formulated on the whitney sum t q tq of the phase space t q and the velocity space tq over the configuration space q the formulation is related to those on t q and tq some ambiguities concerning generalized dynamics that have appeared in the literature are clarified

pseudo randomly generated estimator banks a new tool for improving the threshold performance of direction finding a new powerful tool for improving the threshold performance of direction finding is considered the main idea of our approach is to reduce the number of outliers in the doa estimates using a previously proposed joint estimation strategy jes for this purpose multiple different doa estimators are calculated in a parallel manner for the same batch of data i e for a single data record employing these estimators simultaneously the jes improves the threshold performance because it removes outliers and exploits only successful estimators that are sorted out using a hypothesis testing procedure we consider an efficient modification of the jes with application to the pseudo randomly generated eigenstructure estimator banks based on secondand higher order statistics weighted music estimators based on the covariance and contracted quadricovariance matrices are chosen as appropriate underlying techniques for the second and fourth order estimator banks respectively computer simulations with uncorrelated sources verify the dramatic improvements of threshold performance as compared with the conventional second and fourth order music algorithms simulations also show that in the second order case the threshold performance of our technique is close to that of the wsf method and stochastic deterministic ml methods which are known today as the most powerful in the sense of estimation performance and at the same time as the most computationally expensive doa estimation techniques the computational cost of our algorithm is much lower than that of the wsf and ml techniques because no multidimensional optimization is required

on unique localization of multiple sources by passive sensor arrays necessary and sufficient conditions are derived for the unique localization of narrowband sources having the same known center frequency by passive sensor arrays the conditions specify the maximum number of sources that can be uniquely localized by a general array that satisfies some mild geometric constraints the conditions are expressed in terms of the number of sensors and the rank of the correlation matrix of the sources two different conditions are presented the first guarantees uniqueness for every batch of sampled data the second which is weaker guarantees uniqueness for almost every batch of sampled data with the exception of a set of batches of measure zero it is shown that a condition that is slightly weaker than the second one is also necessary

statistical performance analysis of the algebraic constant modulus algorithm this paper presents a large sample analysis of the covariance of the beamformers computed by the analytical constant modulus algorithm acma method for blindly separating constant modulus sources this can be used to predict the signal to interference plus noise ratio sinr performance of these beamformers as well as their deviation from the nonblind wiener receivers to which they asymptotically converge the analysis is based on viewing acma as a subspace fitting optimization where the subspace is spanned by the eigenvectors of a fourth order covariance matrix the theoretical performance is illustrated by numerical simulations and shows a good match

application of cumulants to array signal processing v sensitivity issues for pt iv see ibid vol 45 p 2265 76 1997 virtual esprit vespa imposes a slight constraint on the array i e only a pair of identical sensors are required we follow the classical procedure to define the sensitivity of vespa with respect to each model parameter and derive closed forms for the sensitivity formulas we justify our derivations by comparing the theoretical formulas with the results from monte carlo simulations additionally we demonstrate by simulations that vespa is more robust to model mismatches than esprit in most situations

effects of repeatability measures on results of fmri sica a study on simulated and real resting state effects spatial independent components analysis sica has become a widely applied data driven method for fmri data especially for resting state studies these sica approaches are often based on iterative estimation algorithms and there are concerns about accuracy due to noise repeatability measures such as icasso raicar and arabica have been introduced as remedies but information on their effects on estimates is limited the contribution of this study was to provide more of such information and test if the repeatability analyses are necessary we compared fastica based ordinary and repeatability approaches concerning mixing vector estimates comparisons included original fastica fsl4 melodic fastica and original and modified icasso the effects of bootstrapping and convergence threshold were evaluated the results show that there is only moderate improvement due to repeatability measures and only in the bootstrapping case bootstrapping attenuated power from time courses of resting state network related ics at frequencies higher than 0 1 hz and made subsets of low frequency oscillations more emphasized ic wise the convergence threshold did not have a significant role concerning the accuracy of estimates the performance results suggest that repeatability measures or strict converge criteria might not be needed in sica analyses of fmri data consequently the results in existing sica fmri literature are probably valid in this sense a decreased accuracy of original bootstrapping icasso was observed and corrected by using centrotype mixing estimates but the results warrant for thorough evaluations of data driven methods in general also given the fmri specific considerations further development of sica methods is strongly encouraged

asymptotic performance analysis of direction finding algorithms based on fourth order cumulants in the narrow band array processing context the use of higher order statistics has been often advocated because consistent and asymptotically unbiased parameter estimates can be obtained without it being necessary to know to model or to estimate the spatial covariance of the noise as long as it is normally distributed however experimentation shows that this noise insensitivity is traded for increased variability of the parameter estimates the main purpose of this contribution is to derive and work out closed form expressions of the asymptotic covariance of music like direction of arrival estimates based on two fourth order cumulant matrices the diagonal slice and the contracted quadricovariance this is compared with the standard covariance based music estimate establishing on a rational basis the domain of applicability of higher order statistics for doa estimation in particular the actual impact of the noise variance and of the dynamic range of the sources is investigated this asymptotic performance analysis is achieved within a general framework which we believe to be of general interest

parameter estimation of superimposed signals using the em algorithm a computationally efficient algorithm for parameter estimation of superimposed signals based on the two step iterative em estimate and maximize with an e step and an m step algorithm is developed the idea is to decompose the observed data into their signal components and then to estimate the parameters of each signal component separately the algorithm iterates back and forth using the current parameter estimates to decompose the observed data better and thus increase the likelihood of the next parameter estimates the application of the algorithm to the multipath time delay and multiple source location estimation problems is considered

music maximum likelihood and cramer rao bound further results and comparisons the problem of determining the direction of arrival of narrowband plane waves using sensor arrays and the related problem of estimating the parameters of superimposed signals from noisy measurements are studied a number of results have been recently presented by the authors on the statistical performance of the multiple signal characterization music and the maximum likelihood ml estimators for the above problems this work extends those results in several directions first it establishes that in the class of weighted music estimators the unweighted music achieves the best performance i e the minimum variance of estimation errors in large samples next it derives the covariance matrix of the ml estimator and presents detailed analytic studies of the statistical efficiency of music and ml estimators these studies include performance comparisons of music and mle with each other as well as with the ultimate performance corresponding to the cramer rao bound finally some numerical examples are given which provide a more quantitative study of performance for the problem of finding two directions with uniform linear sensor arrays

computationally efficient subspace based method for direction of arrival estimation without eigendecomposition a computationally simple direction of arrival doa estimation method with good statistical performance is attractive in many practical applications of array processing in this paper we propose a new computationally efficient subspace based method without eigendecomposition sumwe for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property the coherency of incident signals is decorrelated through subarray averaging and the null space is obtained through a linear operation of a matrix formed from the cross correlations between some sensor data where the effect of additive noise is eliminated consequently the doas can be estimated without performing eigendecomposition and there is no need to evaluate all correlations of the array data furthermore the sumwe is also suitable for the case of partly coherent or incoherent signals and it can be extended to the spatially correlated noise by choosing appropriate subarrays the statistical analysis of the sumwe is studied and the asymptotic mean squared error mse expression of the estimation error is derived the performance of the sumwe is demonstrated and the theoretical analysis is substantiated through numerical examples it is shown that the sumwe is superior in resolving closely spaced coherent signals with a small number of snapshots and at low signal to noise ratio snr and offers good estimation performance for both uncorrelated and correlated incident signals

a dynamical formalism of singular lagrangian system with higher derivatives the singular lagrangian system with higher derivatives is analyzed with the aid of the ostrogradski transformation and the dirac formalism the formulation of canonical theory is developed so that the equivalence between the lagrange formalism and the hamilton one is maintained as a practical example the acceleration dependent potentials appearing in the lagrangian of two point particles interacting gravitationally are dealt with and the equivalence between the two hamiltonians that follow from the two lagrangians which are related by the coordinate transformations is shown it is also shown when the constraints are all first class that a consistent generator of gauge transformation is constructed typical examples are given

in variance of subspace based estimators subspace based estimates i e estimates obtained by exploiting the orthogonality between a sample subspace and a parameter dependent subspace have proved useful in many applications including array processing and system identification the purpose of this paper is to complement the already available theoretical results generally obtained in specific contexts we discuss the generalization of the optimal weighted subspace fitting approach introduced by viberg 1989 in the doa estimation context we exhibit some invariance properties of optimally weighted estimate and we show the equivalence between subspace fitting and subspace matching

the potential performance gain in using spectral information in passive detection localization of wideband sources we address the problem of detecting the presence of wideband point sources and or estimating their location using data collected by an array of sensors this passive localization problem is typical to applications where the radiated signals do not carry information and are of no interest however knowledge of their waveshape or their cross spectral matrix is essential for applying optimal sub optimal detection localization algorithms in this paper we present results of a study in which we compare the optimal procedures for detection localization and their performance to suboptimal procedures that use no spectral information or only partial spectral information we show that if the number of sensors in the array is larger than the number of sources to be localized or detected then the performance gain of the optimal procedures is potentially significant mainly in conditions of small separation and or high correlation between sources the performance gain is also a function of the spectrum it is potentially higher if the sources are known to be correlated and if their spectra is not smooth if however the number of sources is smaller than the number of sensors then the role of the spectral information in improving detection localization performance becomes major only the use of spectral prior enables reliable localization of more sources than sensors

detection and estimation in sensor arrays using weighted subspace fitting the problem of signal parameter estimation of narrowband emitter signals impinging on an array of sensors is addressed a multidimensional estimation procedure that applies to arbitrary array structures and signal correlation is proposed the method is based on the recently introduced weighted subspace fitting wsf criterion and includes schemes for both detecting the number of sources and estimating the signal parameters a gauss newton type method is presented for solving the multidimensional wsf and maximum likelihood optimization problems the global and local properties of the search procedure are investigated through computer simulations most methods require knowledge of the number of coherent noncoherent signals present a scheme for consistently estimating this is proposed based on an asymptotic analysis of the wsf cost function the performance of the detection scheme is also investigated through simulations

cramer rao bounds of doa estimates for bpsk and qpsk modulated signals this paper focuses on the stochastic cramer rao bound crb of direction of arrival doa estimates for binary phase shift keying bpsk and quaternary phase shift keying qpsk modulated signals corrupted by additive circular complex gaussian noise explicit expressions of the crb for the doa parameter alone in the case of a single signal waveform are given these crbs are compared on the one hand with those obtained with different a priori knowledge and on the other hand with crbs under the noncircular and circular complex gaussian distribution and with different deterministic crbs it is shown in particular that the crbs under the noncircular respectively circular complex gaussian distribution are tight upper bounds on the crbs under the bpsk respectively qpsk distribution at very low and very high signal to noise ratios snrs only finally these results and comparisons are extended to the case of two independent bpsk or qpsk distributed sources where an explicit expression of the crb for the doa parameters alone is given for large snr

singular lagrangians with higher derivatives the hamiltonian formalism for systems with singular lagrangians of the second order is constructed a new method is proposed for obtaining the equations of motion in the phase space for theories with singular lagrangians and the connection of the lagrangian and hamiltonian descriptions is traced in detail as an example a generalisation of the relativistic point action is considered it involves both the length and curvature of the point trajectory in spacetime

improved subspace estimation for multivariate observations of high dimension the deterministic signals case we consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude in this context traditional subspace methods tend to fail because the eigenvectors of the sample correlation matrix are heavily biased with respect to the true ones it has recently been suggested that this situation where the sample size is small compared to the observation dimension can be very accurately modeled by considering the asymptotic regime where the observation dimension m and the number of snapshots n converge to at the same rate using large random matrix theory results it can be shown that traditional subspace estimates are not consistent in this asymptotic regime furthermore new consistent subspace estimate can be proposed which outperform the standard subspace methods for realistic values of m and n the work carried out so far in this area has always been based on the assumption that the observations are random independent and identically distributed in the time domain the goal of this paper is to propose new consistent subspace estimators for the case where the source signals are modelled as unknown deterministic signals in practice this allows to use the proposed approach regardless of the statistical properties of the source signals in order to construct the proposed estimators new technical results concerning the almost sure location of the eigenvalues of sample covariance matrices of information plus noise complex gaussian models are established these results are believed to be of independent interest

performance analysis of the cyclic music method of direction estimation for cyclostationary signals the cyclic music algorithm exploits the cyclostationarity exhibited by most man made communication signals to perform signal selective estimation of directions of arrival at an array of sensors in the paper the bias and mean squared error of these direction estimates are derived under the assumption that the signals are complex possibly non gaussian and cyclostationary the analytical results are shown to be excellent predictors of empirical results obtained from computer simulation of the cyclic music algorithm and are also compared with the cramer rao bound which in certain cases can be orders of magnitude less than the cramer rao bound for the directions of arrival of stationary signals

reductions of topologically massive gravity i hamiltonian analysis of second order degenerate lagrangians we present skinner rusk and hamiltonian formalisms of second order degenerate clement and sarioglu tekin lagrangians the dirac bergmann constraint algorithm is employed to obtain hamiltonian realizations of lagrangian theories the gotay nester hinds algorithm is used to investigate skinner rusk formalisms of these systems

the gaussian assumption in second order estimation problems in digital communications this paper deals with the goodness of the gaussian assumption when designing second order blind estimation methods in the context of digital communications the low and high signal to noise ratio snr asymptotic performance of the maximum likelihood estimator derived assuming gaussian transmitted symbols is compared with the performance of the optimal second order estimator which exploits the actual distribution of the discrete constellation the asymptotic study concludes that the gaussian assumption leads to the optimal second order solution if the snr is very low or if the symbols belong to a multilevel constellation such as quadrature amplitude modulation qam or amplitude phase shift keying apsk on the other hand the gaussian assumption can yield important losses at high snr if the transmitted symbols are drawn from a constant modulus constellation such as phase shift keying psk or continuous phase modulations cpm these conclusions are illustrated for the problem of direction of arrival doa estimation of multiple digitally modulated signals

asymptotic performance of second order algorithms this paper re examines the asymptotic performance analysis of second order methods for parameter estimation in a general context it provides a unifying framework to investigate the asymptotic performance of second order methods under the stochastic model assumption in which both the waveforms and noise signals are possibly temporally correlated possibly non gaussian real or complex possibly noncircular random processes thanks to a functional approach and a matrix valued reformulated central limit theorem about the sample covariance matrix the conditions under which the asymptotic covariance of a parameter estimator are dependent or independent of the distribution of the signal involved are specified finally we demonstrate the application of our general results to direction of arrival doa estimation identification of finite impulse response models sinusoidal frequency estimation for mixed spectra time series and frequency estimation of sinusoidal signal with very lowpass envelope

temporal autocorrelation in univariate linear modeling of fmri data in functional magnetic resonance imaging statistical analysis there are problems with accounting for temporal autocorrelations when assessing change within voxels techniques to date have utilized temporal filtering strategies to either shape these autocorrelations or remove them shaping or coloring attempts to negate the effects of not accurately knowing the intrinsic autocorrelations by imposing known autocorrelation via temporal filtering removing the autocorrelation or prewhitening gives the best linear unbiased estimator assuming that the autocorrelation is accurately known for single event designs the efficiency of the estimator is considerably higher for prewhitening compared with coloring however it has been suggested that sufficiently accurate estimates of the autocorrelation are currently not available to give prewhitening acceptable bias to overcome this we consider different ways to estimate the autocorrelation for use in prewhitening after high pass filtering is performed a tukey taper set to smooth the spectral density more than would normally be used in spectral density estimation performs best importantly estimation is further improved by using nonlinear spatial filtering to smooth the estimated autocorrelation but only within tissue type using this approach when prewhitening reduced bias to close to zero at probability levels as low as 1 x 10 5

parallel factor analysis in sensor array processing this paper links multiple invariance sensor array processing mi sap to parallel factor parafac analysis which is a tool rooted in psychometrics and chemometrics parafac is a common name for low rank decomposition of three and higher way arrays this link facilitates the derivation of powerful identifiability results for mi sap shows that the uniqueness of single and multiple invariance esprit stems from uniqueness of low rank decomposition of three way arrays and allows tapping on the available expertise for fitting the parafac model the results are applicable to both data domain and subspace mi sap formulations the paper also includes a constructive uniqueness proof for a special parafac model

merging sensor data from multiple measurement set ups for non stationary subspace based modal analysis processing sensor data from multiple non simultaneously recorded measurement set ups for structural analysis is often achieved by merging identification results obtained from records corresponding to different sensor pools since pole matching and eigenvector gluing might not be consistent in some cases the question arises to merge the data first and then process them globally subspace identification algorithms have proven efficient for performing output only modal analysis of mechanical systems subject to uncontrolled unmeasured and non stationary excitation the purpose of this paper is to investigate as to how subspace based output only modal analysis algorithms can be adapted to handle the multi patch measurements set up numerical results obtained on both laboratory and real application examples are reported which show the relevance and usefulness of the proposed algorithm

gaussian cramer rao bound for direction estimation of noncircular signals in unknown noise fields this paper focuses on the stochastic cramer rao bound crb on direction of arrival doa estimation accuracy for noncircular gaussian sources in the general case of an arbitrary unknown gaussian noise field parameterized by a vector of unknowns explicit closed form expressions of the stochastic crb for doa parameters alone are obtained directly from the slepian bangs formula for general noncircular complex gaussian distributions as a special case the crb under the nonuniform white noise assumption is derived our expressions can be viewed as extensions of the well known results by stoica and nehorai ottersten et al weiss and friedlander pesavento and gershman and gershman et al some properties of these crbs are proved and finally these bounds are numerically compared with the conventional crbs under the circular complex gaussian distribution for different unknown noise field models

a robustness property of doa estimators based on covariance a simple general formula is derived under a gaussian model for the asymptotic covariance of direction of arrival doa estimators based on the covariance of the sensor array data it is then established that the same formula remains valid for a wide class of statistical models for source signals hence under mild assumptions the asymptotic performance of most high resolution covariance based doa estimators is independent of the distribution of the source signals

first order equations of motion for classical mechanics a global canonical first order equation of motion is derived for any mechanical system obeying newton s second law the existence of a lagrangian is not assumed but the properties of the canonical equation are similar to those of the hamiltonian formulation the choice of map f from velocity space to phase space is not determined by the condition that the first order equation of motion be equivalent to a second order equation on configuration space and therefore is left open to be selected on the basis of other considerations the canonical equation is a covector or 1 form equation on the whitney sum t q tq and contains the second order equation condition restriction to the graph of the map f and newton s equation of motion in first order form the last is related to newton s second order equations by the consistency condition that the motions not lead off graph f in t q tq the first order equation of motion can be projected onto phase space if the map f can be inverted

input output versus output only data processing for structural identification application to in flight data analysis the problem of structural model identification under both known and unknown input excitations is addressed in flight data analysis is an important instance of that problem input output and output only eigenstructure identification methods are described and compared within two classes of methods subspace based and prediction error in particular different types of relevant projections for handling the known and unknown inputs are discussed the relevance of the methods is emphasized through numerical results obtained on real flight test data sets

explicit ziv zakai lower bound for bearing estimation the extended ziv zakai bound for vector parameters is used to develop a lower bound on the mean square error in estimating the 2 d bearing of a narrowband planewave signal using planar arrays of arbitrary geometry the bound has a simple closed form expression that is a function of the signal wavelength the signal to noise ratio snr the number of data snapshots the number of sensors in the array and the array configuration analysis of the bound suggests that there are several regions of operation and expressions for the thresholds separating the regions are provided in the asymptotic region where the number of snapshots and or snr are large estimation errors are small and the bound approaches the inverse fisher information this is the same as the asymptotic performance predicted by the local cramer rao bound for each value of bearing in the a priori performance region where the number of snapshots or snr is small estimation errors are distributed throughout the a priori parameter space and the bound approaches the a priori covariance in the transition region both small and large errors occur and the bound varies smoothly between the two extremes simulations of the maximum likelihood estimator mle demonstrate that the bound closely predicts the performance of the mle in all regions

maximum likelihood doa estimation and asymptotic cramer rao bounds for additive unknown colored noise this paper is devoted to the maximum likelihood estimation of multiple sources in the presence of unknown noise with the spatial noise covariance modeled as a function of certain unknown parameters e g an autoregressive ar model a direct and systematic way is developed to find the exact maximum likelihood ml estimates of all parameters associated with the direction finding problem including the direction of arrival doa angles spl theta the noise parameters spl alpha the signal covariance spl phi sub s and the noise power spl sigma sup 2 we show that the estimates of the linear part of the parameter set spl phi sub s and spl sigma sup 2 can be separated from the nonlinear parts spl theta and spl alpha thus the estimates of spl phi sub s and spl sigma sup 2 become explicit functions of spl theta and spl alpha this results in a significant reduction in the dimensionality of the nonlinear optimization problem asymptotic analysis is performed on the estimates of spl theta and spl alpha and compact formulas are obtained for the cramer rao bounds crb s finally a newton type algorithm is designed to solve the nonlinear optimization problem and simulations show that the asymptotic crb agrees well with the results from monte carlo trials even for small numbers of snapshots

fast and robust fixed point algorithms for independent component analysis independent component analysis ica is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible we use a combination of two different approaches for linear ica comon s information theoretic approach and the projection pursuit approach using maximum entropy approximations of differential entropy we introduce a family of new contrast functions for ica these contrast functions enable both the estimation of the whole decomposition by minimizing mutual information and estimation of individual independent components as projection pursuit directions the statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model and it is shown how to choose contrast functions that are robust and or of minimum variance finally we introduce simple fixed point algorithms for practical optimization of the contrast functions

optimal utilization of signal free samples for array processing in unknown colored noise fields many algorithms for direction of arrival doa estimation require the noise covariance matrix to be known or to possess a known structure in many cases the noise covariance is in fact estimated from separate measurements this paper addresses the combined effects of finite sample sizes both in the estimated noise covariance matrix and in the data with signals present it is assumed that a batch of signal free samples is available in addition to the signal containing samples no assumption is made on the structure of the noise covariance in this paper the asymptotic covariance of the weighted subspace fitting wsf algorithm is derived for the case in which the data are whitened using an estimated noise covariance the expression obtained suggests an optimal weighting that improves performance compared to the standard choice in addition a new method based on covariance matching is proposed both methods are asymptotically statistically efficient the cramer rao lower bound crb on the covariance of the estimate for the data model is also derived monte carlo simulations show promising small sample performance for the two new methods and confirm the asymptotic results

multiple invariance esprit a subspace fitting formulation of the esprit problem is presented that provides a framework for extending the algorithm to exploit arrays with multiple invariances in particular a multiple invariance mi esprit algorithm is developed and the asymptotic distribution of the estimates is obtained simulations are conducted to verify the analysis and to compare the performance of mi esprit with that of several other approaches the excellent quality of the mi esprit estimates is explained by recent results which state that under certain conditions subspace fitting methods of this type are asymptotically efficient

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

general asymptotic analysis of the generalized likelihood ratio test for a gaussian point source under statistical or spatial mismodeling this paper investigates the robustness of the generalized likelihood ratio test glrt for a far field gaussian point source given measurements from an array of sensors the performance of the glrt under two types of common modeling errors is investigated the first type is spatial mismodeling which relates to errors due to multipath effects or errors in the assumed number of sources i e deviation from the single point source assumption the second type is statistical mismodeling which relates to errors due to non gaussianity in either the noise or the signal i e deviation from the gaussian assumption it is shown that for some types of modeling errors the detector s performance improves and general conditions for such an improvement are found moreover for both types of errors the change in performance is analyzed and quantified this analysis shows that for a distributed source with small spatial spreading the degradation in performance is significant whereas for a constant modulus point source the performance improves simulations of various cases are shown to verify the analytical results

higher order lagrangian systems geometric structures dynamics and constraints in order to study the connections between lagrangian and hamiltonian formalisms constructed from a perhaps singular higher order lagrangian some geometric structures are constructed intermediate spaces between those of lagrangian and hamiltonian formalisms partial ostrogradski s transformations and unambiguous evolution operators connecting these spaces are intrinsically defined and some of their properties studied equations of motion constraints and arbitrary functions of lagrangian and hamiltonian formalisms are thoroughly studied in particular all the lagrangian constraints are obtained from the hamiltonian ones once the gauge transformations are taken into account the true number of degrees of freedom is obtained both in the lagrangian and hamiltonian formalisms and also in all the intermediate formalisms herein defined

a performance lower bound for quadratic timing recovery accounting for the symbol transition density the symbol transition density in a digitally modulated signal affects the performance of practical synchronization schemes designed for timing recovery this paper focuses on the derivation of simple performance limits for the estimation of the time delay of a noisy linearly modulated signal in the presence of various degrees of symbol correlation produced by the various transition densities in the symbol streams the paper develops high and low signal to noise ratio snr approximations of the so called gaussian unconditional crame spl acute r rao bound ucrb as well as general expressions that are applicable in all ranges of snr the derived bounds are valid only for the class of quadratic non data aided nda timing recovery schemes to illustrate the validity of the derived bounds they are compared with the actual performance achieved by some well known quadratic nda timing recovery schemes the impact of the symbol transition density on the classical threshold effect present in nda timing recovery schemes is also analyzed previous work on performance bounds for timing recovery from various authors is generalized and unified in this contribution

multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

multivectorial generalization of the cartan map a multivectorial generalization of the spinors to vectors cartan map is constructed with space time as a base space constructed from spinors dirac spinors and spinors pairs being particular cases onto a multivector space with two internal symmetries one of them is the fundamental space time clifford group c 1 3 and the other an isotopic space in multivectorial representation related with the more common gauge groups the algebraic properties of this map and of the operators representing observables are studied the inversion map is also presented the quaternion projection of the map is shown as are its properties and its mathematical and physical meaning the procedure presented here is compared with other spinor vector maps used in the literature

detection and estimation of doa s of signals via bayesian predictive densities a new criterion based on bayesian predictive densities and subspace decomposition is proposed for simultaneous detection of signals impinging on a sensor array and estimation of their direction of arrivals doas the solution is applicable for both coherent and noncoherent signals and an arbitrary array geometry the proposed detection criterion is strongly consistent and outperforms the mdl and aic criteria particularly for a small number of sensors and or snapshots and or low snr without increased computational complexity when the prior of the direction of arrival is a uniform distribution the bayesian estimator for the directional parameters coincides with the unconditional maximum likelihood estimator simulation results that demonstrate the performance of the proposed solution are included

on subspace methods for blind identification of single input multiple output fir systems blind identification of single input multiple output simo fir systems based on second order statistics has attracted a great deal of research effort we focus on subspace estimation procedures which exploit the structure of the range space of certain matrix valued statistics constructed by arranging in a prescribed order the covariance coefficients of the observations general subspace identifiability results are obtained based on properties of minimal polynomial bases of rational subspaces several subspace estimation procedures are then derived these estimators are all based on a weighted least square solution of an overdetermined system of linear equations an asymptotic statistical analysis of these estimators is carried out to evaluate the potential of these methods and the impact of the weighting

reductions of topologically massive gravity ii first order realizations of second order lagrangians second order degenerate clement and sarioglu tekin lagrangians are casted into forms of various first order lagrangians the structures of the iterated tangent bundle and acceleration bundle are presented as a suitable geometric framework hamiltonian analyses of these equivalent formalisms are performed by means of the dirac bergmann constraint algorithm all formulations are shown to possess only second class constraints

a geometric setting for higher order dirac bergmann theory of constraints hamilton equations for degenerate time dependent and generally higher order mechanical systems are considered and their geometric meaning is analyzed the local dynamics of constrained systems is clarified and an algorithm for finding it is presented

improved estimation performance using known linear constraints the additional information available in the form of linear or nonlinear constraints are often remain unexplored in the parameter identification problems related to linear dynamic systems our goal in this work is to explore the knowledge of the linear constraints to achieve significant improvement in the accuracy of the parameter estimates in the class of problems being addressed here the unknown boundary conditions appear as nuisance parameters in practice these nuisance parameters are eliminated from the loss function to get a variable projection optimization problem in the parameters of interest in this work we solve a constrained optimization problem instead where the additional linear constraints are imposed in the form of partially known boundary conditions in the process we show how the accuracy of the estimates is improved by taking the constraints into account the theoretical methodology is successfully applied also to numerical simulations as well as in real world experiments

array processing in correlated noise fields based on instrumental variables and subspace fitting accurate signal parameter estimation from sensor array data is a problem which has received much attention in the last decade a number of parametric estimation techniques have been proposed in the literature in general these methods require knowledge of the sensor to sensor correlation of the noise which constitutes a significant drawback this difficulty can be overcome only by introducing alternative assumptions that enable separating the signals from the noise in some applications the raw sensor outputs can be preprocessed so that the emitter signals are temporally correlated with correlation length longer than that of the noise an instrumental variable iv approach can then be used for estimating the signal parameters without knowledge of the spatial color of the noise a computationally simple iv approach has recently been proposed by the authors herein a refined technique that can give significantly better performance is derived a statistical analysis of the parameter estimates is performed enabling optimal selection of certain user specified quantities a lower bound on the attainable error variance is also presented the proposed optimal iv method is shown to attain the bound if the signals have a quasideterministic character

improved optimization for the robust and accurate linear registration and motion correction of brain images linear registration and motion correction are important components of structural and functional brain image analysis most modern methods optimize some intensity based cost function to determine the best registration to date little attention has been focused on the optimization method itself even though the success of most registration methods hinges on the quality of this optimization this paper examines the optimization process in detail and demonstrates that the commonly used multiresolution local optimization methods can and do get trapped in local minima to address this problem two approaches are taken 1 to apodize the cost function and 2 to employ a novel hybrid global local optimization method this new optimization method is specifically designed for registering whole brain images it substantially reduces the likelihood of producing misregistrations due to being trapped by local minima the increased robustness of the method compared to other commonly used methods is demonstrated by a consistency test in addition the accuracy of the registration is demonstrated by a series of experiments with motion correction these motion correction experiments also investigate how the results are affected by different cost functions and interpolation methods

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

on maximum likelihood localization of coherent signals we consider the problem of localizing multiple signal sources in the special case where all the signals are known a priori to be coherent a maximum likelihood estimator mle is constructed for this special case and its asymptotical performance is analyzed via the cramer rao bound crb it is proved that the crb for this case is identical to the crb for the case that no prior knowledge on coherency is exploited thus establishing a quite surprising result that asymptotically the localization errors are not reduced by exploiting this prior knowledge also we prove that in the coherent case the deterministic signals model and the stochastic signals model yield mle s that are asymptotically identical simulation results confirming these theoretical results are included

spatiotemporal independent component analysis of event related fmri data using skewed probability density functions we introduce two independent component analysis ica methods spatiotemporal ica stica and skew ica and demonstrate the utility of these methods in analyzing synthetic and event related fmri data first stica simultaneously maximizes statistical independence over both time and space this contrasts with conventional ica methods which maximize independence either over time only or over space only these methods often yield physically improbable solutions second skew ica is based on the assumption that images have skewed probability density functions pdfs an assumption consistent with spatially localized regions of activity in contrast conventional ica is based on the physiologically unrealistic assumption that images have symmetric pdfs we combine stica and skew ica to form skew stica and use it to analyze synthetic data and data from an event related left right visual hemifield fmri experiment results obtained with skew stica are superior to those of principal component analysis spatial ica sica temporal ica stica and skew sica we argue that skew stica works because it is based on physically realistic assumptions and that the potential of ica can only be realized if such prior knowledge is incorporated into ica methods

optimum localization of multiple sources by passive arrays the maximum likelihood ml estimator of the location of multiple sources and the corresponding cramer rao lower bound on the error covariance matrix are derived the derivation is carried out for the general case of correlated sources so that multipath propagation is included as a special case it is shown that the ml processor consists of a bank of beam formers each focused to a different source followed by a variable matrix filter that is controlled by the assumed location of the sources in the special case of uncorrelated sources and very low signal to noise ratio this processor reduces to an aggregate of ml processors for a single source with each processor matched to a different source iterative algorithms for the actual computation of the ml estimator are also presented

doa estimation of temporally and spatially correlated narrowband noncircular sources in spatially correlated white noise the main contribution of our work consists in developing for the first time a method of estimating the direction of arrival doa parameters assuming noncircular and temporally and spatially correlated signals this new approach based on a significant enhancement of the two sided instrumental variable signal subspace fitting iv ssf method outperforms its classical version in terms of lower bias and error variance moreover it will be shown that our new method is statistically more efficient than the mode method especially in the case of partly and fully coherent signals where only the extended and the classical two sided iv ssf methods are applicable we also derive an explicit expression for the stochastic cramer rao bound crb of the doa estimates from temporally and spatially correlated signals generated from noncircular sources the new crb is compared to those of circular temporally correlated and noncircular independent and identically distributed signals to show that the crb obtained assuming both noncircular sources and temporally correlated signals is lower than the crbs derived considering only one of these two assumptions this illustrates the potential gain that both noncircularity and temporal correlation provide when considered together it will also be proven that the difference between the three crbs increases with the number of snapshots however as the signal to noise ratio snr increases the crbs merge together and decrease linearly moreover at low snr values it will be shown that temporal correlation is more informative about the unknown doa parameters than noncircularity finally the crb derived assuming noncircular and temporally correlated signals depends on the noncircularity rate the circularity phase separation and the doa separation

analysis of the asymptotic relative efficiency of the music algorithm an analytical performance evaluation of the errors of the direction of arrival estimates obtained by the music algorithm for uncorrelated sources is provided explicit asymptotic formulas are derived for the means and the covariance of the estimates the covariances are then compared to the cramer rao lower bound it is shown that for a single course the music algorithm is asymptotically efficient for multiple sources the algorithm is not efficient in general however it approaches asymptotic efficiency when the snrs signal to noise ratios of all sources tend to infinity it is illustrated by several test cases that the relative efficiency of the music algorithm is nearly one under a wide range of parameter variations the analytic performance evaluation thus confirms empirical evidence to the excellent performance of the music algorithm for narrowband signals

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

bearing estimation for a distributed source of nonconstant modulus ounds and analysis the paper considers the problem of estimating the bearing of a single far field source surrounded by local scatterers using passive sensor array measurements an associated source bearing estimation problem is formulated and the crame spl acute r rao lower bound is evaluated in addition a comprehensive analysis is performed of the maximum likelihood estimates that due to mismodeling assume a constant modulus source and the degradation in performance is quantified as a function of the source s empirical variance it is shown that for a limited price in terms of mean square error the constant modulus maximum likelihood estimator can replace the optimal nonconstant modulus estimator

detection of the number of coherent signals by the mdl principle an approach is presented to the problem of detecting the number of sources impinging on a passive sensor array that is based on j rissanen s 1983 minimum description length mdl principle the approach is applicable to any type of sources including the case of sources which are fully correlated referred to as the coherent signals case two slightly different detection criteria are derived both requiring the estimation of the locations of the sources the first is tailored to the detection problem per se whereas the second is tailored to the combined detection estimation problem consistency of the two criteria is proved and their performance is demonstrated by computer simulations

probabilistic independent component analysis for functional magnetic resonance imaging we present an integrated approach to probabilistic independent component analysis ica for functional mri fmri data that allows for nonsquare mixing in the presence of gaussian noise in order to avoid overfitting we employ objective estimation of the amount of gaussian noise through bayesian analysis of the true dimensionality of the data i e the number of activation and non gaussian noise sources this enables us to carry out probabilistic modeling and achieves an asymptotically unique decomposition of the data it reduces problems of interpretation as each final independent component is now much more likely to be due to only one physical or physiological process we also describe other improvements to standard ica such as temporal prewhitening and variance normalization of timeseries the latter being particularly useful in the context of dimensionality reduction when weak activation is present we discuss the use of prior information about the spatiotemporal nature of the source processes and an alternative hypothesis testing approach for inference using gaussian mixture models the performance of our approach is illustrated and evaluated on real and artificial fmri data and compared to the spatio temporal accuracy of results obtained from classical ica and glm analyses

maximum likelihood bearing estimation with partly calibrated arrays in spatially correlated noise fields the problem of using a partly calibrated array for maximum likelihood ml bearing estimation of possibly coherent signals buried in unknown correlated noise fields is shown to admit a neat solution under fairly general conditions more exactly this paper assumes that the array contains some calibrated sensors whose number is only required to be larger than the number of signals impinging on the array and also that the noise in the calibrated sensors is uncorrelated with the noise in the other sensors these two noise vectors however may have arbitrary spatial autocovariance matrices under these assumptions the many nuisance parameters viz the elements of the signal and noise covariance matrices and the transfer and location characteristics of the uncalibrated sensors can be eliminated from the likelihood function leaving a significantly simplified concentrated likelihood whose maximum yields the ml bearing estimates the ml estimator introduced in this paper and referred to as mle is shown to be asymptotically equivalent to a recently proposed subspace based bearing estimator called uncle and rederived herein by a much simpler approach than in the original work a statistical analysis derives the asymptotic distribution of the mle and uncle estimates and proves that they are asymptotically equivalent and statistically efficient in a simulation study the mle and uncle methods are found to possess very similar finite sample properties as well as uncle is computationally more efficient it may be the preferred technique in a given application

maximum likelihood array processing for stochastic coherent sources maximum likelihood ml estimation in array signal processing for the stochastic noncoherent signal case is well documented in the literature we focus on the equally relevant case of stochastic coherent signals explicit large sample realizations are derived for the ml estimates of the noise power and the singular signal covariance matrix the asymptotic properties of the estimates are examined and some numerical examples are provided in addition we show the surprising fact that the ml estimates of the signal parameters obtained by ignoring the information that the sources are coherent coincide in large samples with the ml estimates obtained by exploiting the coherent source information thus the ml signal parameter estimator derived for the noncoherent case or its large sample realizations asymptotically achieves the lowest possible estimation error variance corresponding to the coherent cramer rao bound

symplectic reduction of higher order lagrangian systems with symmetry one can develop a symplectic reduction procedure for higher order lagrangian systems with symmetry the reconstruction procedure of the dynamics is also studied and an application spinning particle is given at the end of the work

vector sensor array processing for electromagnetic source localization the authors present a new approach for localizing electromagnetic sources using sensors where the output of each is a vector consisting of the complete six electric and magnetic field components two types of source transmissions are considered 1 single signal transmission sst and 2 dual signal transmission dst the model is given in terms of several parameters including the wave direction of arrival doa and state of polarization a compact expression is derived for the cramer rao bound crb on the estimation errors of these parameters for the multi source multi vector sensor model quality measures including mean square angular error msae and covariance of vector angular error cvae are introduced and their lower bounds are derived the advantage of using vector sensors is highlighted by explicit evaluation of the msae and cvae bounds for source localization with a single vector sensor a simple algorithm for estimating the source doa with this sensor is presented along with its statistical performance analysis

maximum likelihood direction of arrival estimation in the presence of unknown nonuniform noise we consider the problem of estimating directions of arrival doas of multiple sources observed on the background of nonuniform white noise with an arbitrary diagonal covariance matrix a new deterministic maximum likelihood ml doa estimator is derived its implementation is based on an iterative procedure which includes a stepwise concentration of the log likelihood ll function with respect to the signal and noise nuisance parameters and requires only a few iterations to converge new closed form expressions for the deterministic and stochastic direction estimation cramer rao bounds crbs are derived for the considered nonuniform model our expressions can be viewed as an extension of the well known results by stoica and nehorai 1989 1990 and weiss and friedlander 1993 to a more general noise model than the commonly used uniform one in addition these expressions extend the results obtained by matveyev et al see circuits syst signal process vol 18 p 479 87 1999 to the multiple source case comparisons with the above mentioned earlier results help to discover several interesting properties of doa estimation in the nonuniform noise case to compare the estimation performance of the proposed ml technique with the results of our crb analysis and with the performance of conventional uniform ml simulation results are presented additionally we test our technique using experimental seismic array data our simulations and experimental results both validate essential performance improvements achieved by means of the approach proposed

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

asymptotic performance analysis of doa finding algorithms with temporally correlated narrowband signals this article focuses on the asymptotic performance analysis of general direction of arrival doa finding algorithms under the stochastic model assumption in which source and noise signals are possibly non gaussian and possibly temporally correlated we prove in particular that all the covariance based doa estimators are sensitive to the temporal correlation of the sources when the noise is temporally correlated otherwise most of them are insensitive to the temporal correlation of the sources except for the toeplitzation and the augmentation techniques

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

high resolution direction finding the missing data case this paper considers the problem of estimating the direction of arrival doa of one or more signals using an array of sensors where some of the sensors fail to work before the measurement is completed methods for estimating the array output covariance matrix are discussed in particular the maximum likelihood ml estimate of this covariance matrix and its asymptotic accuracy are derived and discussed different covariance matrix estimates are used for doa estimation together with the music algorithm and with a covariance matching technique in contrast to music the covariance matching technique can utilize information on the estimation accuracy of the array covariance matrix and it is demonstrated that this yields a significant performance gain

an alternative approach to the cartan form in lagrangian field theories an operator analogous to the almost tangent structure on a tangent bundle is defined on jet bundles of a fibred manifold this operator is used to construct a cartan form the construction is unique for first order lagrangians and is also unique when restricted to higher order mechanics

an invariance property of some subspace based detection algorithms subspace fitting estimates involve multidimensional parameter estimating functions having a particular product form based on estimating functions the statistical local approach builds detection algorithms that enjoy a simple invariance property this article investigates that invariance property for the detectors built on those two concepts

unambiguous formalism for higher order lagrangian field theories the aim of this paper is to propose an unambiguous intrinsic formalism for higher order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories and implies the existence of different cartan forms and legendre transformations we propose a differential geometric setting for the dynamics of a higher order field theory based on the skinner and rusk formalism for mechanics this approach incorporates aspects of both the lagrangian and the hamiltonian description since the field equations are formulated using the lagrangian on a higher order jet bundle and the canonical multisymplectic form on its affine dual as both of these objects are uniquely defined the skinner rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions the result is that we obtain a unique and global intrinsic version of the euler lagrange equations for higher order field theories several examples illustrate our construction

unconditional maximum likelihood performance at finite number of samples and high signal to noise ratio this correspondence deals with the problem of estimating signal parameters using an array of sensors in source localization two main maximum likelihood methods have been introduced the conditional maximum likelihood method which assumes the source signals nonrandom and the unconditional maximum likelihood method which assumes the source signals random many theoretical investigations have been already conducted for the large samples statistical properties this correspondence studies the behavior of unconditional maximum likelihood at high signal to noise ratio for finite samples we first establish the equivalence between the unconditional and the conditional maximum likelihood criterions at high signal to noise ratio then thanks to this equivalence we prove the non gaussianity and the non efficiency of the unconditional maximum likelihood estimator we also rediscover the closed form expressions of the probability density function and of the variance of the estimates in the one source scenario and we derive a closed form expression of this estimator variance in the two sources scenario

min norm interpretations and consistency of music mode and ml the multiple signal characterization music approach its generalization to correlated signals known as the method of direction estimation mode and the deterministic maximum likelihood ml approach for bearing estimation in array processing are shown to be signal subspace fitting approaches in a minimum norm sense mode for example is shown to be an approach in which the array manifold is linearly estimated from principal empirical eigenvectors in a minimum weighted frobenius norm sense using the min norm interpretations a unified proof for strong consistency of the three approaches is provided for stationary and ergodic signals

doa and polarization estimation for arbitrary array configurations in this paper algorithms for joint high resolution direction of arrival doa and polarization estimation using real world arrays with imperfections are proposed both azimuth and elevation angles are considered partially correlated and coherent signals may be handled as well unlike most of the work available in the open literature we consider the case when polarization sensitive antenna arrays which may be disposed on a conformal surface may have unknown but fixed geometries be composed of elements with individual beampatterns and be subject to cross polarization as well as mounting platform effects herein recent results on steering vector modeling from noise corrupted array calibration measurements are employed this allows for incorporating all nonidealities of an antenna array into the estimation algorithms in a general and convenient manner the proposed estimators can be implemented using the fast fourier transform or polynomial rooting techniques regardless of the array configuration the stochastic cramer rao lower bound for the estimation problem at hand is established using the results from array steering vector modeling as well the proposed expression takes into account array nonidealities making such a bound tight even for real world arrays extensive simulation results are provided using several real world antenna arrays the proposed algorithms outperform conventional algorithms available in the literature and have a performance close to the stochastic cramer rao lower bound