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

multisource self calibration for sensor arrays calibration of a sensor array is more involved if the antennas have direction dependent gains and multiple calibrator sources are simultaneously present we study this case for a sensor array with arbitrary geometry but identical elements i e elements with the same direction dependent gain pattern a weighted alternating least squares wals algorithm is derived that iteratively solves for the direction independent complex gains of the array elements their noise powers and their gains in the direction of the calibrator sources an extension of the problem is the case where the apparent calibrator source locations are unknown e g due to refractive propagation paths for this case the wals method is supplemented with weighted subspace fitting wsf direction finding techniques using monte carlo simulations we demonstrate that both methods are asymptotically statistically efficient and converge within two iterations even in cases of low snr

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

detection and localization of multiple sources in noise with unknown covariance the authors present a novel technique for the detection and localization of multiple sources in the presence of noise with unknown and arbitrary covariance the technique is applicable to coherent and noncoherent signals and to arbitrary array geometry and is based on rissanen s minimum description length mdl principle 1989 for model selection its computational load is comparable to that of analogous techniques for white noise simulation results demonstrating the performance of this technique are included

a model selection rule for sinusoids in white gaussian noise the model selection problem for sinusoidal signals has often been addressed by employing the akaike 1974 information criterion aic and the minimum description length principle mdl the popularity of these criteria partly stems from the intrinsically simple means by which they can be implemented they can however produce misleading results if they are not carefully used the aic and mdl have a common form in that they comprise two terms a data term and a penalty term the data term quantifies the residuals of the model and the penalty term reflects the desideratum of parsimony while the data terms of the aic and mdl are identical the penalty terms are different in most of the literature the aic and mdl penalties are however both obtained by apportioning an equal weight to each additional unknown parameter be it phase amplitude or frequency by contrast we demonstrate that the penalties associated with the amplitude and phase parameters should be weighted differently than the penalty attached to the frequencies following the bayesian methodology we derive a model selection criterion for sinusoidal signals in gaussian noise which also contains the log likelihood and the penalty terms the simulation results disclose remarkable improvement in our selection rule over the commonly used mdl and aic

detection of coherent signals using weighted subspace smoothing a new approach to detecting the number of coherent signals incident upon a uniformly spaced linear array is presented the approach combines a modified spatial smoothing scheme and a modified mdl criterion the modified spatial smoothing scheme referred to as weighted subspace smoothing is actually a generalization of the post smoothing approach proposed by krim and proakis in 1994 it is shown that the noise eigenvalues obtained with weighted subspace smoothing are more accurate than those obtained with the original spatial smoothing we thus attempt to improve the detection performance using these more accurate eigenvalues a novel modification of the minimum description length mdl criterion is proposed to accomplish this computer simulations are presented to study the performance improvement of this new approach

nonparametric detection of signals by information theoretic criteria performance analysis and an improved estimator determining the number of sources from observed data is a fundamental problem in many scientific fields in this paper we consider the nonparametric setting and focus on the detection performance of two popular estimators based on information theoretic criteria the akaike information criterion aic and minimum description length mdl we present three contributions on this subject first we derive a new expression for the detection performance of the mdl estimator which exhibits a much closer fit to simulations in comparison to previous formulas second we present a random matrix theory viewpoint of the performance of the aic estimator including approximate analytical formulas for its overestimation probability finally we show that a small increase in the penalty term of aic leads to an estimator with a very good detection performance and a negligible overestimation probability

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

localizing thin metallic cylinders by a 2 5 d linear distributional approach experimental results the problem of detecting and localizing thin metallic scatterers from electromagnetic scattered field measurements is addressed the scatterers are assumed to be infinitely long and a 2 5 dimensional mathematical model is adopted according to the distributional approach the problem is cast as the inversion of a linear integral operator acting on 6 distributions whose supports are representative of the scatterers locations in this paper we present the experimental validation of such an approach to this end we perform the reconstructions by exploiting experimental scattered field data collected in controlled conditions at the electromagnetic diagnostics laboratory of the second university of naples the experiments are conducted in an anechoic chamber where the scatterers are embedded in a homogenous and lossless background medium the multistatic single view multifrequency and the multistatic multiview multifrequency configurations are both considered

simple and efficient nonparametric method for estimating the number of signals without eigendecomposition inspired by the computational simplicity and numerical stability of qr decomposition a nonparametric method for estimating the number of signals without eigendecomposition mense is proposed for the coherent narrowband signals impinging on a uniform linear array ula by exploiting the array geometry and its shift invariance property to decorrelate the coherency of signals through subarray averaging the number of signals is revealed in the rank of the qr upper trapezoidal factor of the autoproduct of a combined hankel matrix formed from the cross correlations between some sensor data since the infection of additive noise is defused signal detection capability is improved a new detection criterion is then formulated in terms of the row elements of the qr upper triangular factor when finite array data are available and the number of signals is determined as a value of the running index for which this ratio criterion is maximized where the qr decomposition with column pivoting is also used to improve detection performance the statistical analysis clarifies that the mense detection criterion is asymptotically consistent furthermore the proposed mense algorithm is robust against the array uncertainties including sensor gain and phase errors and mutual coupling and against the deviations from the spatial homogeneity of noise model the effectiveness of the mense is verified through numerical examples and the simulation results show that the mense is superior in detecting closely spaced signals with a small number of snapshots and or at relatively low signal to noise ratio snr

nonlinear boundary stabilization for a transmission problem in elasticity in this article we study the uniform stability for the solutions of a transmission problem in non homogeneous anisotropic elasticity we consider a boundary dissipation given for a frictional damping and explicit rates of decay are obtained

inverse observability estimates for second order hyperbolic equations with variable coefficients abstract we consider a general second order hyperbolic equation defined on an open bounded domain r n with variable coefficients in both the elliptic principal part and in the first order terms as well at first no boundary conditions b c are imposed our main result theorem 3 5 is a reconstruction or inverse estimate for solutions w under checkable conditions on the coefficients of the principal part the h1 l2 energy at time t t or at time t 0 is dominated by the l2 norms of the boundary traces w a and wt modulo an interior lower order term once homogeneous b c are imposed our results yield under a uniqueness theorem needed to absorb the lower order term continuous observability estimates for both the dirichlet and neumann case with an explicit sharp observability time hence by duality exact controllability results moreover no artificial geometrical conditions are imposed on the controlled part of the boundary in the neumann case in contrast with existing literature the first step of our method employs a riemann geometry approach to reduce the original variable coefficient principal part problem in r n to a problem on an appropriate riemann manifold determined by the coefficients of the principal part where the principal part is the laplacian in our second step we employ explicit carleman estimates at the differential level to take care of the variable first order energy level terms in our third step we employ micro local analysis yielding a sharp trace estimate to remove artificial geometrical conditions on the controlled part of the boundary in the neumann case

observability inequalities for the transmission of shallow shells in this paper we establish some observability inequalities from both boundary and distributed controls for the transmission of shallow shell with a middle surface of any shape in particular if only the boundary controls are allowed we obtain the condition for the observability inequality on young s modulus and poisson s coefficient of the material which is similar as those in the case of wave and plate equations

noniterative analytical formula for inverse scattering of multiply scattering point targets this paper derives in the exact framework of multiple scattering theory for point targets a noniterative analytical formula for the nonlinear inversion of the target scattering strengths from the scattering or response matrix that can be applied after the target positions have been estimated in a previous step via e g time reversal multiple signal classification or another approach the new formula provides a noniterative analytical alternative to the iterative numerical solution approach for the same problem presented in a recent paper a j devaney e a marengo and f k gruber time reversal based imaging and inverse scattering of multiply scattering point targets j acoust soc am 118 3129 3138 2005 the two methods noniterative versus iterative are comparatively investigated with two numerical examples

stabilization and controllability for the transmission wave equation we address the problem of control of the transmission wave equation in particular we consider the case where due to total internal reflection of waves at the interface the system may not be controlled from exterior boundaries we show that such a system can be controlled by introducing both boundary control along the exterior boundary and distributed control near the transmission boundary and give a physical explanation why the additional control near the transmission boundary might be needed for some domains

time reversal imaging for sensor networks with optimal compensation in time using extensive numerical simulations several distributed sensor imaging algorithms for localized damage in a structure are analyzed given a configuration of ultrasonic transducers a full response matrix for the healthy structure is assumed known it is used as a basis for comparison with the response matrix that is recorded when there is damage numerical simulations are done with the wave equation in two dimensions the healthy structure contains many scatterers the aim is to image point like defects with several regularly distributed sensors because of the complexity of the environment the recorded traces have a lot of delay spread and travel time migration does not work so well instead the traces are back propagated numerically assuming that there is some knowledge of the background since the time at which the back propagated field will focus on the defects is unknown the shannon entropy or the bounded variation norm of the image is computed and the time where it is minimal is picked this imaging method performs well because it produces a tight image near the location of the defects at the time of refocusing when there are several defects the singular value decomposition of the response matrix is also carried out

controllability for transmission wave plate equations on riemannian manifolds abstract in this paper we consider controllability for transmission system of coupling wave equations with euler bernoulli equations on riemannian manifolds we show that such a system is exactly controllable by boundary controls only along the exterior boundary which means there is no control on the interface of the transmission system our proofs rely on the hilbert uniqueness method hum and geometric multiplier method

a relationship between time reversal imaging and maximum likelihood scattering estimation time reversal methods have attracted increasing interest recently the so called computational time reversal approach creates an image of the illuminated scene by computing the back propagated field and is useful for detecting and estimating targets in the scene in shi and nehorai ldquomaximum likelihood estimation of point scatterers for computational time reversal imaging rdquo communications in information and systems vol 5 no 2 pp 227 256 2005 we estimated point scatterers by maximum likelihood estimate mle using the born approximated physical model as well as the foldy lax model in this correspondence we further find an explicit relationship between energy based basic time reversal imaging and the mle approach the time reversal imaging function differs by only a scaling factor from the likelihood imaging function using the estimated scattering potential when a single scatterer model is employed furthermore this scaling factor is a function of the imaging position only we show that as a result time reversal imaging has a near far problem that tends to produce a weaker image for areas further away from the imaging arrays whereas the mle based image is more balanced experimental results confirm this conclusion

back propagation and correlation imaging using phase space gaussian beams processing we present a beam based imaging scheme for targets in homogeneous medium whereby the fields of the source and receiver arrays are expanded using special phase space bases of collimated beam fields thus converting the physical data into a beam domain data describing the scattering amplitudes seen synthetically by the receiver beams due to excitation by the source beams the image is then formed by correlating the backpropagated beam data with the incident beams the formulation utilizes the ultra wideband phase space beam summation method where the beam bases consist of gaussian beams that emerge from a discrete set of points and directions in the source and the receiver domains an important feature of this method is that the beam sets are frequency independent and hence are calculated once and then used for all frequencies a closed form expression for the data transformation matrix from the physical domain to the beam domain is derived leading to sparse beam domain data the beam approach enables local imaging of any sub domain of interest by retaining only the subset of source and receiver beams that pass through that domain thus reducing the overall computation complexity the method properties are explored via numerical simulations in a noisy environment

generalized bayesian information criterion for source enumeration in array processing we investigate the problem of enumerating source signals impinging on an array of sensors in an information theoretic framework the conventional bayesian information criterion bic does not yield satisfactory performance for this problem because it only considers the density of the observations in order to remedy the limitations of the bic we propose a generalized bayesian information criterion gbic rule by incorporating the density of the sample eigenvalues or corresponding statistics such a density contains extra information and complements the density of the observations in constructing the gbic as a result two different expressions for the gbic are suggested simulation results validate the superiority of the proposed gbic over the conventional bic in terms of correctly determining the number of sources while their computational costs are comparable

a universal prior for integers and estimation by minimum description length of the number of bits required to write down the observed data has been reformulated to extend the classical maximum likelihood principle the principle permits estimation of the number of the parameters in statistical models in addition to their values and even of the way the parameters appear in the models i e of the model structures the principle rests on a new way to interpret and construct a universal prior distribution for the integers which makes sense even when the parameter is an individual object truncated realvalued parameters are converted to integers by dividing them by their precision and their prior is determined from the universal prior for the integers by optimizing the precision 1 introduction in this paper we study estimation based upon the principle of minimizing the total number of binary digits required to rewrite the observed data when each observation is given with some precision instead of attempting at an absolutely shortest description which would be futile we look for the optimum relative to a class of parametrically given distributions this minimum description length mdl principle which we introduced in a less comprehensive form in 25 turns out to degenerate to the more familiar maximum likelihood ml principle in case the number of parameters in the models is fixed so that the description length of the parameters themselves can be ignored in another extreme case where the parameters determine the data it similarly degenerates to jaynes s principle of maximum entropy 14 but the main power of the new criterion is that it permits estimates of the entire model its parameters their number and even the way the parameters appear in the model i e the model structure hence there will be no need to supplement the estimated parameters with a separate hypothesis test to decide whether a model is adequately parameterized or perhaps over parameterized

analysis of the time reversal operator for a scatterer undergoing small displacements the method of the time reversal operator decomposition is usually employed to detect and characterize static targets using the invariants of the time reversal operator this paper presents a theoretical and experimental investigation into the impact of small displacements of the target on these invariants to find these invariants the time reversal operator is built from the multistatic response matrix and then diagonalized two methods of recording the multistatic response matrix while the target is moving are studied acquisition either element by element or column by column it is demonstrated that the target displacement generates new significant eigenvalues using a perturbation theory the analytical expressions of the eigenvalues of the time reversal operator for both acquisition methods are derived we show that the distribution of the new eigenvalues strongly depends on these two methods it is also found that for the column by column acquisition the second eigenvector is simply linked to the scatterer displacements at last the implications on the maximum likelihood and multiple signal classification detection are also discussed the theoretical results are in good agreement with numerical and 3 4 mhz ultrasonic experiments

boundary exact controllability of interface problems with singularities ii addition of internal controls we prove the exact controllability by boundary action of hyperbolic interface problems with singularities the two proposed methods consist of acting by a classical boundary control whose support does not contain a neighborhood of the singular points and adding internal controls located near these singular points see m t niane and o seck c r acad sci paris ser i 318 1994 pp 945 948 a heibig and m moussaoui disc cont dynam syst 2 1996 pp 367 386 m t niane and o seck c r acad sci paris ser i 316 1993 pp 695 700 where such a method was introduced

stochastic maximum likelihood estimation under misspecified numbersof signals the maximum likelihood ml approach for estimating direction of arrival doa plays an important role in array processing its consistency and efficiency have been well established in the literature a common assumption is that the number of signals is known in many applications this information is not available and needs to be estimated however the estimated number of signals does not always coincide with the true number of signals thus it is crucial to know whether the ml estimator provides any relevant information about doa parameters under a misspecified number of signals in a previous study by this author ml estimation under misspecified number of signals presented at the thirty ninth asilomar conference on signals systems and computers pacific grove ca november 2005 he focused on the deterministic signal model and showed that the ml estimator under a misspecified number of signals converges to a well defined limit under mild conditions the ml estimator converges to the true parameters in the current correspondence we extend those results to the stochastic signal model and validate our analysis by simulations

two numerical methods for recovering small inclusions from the scattering amplitude at a fixed frequency in this paper two noniterative algorithms for locating small electromagnetic inclusions from the scattering amplitude at a fixed frequency are developed in particular a variety of numerical results is presented to highlight their potential and their limitations

on the observability inequalities for exact controllability of wave equations with variable coefficients this paper deals with boundary exact controllability for the dynamics governed by the wave equation with nonconstant coefficients in the principal part subject to dirichlet or neumann boundary controls the observability inequalities are established by the riemannian geometry method under some geometric condition for the dirichlet problem and for the neumann problem respectively next a number of nontrivial examples are presented to verify the observability inequality in particular a counterexample is given without boundary exact controllability where the control is exerted on the whole boundary

stabilization of euler bernoulli plate equation with variable coefficients by nonlinear boundary feedback abstract the aim of this paper is to investigate the uniform stabilization of euler bernoulli plate equation with variable coefficients in the principle part subject to nonlinear boundary feedback laws the exponential or rational energy decay rate is obtained by the multiplier method and the riemannian geometry method

detection of the number of signals using the benjamini hochberg procedure this paper presents a novel approach to detect multiple signals embedded in noisy observations from a sensor array we formulate the detection problem as a multiple hypothesis test to control the global level of the multiple test we apply the false discovery rate fdr criterion proposed by benjamini and hochberg compared to the classical familywise error rate fwe criterion the fdr controling procedure leads to a significant gain in power for large size problems in addition we apply the bootstrap technique to estimate the observed significance level required by the fdr controling procedure simulations show that the fdr controling procedure always provides higher probability of correct detection than the fwe controling procedure furthermore the reliability of the proposed test procedure is not affected by the gain in power of the test

multiple source location the signal subspace approach the multiple source location problem is solved for a general array geometry using the principal of least squares modeling the incident wavefields may be a mixture of coherent and noncoherent sources that are broadband and or narrowband furthermore the wavefields may be plane waves and or spherical waves an effective algorithmic approach is developed for solving the multiple source location problem in the signal and covariance domains in each domain it is necessary to represent a set of vectors as a linear combination of array steering vectors using this property a generic descent algorithmic approach is developed for estimating the wavefield directions of arrival the success of such iterative approaches is critically dependent on the generation of good estimates to initialize the algorithm an effective initialization procedure is developed for this purpose direction of arrival estimates which arise from the proposed procedure are empirically found to be unbiased and low variance

an information theoretic approach to source enumeration in array signal processing in this paper a new information theoretic algorithm is proposed for signal enumeration in array processing the approach is based on predictive description length pdl that is defined as the length of a predictive code for the set of observations we assume that several models with each model representing a certain number of sources will compete the pdl criterion is computed for the candidate models and is minimized over all models to select the best model and to determine the number of signals in the proposed method the correlation matrix is decomposed into two orthogonal components in the signal and noise subspaces the maximum likelihood ml estimates of the angles of arrival are used to find the projection of the sample correlation matrix onto the signal and noise subspaces the summation of the ml estimates of these matrices is the ml estimate of the correlation matrix this method can detect both coherent and noncoherent signals the proposed method can be used online and can be applied to time varying systems and target tracking

source enumeration for high resolution array processing using improved gerschgorin radii without eigendecomposition accurate detection of sources with low complexity is of considerable interest in practical applications of high resolution array processing this paper addresses a new computationally efficient method for source enumeration by using enhanced gerschgorin radii without eigendecompositofion the proposed method can calculate the gerschgorin radii in a more efficient manner in which the additive background noise can be efficiently suppressed and the computational complexity can be considerably reduced therefore the method is more accurate and computationally attractive furthermore the method does not rely on the eigenvalues of a covariance matrix or the signal noise power making it robust against deviations from the assumption of spatially white noise model numerical results are presented to demonstrate the performance of the method

experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix the d o r t method french acronym for decomposition of the time reversal operator is an active remote sensing technique using arrays of antennas for the detection and localization of scatterers prada et al j acoust soc am 99 2067 2076 1996 the analogy between the time reversal operator and the covariance matrix used for classical sources separation in passive remote sensing bienvenu et al ieee trans assp 31 1235 1247 1983 is established then an experiment of subwavelength detection and localization of point like scatterers with a linear array of transducers is presented using classical estimators in reception like maximum likelihood and multiple signal characterization music two point like scatterers separated by 3 and placed at 100 from the array of transducers are resolved in these experiments the role of multiple scattering and the existence of additional eigenvectors associated with dipolar and monopolar radiation of each scatterer is discussed

observability inequalities for shallow shells we consider some observability inequalities from boundary for a general shallow shell with a middle surface of any shape at first an estimate is established by the geometric multiplier method in the case that no boundary conditions are imposed under some checkable geometric conditions then our results yield continuous observability estimates for two kinds of boundary conditions which have a physical meaning with an explicit observability time and hence by duality exact controllability results

localized defects in a cellular automaton model for traffic flow with phase separation the impact of a localized defect in a cellular automaton model for traffic flow which exhibits metastable states and phase separation is studied the defect is implemented by locally increasing the deceleration probability depending on the magnitude three phases can be identified in the system one of them shows the characteristics of stop and go traffic which can not be found in the model without lattice defect from a physical point of view the model describes the competition between two mechanisms of phase separation

time reversal imaging with multiple signal classification considering multiple scattering between the targets the time reversal imaging with multiple signal classification method for the location of point targets developed within the framework of the born approximation in lehman and devaney transmission mode time reversal super resolution imaging j acoust soc am 113 2742 2753 2003 is generalized to incorporate multiple scattering between the targets it is shown how the same method can be used in the location of point targets even if there is multiple scattering between them on the other hand both the conventional images and the calculated values of the target scattering amplitudes are scattering model dependent

detection of the number of signals a predicted eigen threshold approach a novel method for detecting the number of signals incident upon an array of sensors is described the method is based on finding upper thresholds for the observed eigenvalues of the correlation matrix of the array output the asymptotic normality of the multifold eigenvalue estimate is used to derive a prediction formula for the thresholds due to the fact that the detection error of the method can be controlled by a parameter t the performance of the method is superior to the mdl minimum description length under low snr signal to noise ratio and superior to an aic akaike information criterion under high snr the distribution functions of both missing and false alarm errors are evaluated so that the performance of the method can be analyzed and so that t can be chosen simulation results are presented to confirm the analysis

spatio temporal invariants of the time reversal operator the decomposition of the time reversal operator known by the french acronym dort is a technique to extract point scatterers monochromatic green s functions from a medium it is used to detect locate and focus on scatterers in various domains such as underwater acoustics medical ultrasound and nondestructive evaluation a limitation of the method arises from its single frequency nature when the signals used in acoustics are often broadband reconstruction of the broadband green s functions from the single frequency green s functions can be very difficult when numerous scatterers are present in the medium moreover the method does not take advantage of the axial resolution associated with broadband signals time domain methods are investigated here as an answer to these problems it is shown that the time reversal operator in the time domain takes the form of a tensor the properties of the invariants are discussed it is shown they do not have all the expected properties another method is proposed that requires a priori information on the medium

stabilization of transmission coupled wave and euler bernoulli equations on riemannian manifolds by nonlinear feedbacks abstract we consider the transmission system of coupling wave equations with euler bernoulli equations on riemannian manifolds by introducing nonlinear boundary feedback controls we establish the exponential and rational energy decay rate for the problem our proofs rely on the geometric multiplier method

cellular automation models and traffic flow a cellular automaton model for the description of traffic flow is investigated it generalizes asymmetric exclusion models which have attracted a lot of interest in the past the authors calculate the so called fundamental diagram flow versus density for parallel dynamics using an improved mean field approximation which takes into account short range correlations for maximum velocity they find that the simplest of these non trivial approximations gives the exact result for higher velocities their results are in excellent agreement with numerical data

joint estimation of time delays and directions of arrival of multiple reflections of a known signal we present an efficient algorithm for estimating the time delays and the directions of arrival doas of multiple reflections of a known signal the algorithm is based on an iterative scheme that transforms the multidimensional maximum likelihood criterion into two sets of simple one dimensional 1 d maximization problems simulation results illustrating the performance of the algorithm in comparison with the cramer rao bound are included

implications of sharp trace regularity results on boundary stabilization of the system of linear elasticity abstract uniform exponential decay of solution is established for the elastodynamic system of elasticity using boundary feedback control energy dissipation is introduced via linear velocity feedbacks acting through a portion of the boundary as traction forces two primary goals are achieved first these results are proven without the imposition of strong geometric assumptions on the controlled portion of the boundary thus extending earlier work which required that the domain be star shaped second the feedback is only a function of velocity as opposed to also containing the tangential derivative of the displacement resulting in a physically viable feedback proof is based on the multiplier method and relies critically on sharp trace estimates for the tangential derivative of the displacement on the boundary as well as on unique continuation results for the corresponding static system

on some nonparametric methods for detection of the number of signals a simpler more elegant and more flexible method for estimating the number of signals is proposed strong consistency is proved bounds for error probabilities are given this method depends on choosing a function with a parameter r the previous methods correspond to the case r 1 it seems the larger the r the faster the convergence we can choose r as any positive integer even applications are discussed including the coherent cases

analytical results for the steady state of traffic flow models with stochastic delay exact mean field equations are derived analytically to give the fundamental diagrams i e the average speed car density relations for the fukui ishibashi one dimensional traffic flow cellular automaton model of high speed vehicles v max5m 1 with stochastic delay starting with the basic equation describing the time evolution of the number of empty sites in front of each car the concepts of intercar spacings longer and shorter than m are introduced the probabilities of having long and short spacings on the road are calculated for high car densities r 1 m it is shown that intercar spacings longer than m will be shortened as the traffic flow evolves in time and any initial configurations approach a steady state in which all the intercar spacings are of the short type similarly for low car densities r 1 m it can be shown that traffic flow approaches an asymptotic steady state in which all the intercar spacings are longer than m22 the average traffic speed is then obtained analytically as a function of car density in the asymptotic steady state the fundamental diagram so obtained is in excellent agreement with simulation data s1063 651x 98 04709 6

on smoothed rank profile tests in eigenstructure methods for directions of arrival estimation we propose a statistical procedure known as the smoothed rank profile srp test that can be applied to an array covariance matrix to determine the source coherency structure and solvability of the directions of arrival estimation problem in the presence of coherent sources the srp is the rank profile of a telescoping series of matrices extracted from the observed array covariance matrix

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

detection and localization of multiple sources via the stochastic signals model a method for the detection of coherent and noncoherent signals based on the application of j rissanen s 1978 minimum description length principle for model selection to the stochastic signals model is presented the detection and localization are done simultaneously with the location estimator coinciding with the maximum likelihood estimator derived by j f bohme 1986 the proposed method outperforms the method of m wax and i ziskind 1989 especially in the threshold region simulation results demonstrating the improved performance are included

the iterative time reversal process analysis of the convergence the efficiency of a time reversal acoustic mirror to focus on a reflective target through an inhomogeneous media has been demonstrated in a multitarget media the ability of such a mirror to work in an iterative mode in order to focus selectively on the strongest target was shown c prada f wu and m fink j acoust soc am 90 1119 1991 the theory of how the iterative time reversal process is built is based on a matrix formalism and treats the array of l transducers in a given medium as a linear system of l inputs l outputs the system is characterized at each frequency by its transfer matrix k and the time reversal iterative process is then described by a time reversal operator k k because of the reciprocity principle this operator is hermitian the following result is shown if the scattering medium is a set of well resolved targets of different reflectivities then each eigenvector of the operator k k with nonzero eigenvalue corresponds to one of the targets in the set and provides the opt

automatic determination of the number of targets present when using the time reversal operator acoustical time reversal mirrors have been shown to provide a highly accurate means of studying and focusing on acoustical sources the dort method is a derivation of the time reversal process which allows for focusing on multiple targets an important step in this process is the determination of the number of targets or sources present this is achieved by examining the eigenvalues of the time reversal operator tro the number of significant eigenvalues is then chosen as the number of sources present however as mentioned in n mordant c prada and m fink j acoust soc am 105 2634 2642 1999 and c prada m tanter and m fink in proceedings of the ieee symposium 1997 pp 679 683 factors such as low signal to noise ratio snr small data sample array configuration and the target location may result in the eigenvalues corresponding to the targets no longer being distinguishable from the background noise eigenvalues this paper proposes a robust method of automatically determining the

stabilization of a transmission wave plate equation abstract we consider a stabilization problem for a model arising in the control of noise coupling the damped wave equation with a damped kirchhoff plate equation we prove an exponential stability result under some geometric condition our method is based on an identity with multipliers that allows to show an appropriate energy estimate

an improved imaging method for extended targets when we use direct imaging methods for solving inverse scattering problems we observe artificial lines which make it hard to determine the shape of targets we propose a signal space test to study the cause of the artificial lines and we use multiple frequency data to reduce the effect from them finally we use the active contour without edges acwe method to further improve the imaging results the final reconstruction is accurate and robust the computational cost is lower than iterative imaging methods which need to solve the forward problem in each iteration

the prolate spheroidal wave functions as invariants of the time reversal operator for an extended scatterer in the fraunhofer approximation the decomposition of the time reversal operator known by the french acronym dort is widely used to detect locate and focus on scatterers in various domains such as underwater acoustics medical ultrasound and nondestructive evaluation in the case of point scatterers the theory is well understood the number of nonzero eigenvalues is equal to the number of scatterers and the eigenvectors correspond to the scatterers green s function in the case of extended objects however the formalism is not as simple it is shown here that in the fraunhofer approximation analytical solutions can be found and that the solutions are functions called prolate spheroidal wave functions these functions have been studied in information theory as a basis of band limited and time limited signals they also arise in optics the theoretical solutions are compared to simulation results most importantly the intuition that for an extended objects the number of nonzero eigenvalues is proportional to the number of resol

multiple signal classification method for detecting point like scatterers embedded in an inhomogeneous background medium the multiple signal classification music type method has been widely used to detect point like scatterers embedded in a homogeneous background medium this paper extends the music type method to the detection of point like scatterers that are embedded in an inhomogeneous background although the background green s function at each test point is not directly available in inhomogeneous background scenario this paper proposes an approach based on the finite element method to simultaneously obtain the green s function at all test points numerical simulations illustrate the efficacy of the proposed theory and algorithm presented in this paper and some interesting observations which are absent in homogeneous background scenario are highlighted and discussed

music imaging using phase space gaussian beams processing in a recent paper we presented a beam based backpropagation and correlation imaging scheme for targets in a homogeneous medium this beam based approach is extended here for music imaging algorithms in the beam approach the fields of the physical arrays of point sources and point receivers are expanded using special sets of collimated beam sources and beam receivers this converts the physical scattering data into a beam domain data describing the scattering amplitudes seen synthetically by receiver beams due to excitation by source beams the image is then formed by applying the music algorithm directly in the beam domain we derive a closed form expression for the data transformation to the beam domain and then derive multi experiments music imaging algorithms that accommodate the measurement noise the beam approach enables local imaging of any given sub domain of interest by retaining only the subset of beams that pass through that domain thus reducing the overall computation complexity relative to the conventional green function approach and filtering out of data and noise that arrive from non relevant directions numerical investigations reveal that the beam approach also provides a better resolution under low s n conditions

a detailed derivation of arrays free of higher rank ambiguities since linear dependence of steering vectors would lead to ambiguous direction of arrival doa estimates it is crucial to employ array with linearly independent steering vectors in doa estimation applications in fact it is well known that in order to determine uniquely the doas of spl nu uncorrelated signals one requires an array that is free of up to rank spl nu ambiguities i e an array whose every spl nu 1 steering vectors with distinct doas are linearly independent however the question as to the sensor arrangement that gives rise to an array that is free of up to rank spl nu ambiguities where spl nu spl isin 3 remains unanswered we construct a class of cross arrays that are free of up to rank spl nu ambiguities where spl nu spl isin 1 through this study we derive a theorem for characterizing inherent ambiguities associated with cross arrays we also provide counterexamples to the conjecture for characterizing higher rank ambiguity proposed by lo and marple see ibid vol 40 p 2641 50 1992 and that proposed by wang et al see icassp 9 vol iv p 509 12 1994

decomposition of the time reversal operator detection and selective focusing on two scatterers the decomposition of the time reversal operator dort method is a selective detection and focusing technique using an array of transmit receive transducers it relies on the theory of iterative time reversal mirrors which was presented by prada et al c prada j l thomas and m fink j acoust soc am 97 62 71 1995 the time reversal operator was defined as k k where is the frequency means complex conjugate and k is the transfer matrix of the array of l transducers insonifying a time invariant scattering medium it was shown that this time reversal operator can be diagonalized and that for ideally resolved scatterers of different reflectivities each of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatterers the dort method consists in determining these eigenvectors and using them for the selective focusing this paper presents a complete analysis of this method in the case of two scatterers the

multiple source location a matrix decomposition approach in this paper we present a new method without using the eigenstructure of the sensor covariance matrix for estimating the number of sources d and the direction of arrival of sources based on the matrix decomposition this method uniformly handles coherent and noncoherent sources alike in our procedure a number p is calculated and used for determination of the maximum number of distinguishable sources by a given linear array system

a phase and space coherent direct imaging method a direct imaging algorithm for point and extended targets is presented the algorithm is based on a physical factorization of the response matrix of a transducer array the factorization is used to transform a passive target problem to an active source problem and to extract principal components tones in a phase consistent way the multitone imaging function can superpose multiple tones spatial diversity aperture of the array and frequencies bandwidth of the probing signal based on phase coherence the method is a direct imaging algorithm that is simple and efficient since no forward solver or iteration is needed robustness of the algorithm with respect to noise is demonstrated via numerical examples

time reversal based imaging and inverse scattering of multiply scattering point targets the treatment of time reversal imaging of multiply scattering point targets developed by the present authors in gruber et al time reversal imaging with multiple signal classification considering multiple scattering between the targets j acoust soc am 115 3042 3047 2004 is reformulated and extended to the estimation of the target scattering strengths using the foldy lax multiple scattering model it is shown that the time reversal multiple signal classification music pseudospectrum computed using the background green function as the steering vector yields accurate estimates of the target locations even in the presence of strong multiple scattering between the targets and that the target scattering strengths are readily computed from the so determined target locations using a nonlinear iterative algorithm the paper includes computer simulations illustrating the theory and algorithms presented in the paper

cellular automata models for general traffic conditions on a line abstract by the use of the methods proposed in a recent article we were able to shed some light on the experimentally obtained flux density relation in traffic flow we suggest an order parameter showing the existence of two regimes in freeway traffic we also introduce the case of traffic at signal condition analysing the effects of convenient traffic parameters on the flux density diagram

robust blind multiuser detection based on the worst case performance optimization of the mmse receiver the conventional minimum mean square error mmse multiuser receiver requires that each particular user transmits a sequence of training symbols known to the receiver and the receiver estimates the user signatures using this knowledge however in the presence of multiaccess interference mai during the training period and or in scenarios with short training sequence length the signature estimates can be erroneous and the performance of the mmse multiuser receiver can degrade substantially in this paper we propose a new blind multiuser receiver that is robust against the effects of erroneously presumed desired user signature and short data length our approach is based on the explicit modeling of possible mismatches in the mean square error cost function and worst case performance optimization we show that this approach leads to a multiuser receiver which uses the data covariance matrix with an adaptive diagonal loading the proposed method has simple implementation with a computational complexity comparable with that of the fixed diagonal loading based multiuser receiver simulation results show performance improvements achieved by our approach relative to existing techniques

application of maximum likelihood estimation to radar imaging an efficient maximum likelihood ml estimator to obtain the scattering center locations of a target and the relative scattering level of these scattering centers from the scattered field data is described in the proposed method ml estimation is carried out in the image domain rather than in the frequency aspect domain a two dimensional 2 d inverse fourier transform is used to transfer the scattered field data from frequency aspect domain to the image domain down range cross range as expected the scattered field data in the image domain has some regions with high energy the samples in the high energy regions are used to obtain the initial guess for the ml estimator as well as for ml estimation the ml estimator in the image domain is applied to both simulated and experimental scattered fields of some targets

stabilization of the variable coefficient structural acoustic model with curved middle surface and delay effects in the structural component abstract this paper is concerned with the uniform energy decay rates of a structural acoustic model which describes the interactions between the acoustic medium and the elastic structural in an acoustic chamber where one wall is flexible and curved the coupled system considered consists of a variable coefficient wave equation and a variable coefficient plate equation defined on the riemannian manifold with the coupling on the interface between the acoustic medium and the flexible wall both the components of the dynamics are subject to nonlinear boundary damping furthermore a nonlinear delay term acting in the boundary feedbacks of the structure component is considered the riemannian geometry method is applied to derive the energy estimates of the nonlinear coupled system with variable coefficients the uniform energy decay rates of the nonlinear variable coefficient structural acoustic system with delay effects on the riemannian manifold are quantified by a solution to a constructed nonlinear ode

on the behavior of information theoretic criteria for model order selection the akaike 1974 information criterion aic and the minimum description length mdl are two well known criteria for model order selection in the additive white noise case our aim is to study the influence on their behavior of a large gap between the signal and the noise eigenvalues and of the noise eigenvalue dispersion our results are mostly qualitative and serve to explain the behavior of the aic and the mdl in some cases of great practical importance we show that when the noise eigenvalues are not clustered sufficiently closely then the aic and the mdl may lead to overmodeling by ignoring an arbitrarily large gap between the signal and the noise eigenvalues for fixed number of data samples overmodeling becomes more likely for increasing the dispersion of the noise eigenvalues for fixed dispersion overmodeling becomes more likely for increasing the number of data samples undermodeling may happen in the cases where the signal and the noise eigenvalues are not well separated and the noise eigenvalues are clustered sufficiently closely we illustrate our results by using simulations from the effective channel order determination area

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

reconstruction of a small inclusion in a two dimensional open waveguide we consider wave propagation in a perturbed open waveguide we provide a new asymptotic expansion for the scattered wave when the inclusion is of small diameter we design a music multiple signal classification type of algorithm for locating the inclusion and illustrate its viability in numerical examples

applications of cumulants to array processing i aperture extension and array calibration an interpretation for the use of cumulants in narrowband array processing problems is proposed it is shown how fourth order cumulants of multichannel observations increase the directional information compared with second order statistics based on the interpretation it is shown how cumulants can be used to increase the effective aperture of an arbitrary antenna array the amount of partial information necessary to jointly calibrate an arbitrary array and estimate the directions of far field sources is also investigated it is proven that the presence of a doublet and use of fourth order cumulants is sufficient to accomplish this task the proposed approach is computationally efficient and more general than covariance based algorithms that have addressed the calibration problem under constraints a class of beamforming techniques is proposed to recover the source waveforms proposed estimation procedures are based on cumulants which bring insensitivity to the spatial correlation structure of additive gaussian measurement noise simulations are provided to illustrate the use of the proposed algorithms

blind channel approximation effective channel order determination a common assumption of blind channel identification methods is that the order of the true channel is known this information is not available in practice and we are obliged to estimate the channel order by applying a rank detection procedure to an overmodeled data covariance matrix information theoretic criteria have been widely suggested approaches for this task we check the quality of their estimates in the context of order estimation of measured microwave radio channels and confirm that they are very sensitive to variations in the snr and the number of data samples this fact has prohibited their successful application for channel order estimation and hits created some confusion concerning the classification into under and over modeled cases recently it has been shown that blind channel approximation methods should attempt to model only the significant part of the channel composed of the large impulse response terms because efforts toward modeling small leading and or trailing terms lead to effective overmodeling which is generically ill conditioned and thus should be avoided this can be achieved by applying blind identification methods with model order equal to the order of the significant part of the true channel called the effective channel order toward developing an efficient approach for the detection of the effective channel order we use numerical analysis arguments the derived criterion provides a maximally stable decomposition of the range space of an overmodeled data covariance matrix into signal and noise subspaces it is shown to be robust to variations in the snr and the number of data samples furthermore it provides useful effective channel order estimates leading to sufficiently good blind approximation equalization of measured real world microwave radio channels

imaging of location and geometry for extended targets using the response matrix in this paper we study how to image both the location and the shape of extended targets using the response matrix obtained from inter element response of an active array of transducers in particular the time reversal technique is used for efficient initial localization of the target and the level set method is used for shape reconstruction we then show how to couple the location estimation and shape reconstruction in a complementary way to improve accuracy for range estimation resolution analysis for active arrays in remote sensing regime is also presented we illustrate with numerical experiments which show that the method is capable of imaging objects with complicated shapes and that the method is robust with respect to noisy data

exact results of 1d traffic cellular automata the low density behavior of the fukui ishibashi model abstract the maximum entropy states of the cellular automata models for traffic flow in a single lane with no anticipation are presented and discussed the exact analytical solutions for the low density behavior of the stochastic fukui ishibashi traffic model were obtained and compared with computer simulations of the model an excellent agreement was found

maximum likelihood localization of multiple sources by alternating projection an algorithm referred to as apm for computing the maximum likelihood estimator of the locations of simple sources in passive sensor arrays is presented the algorithm is equally applicable to the case of coherent signals and to the case of a single snapshot the algorithm is iterative the maximum of the likelihood function is computed by successive approximations the convergence of the algorithm to the global maximum is demonstrated for a variety of scenarios the key to this global convergence is the initialization scheme

stochastic boundary conditions in the deterministic nagel schreckenberg traffic model we consider open systems where cars move according to the deterministic nagel schreckenberg rules k nagel and m schreckenberg j phys i 2 2221 1992 and with maximum velocity v max 1 which is an extension of the asymmetric exclusion process asep it turns out that the behavior of the system is dominated by two features a the competition between the left and the right boundary b the development of so called buffers due to the hindrance that an injected car feels from the front car at the beginning of the system as a consequence there is a first order phase transition between the free flow and the congested phase accompanied by the collapse of the buffers and the phase diagram essentially differs from that for v max 1 asep

discrete stochastic models for traffic flow we investigate a probabilistic cellular automaton model which has been introduced recently this model describes single lane traffic flow on a ring and generalizes the asymmetric exclusion process models we study the equilibrium properties and calculate the so called fundamental diagrams flow versus density for parallel dynamics this is done numerically by computer simulations of the model and by means of an improved mean field approximation which takes into account short range correlations for cars with a maximum velocity of 1 the simplest nontrivial approximation gives the exact result for higher velocities the analytical results obtained by iterated application of the approximation scheme are in excellent agreement with the numerical simulations

on the performance of signal subspace processing part i narrow band systems this paper presents an analytical evaluation of detection determination of the number of sources and estimation performances of narrow band signal subspace processing for multiple source direction finding the probabilities of underestimating and overestimating the number of sources are derived under asymptotic conditions and around the threshold regions in terms of the choice of a penalty function and signal noise and array parameters for the cases of at most two closely spaced sources in the spatially white noise a scalar measure is introduced for the evaluation of the quality of the estimated signal subspace based on the statistics of this measure performance thresholds are demonstrated for the signal to noise ratio angle separation and correlation between two equipowered sources

multistatic response matrix of a 3 d inclusion in half space and music imaging recent work on the retrieval of 3 d bounded dielectric and or magnetic inclusions in free space is extended to burial in a half space though emphasis is on the case of a single inclusion enabling the derivation of closed form mathematical results in illuminating fashion the approach extends to the case of an unknown number of well separated inclusions within an asymptotic field formulation derived from exact contrast source vector integral formulations satisfied by the time harmonic fields and using proper reciprocity relationships of the dyadic green s functions the multistatic response matrix of the inclusion is constructed from the leading order term of the fields its singular value structure is analyzed in detail for a dielectric or a magnetic contrast or both contrasts this is performed in the case of a unique electric dipole array operated in the transmit receive mode at a single frequency a multiple signal classification type algorithm follows from the decomposition yielding a cost functional the magnitude of which peaks at the inclusion center numerical results illustrate the above as a function of the geometric and electromagnetic parameters of the configuration imaging of a spherical inclusion is in particular investigated from severely noisy synthetic data as well as of two inclusions embedded within a non conductive or conductive half space

uniform stability of transmission of wave plate equations with source on riemannian manifold abstract this paper is concerned with the semilinear transmission of wave plate system with source term on riemannian manifold we prove the existence of weak solutions by using faedo galerkin s method furthermore by introducing nonlinear boundary feedbacks acting only on plate we establish the explicit and general decay rates of the system our proofs are based on the geometric multiplier method and the riemannian geometry method

an improved cellular automaton traffic model considering gap dependent delay probability abstract in this paper the delay probability of the original nagel and schreckenberg model is modified to simulate one lane traffic flow the delay probability of a vehicle depends on its corresponding gap according to simulation results it has been found that the structure of the fundamental diagram of the new model is sensitively dependent on the values of the delay probability in comparison with the ns model one notes that the fundamental diagram of the new model is more consistent with the results measured in the real traffic and the velocity distributions of the new model are relatively reasonable

optimality of high resolution array processing using the eigensystem approach in the classical approach to underwater passive listening the medium is sampled in a convenient number of look directions from which the signals are estimated in order to build an image of the noise field in contrast a modern trend is to consider the noise field as a global entity depending on few parameters to be estimated simultaneously in a gaussian context it is worthwhile to consider the application of likelihood methods in order to derive a detection test for the number of sources and estimators for their locations and spectral levels this paper aims to compute such estimators when the wavefront shapes are not assumed known a priori this justifies results previously found using the asymptotical properties of the eigenvalue eigenvector decomposition of the estimated spectral density matrix of the sensor signals they have led to a variety of high resolution array processing methods more specifically a covariance matrix test for equality of the smallest eigenvalues is presented for source detection for source localization a best fit method and a test of orthogonality between the smallest eigenvectors and the source vectors are discussed

multiple scattering between two elastic cylinders and invariants of the time reversal operator theory and experiment the decomposition of the time reversal operator method is an ultrasonic method based on the analysis of the array response matrix used for detection and characterization the eigenvalues and the eigenvectors of the time reversal operator equivalent to the singular values and the singular vectors of the array response matrix provide information on the localization and nature of scatterers in the insonified medium here the eigenmodes of the time reversal operator are studied for two elastic cylinders the effects of multiple scattering and anisotropic scattering are considered analytical expressions for the singular values are established within the isotropic scattering approximation then the comparison with a complete model is presented putting in evidence the importance of the anisotropy of the scattering experiments carried out at central frequency 1 5mhz on 0 25mm diameter nylon and copper cylinders embedded in water confirm the theory in particular the small cylinder limit and the effect o

green s function estimation in speckle using the decomposition of the time reversal operator application to aberration correction in medical imaging the fdort method french acronym for decomposition of the time reversal operator using focused beams is a time reversal based method that can detect point scatterers in a heterogeneous medium and extract their green s function it is particularly useful when focusing in a heterogeneous medium this paper generalizes the theory of the fdort method to random media speckle and shows that it is possible to extract green s functions from the speckle signal using this method therefore it is possible to achieve a good focusing even if no point scatterers are present moreover a link is made between fdort and the van cittert zernike theorem it is deduced from this interpretation that the normalized first eigenvalue of the focused time reversal operator is a well known focusing criterion the concept of an equivalent virtual object is introduced that allows the random problem to be replaced by an equivalent deterministic problem and leads to an intuitive understanding of fdort in speckle applications to aberration correction are presented the reduction of the variance of the green s function estimate is discussed finally it is shown that the method works well in the presence of strong interfering scatterers