on focusing matrices for wide band array processing a general class of transformation matrices for coherent signal subspace processing is presented these signal subspace transformation sst matrices are shown to generate a sufficient statistic for maximum likelihood bearing estimation two general forms for calculating sst matrices are presented and the rotational signal subspace rss focusing matrices proposed by h hung and m kaveh 1988 are shown to be a special case of the sst matrices an efficient procedure for computing a subset of the sst matrices utilizing householder transformations is presented the procedure reduces the computational load by a factor of 10 compared with that for the rss matrices the application of music to the coherently combined covariance matrix is also discussed and monte carlo simulations comparing the performance of householder sst matrices and rss matrices are performed

a low complexity mvdr beamformer for use with short observation times it is demonstrated via simulation examples that the steered minimum variance subarray beamformer is a simple viable and computationally efficient approach to partially adaptive beamforming with the additional advantage that it is available for use with short observation intervals where time is traded for bandwidth a quadratically constrained version is also examined

array interpolation and doa mse reduction interpolation or mapping of data from a given real array to data from a virtual array of more suitable geometry is well known in array signal processing this operation allows arrays of any geometry to be used with fast direction of arrival doa estimators designed for linear arrays in an earlier companion paper a first order condition for zero doa bias under such mapping was derived and was also used to construct a design algorithm for the mapping matrix that minimized the doa estimate bias this bias minimizing theory is now extended to minimize not only bias but also to consider finite sample effects due to noise and reduce the doa mean square error mse an analytical first order expression for mapped doa mse is derived and a design algorithm for the transformation matrix that minimizes this mse is proposed generally doa mse is not reduced by minimizing the size of the mapping errors but instead by rotating these errors and the associated noise subspace into optimal directions relative to a certain gradient of the doa estimator criterion function the analytical mse expression and the design algorithm are supported by simulations that show not only conspicuous mse improvements in relevant scenarios but also a more robust preprocessing for low signal to noise ratios snrs as compared with the pure bias minimizing design developed in the previous paper

broadband doa estimation using frequency invariant beamforming a new method of direction of arrival doa estimation for multiple broadband farfield signals is presented the technique uses a beamspace preprocessing structure based on frequency invariant beamforming specifically a set of beam shaping filters focus the received array data in the time domain thereby avoiding the need for frequency decomposition hence the proposed method is conceptually different from most other broadband doa estimators which require frequency decomposition numerical results are presented to demonstrate the use of the new method and compare it with conventional coherent signal subspace methods

space time music consistent signal subspace estimation for wideband sensor arrays wideband direction of arrival doa estimation with sensor arrays is an essential task in sonar radar acoustics biomedical and multimedia applications many state of the art wideband doa estimators coherently process frequency binned array outputs by approximate maximum likelihood ml weighted subspace fitting or focusing techniques this paper shows that bin signals obtained by filter bank approaches do not obey the finite rank narrow band array model because spectral leakage and changes of the array response with frequency within the bin create ghost sources dependent on the particular realization of the source process therefore existing doa estimators based on binning are not consistent even when the array response is perfectly known in this paper under a more realistic array model which still has finite rank under a space time formulation signal subspaces at arbitrary frequencies can be consistently recovered under mild conditions by applying space time music type st music estimators to the dominant eigenvectors of the wideband space time sensor cross correlation matrix a novel consistent ml based st music subspace estimate is developed to estimate the number of sources active at each frequency by information theoretic criteria empirical st music subspaces are fed to any subspace fitting doa estimator at single or multiple frequencies simulations confirm that this approach allows better performance over binning approaches at sufficiently high signal to noise ratio when model mismatches exceed the noise floor

estimating parameters of multiple wideband polynomial phase sources in sensor arrays we consider the problem of estimating the parameters of multiple wideband polynomial phase signal pps sources in sensor arrays a new maximum likelihood ml direction of arrival doa estimator is introduced and the exact cramer rao bound crb is derived for the general case of multiple constant amplitude polynomial phase sources since the proposed exact ml estimator is computationally intensive an approximate solution is proposed originating from the analysis of the log likelihood ll function in the single chirp signal case as a result a new form of spatio temporal matched filter referred to as the chirp beamformer is derived which is applicable to well separated sources that have distinct time frequency or and spatial signatures this beamforming approach requires solving a three dimensional 3 d optimization problem and therefore enjoys essentially simpler implementation than that entailed by the exact ml simulation results are presented illustrating the performance of the estimators and validating our theoretical crb analysis

spatio temporal spectral analysis by eigenstructure methods this paper presents new algorithms for estimating the spatio temporal spectrum of the signals received by a passive array the algorithms are based on the eigenstructure of the covariance and spectral density matrices of the received signals they allow partial correlation between the sources and thus are applicable to certain kinds of multipath problems simulation results that illustrate the performance of the new algorithms are presented

direction of arrival estimation for nonuniform sensor arrays from manifold separation to fourier domain music methods in this paper the problem of spectral search free direction of arrival doa estimation in arbitrary nonuniform sensor arrays is addressed in the first part of the paper we present a finite sample performance analysis of the well known manifold separation ms based root music technique then we propose a new class of search free doa estimation methods applicable to arrays of arbitrary geometry and establish their relationship to the ms approach our first technique is referred to as fourier domain fd root music and is based on the fact that the spectral music function is periodic in angle it uses the fourier series to expand this function and reformulate the underlying doa estimation problem as an equivalent polynomial rooting problem our second approach applies the zero padded inverse fourier transform to the fd root music polynomial to avoid the polynomial rooting step and replace it with a simple line search our third technique refines the fd root music approach by using weighted least squares approximation to compute the polynomial coefficients the proposed techniques are shown to offer substantially improved performance to complexity tradeoffs as compared to the ms technique

the signal subspace approach for multiple wide band emitter location the rational vector space generalization of the signal subspace approach is presented and applied to the estimation of multiple wide band emitter locations from the signals received at multiple sensors the signal subspace and array manifold concepts first introduced by schmidt are generalized to rational vector space these concepts are used to develop the rational signal subspace theory and prove the signal subspace theorem on which signal subspace algorithms are based the theory is applied in discrete time to derive a class of rational signal subspace algorithms for source location and spectral estimation using unit circle eigendecomposition of multivariate rational models of sensor outputs simulation results are presented for an algorithm in this class including sample statistics from monte carlo trials and comparisons with the cramer rao bound

multiple broad band source location using steered covariance matrices the authors present an approach for reducing the threshold observation time required to achieve high resolution localization of multiple broadband sources the proposed techniques are based on a space time statistic called the steered covariance matrix stcm the stcm like the well known cross spectral density matrix csdm has asymptotic properties which facilitate high resolution source localization in broadband settings however the stcm has the advantage that it can be estimated with much greater statistical stability than the csdm the stcm is used in conjunction with minimum variance and linear predictive spectral estimation to obtain the steered minimum variance stmv and steered linear prediction stlp methods analytical and simulation results are presented that indicate that the stmv and stlp methods exhibit lower threshold observation times than their csdm based counterparts

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

efficient wideband source localization using beamforming invariance technique a novel scheme for wideband direction of arrival doa estimation is proposed the technique performs coherent signal subspace transformation by a set of judiciously constructed beamforming matrices the beamformers are chosen to transform each of the narrowband array manifold vectors into the one corresponding to the reference frequency regardless of the actual spatial distribution of the sources the focused data correlation matrix can thus be obtained without any preliminary doa estimation or iteration a simplified version of the beamspace root music algorithm is developed and used in conjunction with the proposed method to efficiently localize multiple wideband sources with a linear equally spaced array numerical simulations are conducted to demonstrate the efficacy of the new scheme

performance analysis of music type high resolution estimators for direction finding in correlated and coherent scenes an asymptotic analysis is presented of a class of high resolution estimators for resolving correlated and coherent plane waves in noise these estimators are in turn constructed from certain eigenvectors associated with spatially smoothed or unsmoothed covariance matrices generated from a uniform array the analysis is first carried out for the smoothed case and from this the conventional i e unsmoothed multiple signal classification music scheme follows as a special case independent of the total number of sources present in the scene the variance of the conventional music estimator along the true arrival angles is shown to be zero within a first order approximation the bias expressions in the smoothed case are used to obtain a resolution threshold for two coherent equipowered plane waves in white noise and the result is compared to the one derived by kaveh et al 1986 for two uncorrelated equipowered plane waves

estimation of spatial and spectral parameters of multiple sources the problem of estimating spatial and spectral parameters of multiple sources by sensor arrays is considered a parametric model is derived for the multichannel measurement vector tbe model parameters are the time delays and the autoregressive moving average parameters of all the sources a suboptimal parameter estimation procedure is proposed and simulation results are presented to illustrate its performance

some projection properties of orthogonal arrays the definition of an orthogonal array imposes an important geometric property the projection of an oa 2 t 2 k t a 2 t run orthogonal array with k two level factors and strength t onto any t factors consists of copies of the complete 2 t factorial in this article projections of an oa n 2 k t onto t 1 and t 2 factors are considered the projection onto any t 1 factors must be one of three types one or more copies of the complete 2 t 1 factorial one or more copies of a half replicate of 2 t 1 or a combination of both it is also shown that for k t 2 only when n is a multiple of 2 t 1 can the projection onto some t 1 factors be copies of a half replicate of 2 t 1 therefore if n is not a multiple of 2 t 1 then the projection of an oa n 2 k t with k t 2 onto any t 1 factors must contain at least one complete 2 t 1 factorial some properties of projections onto t 2 factors are established and are applied to show that if n is not a multiple of 8 then for any oa n 2 k 2 with k 4 the projection onto any four factors has the property that all the main effects and two factor interactions of these four factors are estimable when the higher order interactions are negligible

wideband multiple diversity tensor array processing this paper establishes a tensor model for wideband coherent array processing including multiple physical diversities a separable coherent focusing operation is proposed as a preprocessing step in order to ensure the multilinearity of the interpolated data we propose an alternating least squares algorithm to process tensor data taking into account the noise correlation structure introduced by the focusing operation we show through computer simulations that the estimation of direction of arrival and polarization parameters improves compared to existing narrowband tensor processing and wideband multiple signal classification the performance is also compared to the cramer rao bounds of the wideband tensor model

indicator function and its application in two level factorial designs a two level factorial design can be uniquely represented by a polynomial indicator function therefore properties of factorial designs can be studied through their indicator functions this paper shows that the indicator function is an effective tool in studying two level factorial designs the indicator function is used to generalize the aberration criterion of a regular two level fractional factorial design to all two level factorial designs an important identity of generalized aberration is proved the connection between a uniformity measure and aberration is also extended to all two level factorial designs

on the memory function for the dynamic structure factor of interacting brownian particles abstract it is shown that the memory function of concentration fluctuations m k t derived from the generalized smoluchowski equation is not a one particle irreducible quantity a new function m k t which is one particle irreducible is derived and the relation between both functions is established the irreducible memory function m k t can be interpreted as a dynamic viscosity in contrast to earlier statements there is no discrepancy in the results which are obtained from phase space approach fokker planck equation and those obtained from the smoluchowski equation

performance of spatial smoothing algorithms for correlated sources the problem of identifying the angles of arrival of a set of plane waves impinging on a narrowband array of sensors and related spectral analysis problems have been addressed with a large number of algorithms one of the most popular techniques is the multiple signal classification music the major shortcoming of the music algorithm is that it performs poorly when the sources are highly correlated fortunately two algorithms exist to overcome this problem spatial smoothing ss and forward backward spatial smoothing fbss the performance of the ss technique depends on signal bearings and spatial separation for the same smoothing fbss can offer improved performance but this depends on the signal phases numerical results for the variance of the algorithms are given to illustrate the points made

time dependent self diffusion in model suspensions of highly charged brownian particles abstract a quantitative comparison is reported between the predictions of two theories of the time dependent self diffusion properties of suspensions of highly charged brownian particles the first theory based on the overdamped n body fokker planck dynamics involves a mode mode coupling approximation for the time dependent self friction function whereas the second one makes use of short time conditions derived from the n body smoluchowski equation in both cases the relevant dynamic properties can be expressed in terms solely of the radial distribution function g r this quantity is first calculated using the rescaled mean spherical approximation rmsa by comparing with computer simulation results for g r it is found that the rmsa becomes increasingly inaccurate as the freezing transition is approached we observe however that the rmsa itself provides a device to fit the simulation results for g r using this procedure the time dependent self diffusion coefficient calculated from both theories is in good agreement with brownian dynamics simulations

forward backward spatial smoothing techniques for coherent signal identification a spatial smoothing scheme is further investigated in the context of coherent signal classification it is shown that by making use of a set of forward and complex conjugated backward subarrays simultaneously it is always possible to estimate any k directions of arrival using at most 3k 2 sensor elements this is achieved by creating a smoothed array output covariance matrix that is structurally identical to a covariance matrix in some noncoherent situation by incorporating eigenstructure based techniques on this smoothed covariance matrix it then becomes possible to correctly identify all directions of arrival irrespective of their correlation

some hidden projection properties of orthogonal arrays with strength three summary it is shown that a two level orthogonal array with strength three whose run size is not a multiple of 16 has the hidden projection property that in its projection on to any five factors all the main effects and two factor interactions are estimable if the higher order interactions are negligible the result applies to the fold over of any strength two orthogonal array whose run size is not a multiple of 8 this extends diamond s 1995 result on the fold over of the 12 run plackett burman design some connections with search designs are also presented

theory of j characteristics for fractional factorial designs and projection justification of minimum g2 aberration deng tang 1999 introduced the generalised resolution and minimum g aberration criteria for assessing nonregular fractional factorials in tang deng 1999 a relaxed variant of minimum g aberration called minimum g 2 aberration is proposed and studied these criteria are defined using a set of j values called j characteristics in this paper we show that a factorial design is uniquely determined by its j characteristics just as a regular factorial design is uniquely determined by its defining relation the theorem is given through an explicit formula that relates the set of design points to that of j characteristics through this formula projection justification of minimum g 2 aberration is established

waves weighted average of signal subspaces for robust wideband direction finding existing algorithms for wideband direction finding are mainly based on local approximations of the gaussian log likelihood around the true directions of arrival doas assuming negligible array calibration errors suboptimal and costly algorithms such as classical or sequential beamforming are required to initialize a local search that eventually furnishes doa estimates this multistage process may be nonrobust in the presence of even small errors in prior guesses about angles and number of sources generated by inherent limitations of the preprocessing and may lead to catastrophic errors in practical applications a new approach to wideband direction finding is introduced and described the proposed strategy combines a robust near optimal data adaptive statistic called the weighted average of signal subspaces waves with an enhanced design of focusing matrices to ensure a statistically robust preprocessing of wideband data the overall sensitivity of waves to various error sources such as imperfect array focusing is also reduced with respect to traditional cssm algorithms as demonstrated by extensive monte carlo simulations

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

direction finding for diversely polarized signals using polynomial rooting a direction finding algorithm for diversely polarized arrays that is based on polynomial rooting is presented using polynomial rooting instead of search reduces significantly the computational requirements of the algorithm and enhances resolution the basic method is limited to linear uniformly spaced arrays however using an interpolation technique the algorithm is extended to a larger class of arrays the performance of the proposed algorithm is analyzed computer simulations are used to demonstrate the performance of the new technique and to verify the performance analysis

small composite designs small second order composite designs were suggested by hartley 1959 westlake 1965 provided even smaller designs for k 5 7 and 9 factors for which intricate construction methods were needed here simple designs formed using plackett and burman 1946 designs are offered for k 5 7 and 9 designs with one run fewer than westlake s for k 5 and 7 and three fewer for k 9 are feasible by deleting repeat points that occur in some of the designs

k circulant supersaturated designs a class of supersaturated designs called k circulant designs is explored these designs are constructed from cyclic generators by cycling k elements at a time the class of designs includes many es2 optimal designs some of which are already known and some of which are more efficient than known designs for model estimation under factor sparsity generators for the most efficient designs are listed and projection properties of some of the designs are explored we also illustrate that some k circulant supersaturated designs can be augmented with interaction columns to produce efficient designs for a larger number of factors or for estimating interactions

linear kinetic theory of a suspension of interacting brownian particles ii density density autocorrelation function abstract we analyze the density density equilibrium time correlation function of interacting brownian particles by a method which we have described earlier the generalized diffusion coefficient related to this function is expressed in terms of an evolution operator in which single particle diffusion and interparticle collisions are renormalized by the equilibrium correlations this result is then used to show some general relations for the dynamical properties of suspensions and to propose an approximation scheme similar to that leading to the enskog equation in the kinetic theory of fluids

escape by diffusion from a square well across a square barrier abstract the problem of escape of a particle by diffusion from a square potential well across a square barrier is studied on the basis of the one dimensional smoluchowski equation for the space and time dependent probability distribution for the model potential the smoluchowski equation is solved exactly by a laplace transform with respect to time in the limit of a high barrier the rate of escape is given by an asymptotic result similar to that derived by kramers for a curved well and a curved barrier an approximate analytic formula is derived for the outward time dependent probability current in terms of the width and depth of the well and the width and height of the barrier a similar expression holds for the complete probability distribution

focussing matrices for coherent signal subspace processing a class of focussing matrices is proposed for use in the coherent signal subspace method csm h wang and m kaveh ibid vol assp 33 aug 1985 when the directions of arrival of wideband sources fall into more than one group of one beamwidth each this class leads to performance substantially better than those suggested in previous studies on direction of arrival estimation new insight into the structures of various focussing matrices and their effect on the performance of csm is presented the performance of csm is compared for several classes of these matrices on the simulations as well as relative sufficiency analyses

maximum likelihood source localization and unknown sensor location estimation for wideband signals in the near field in this paper we derive the maximum likelihood ml location estimator for wideband sources in the near field of the sensor array the ml estimator is optimized in a single step as opposed to other estimators that are optimized separately in relative time delay and source location estimations for the multisource case we propose and demonstrate an efficient alternating projection procedure based on sequential iterative search on single source parameters the proposed algorithm is shown to yield superior performance over other suboptimal techniques including the wideband music and the two step least squares methods and is efficient with respect to the derived cramer rao bound crb from the crb analysis we find that better source location estimates can be obtained for high frequency signals than low frequency signals in addition large range estimation error results when the source signal is unknown but such unknown parameter does not have much impact on angle estimation in some applications the locations of some sensors may be unknown and must be estimated the proposed method is extended to estimate the range from a source to an unknown sensor location after a number of source location frames the location of the uncalibrated sensor can be determined based on a least squares unknown sensor location estimator

cluster expansion of the diffusion kernel of a suspension of interacting brownian particles abstract we derive a cluster expansion for the wavenumber and frequency dependent diffusion coefficient of a suspension of interacting brownian particles the diffusion coefficient is expressed in terms of evolution operators of progressively increasing complexity we expect that at low frequency only the low order terms contribute effectively we propose an expression for the wavenumber dependent collective diffusion coefficient at zero frequency which involves the dynamics of only two particles a similar expression is obtained for the wave number dependent self diffusion coefficient

diffusion and convection after escape from a potential well abstract the escape by diffusion of a particle from a potential well in one dimension is strongly influenced by the application of a field in the adjacent half space at long times the probability distribution becomes a uniformly moving and steadily broadening gaussian in this half space the mean time of escape from the well is given by a simple expression in terms of the mean first passage time and the coefficient of the long time tail in the occupation probability of the well in the absence of the field transient effects in space and time are studied in explicit form for a parabolic potential well

brownian dynamics divergence of mobility tensor abstract the mobility tensor for many spheres suspended in a viscous fluid is considered an analytical formula for the divergence of this tensor is derived it is then applied in calculations of long time collective diffusion coefficient of hard sphere suspension by means of brownian dynamics method

tops new doa estimator for wideband signals this paper introduces a new direction of arrival doa estimation algorithm for wideband sources called test of orthogonality of projected subspaces tops this new technique estimates doas by measuring the orthogonal relation between the signal and the noise subspaces of multiple frequency components of the sources tops can be used with arbitrary shaped one dimensional 1 d or two dimensional 2 d arrays unlike other coherent wideband methods such as the coherent signal subspace method cssm and waves the new method does not require any preprocessing for initial values the performance of those wideband techniques and incoherent music is compared with that of the new method through computer simulations the simulations show that this new technique performs better than others in mid signal to noise ratio snr ranges while coherent methods work best in low snr and incoherent methods work best in high snr thus tops fills a gap between coherent and incoherent methods

asymptotically perfect wideband focusing of multiring circular arrays the concept of coherent focusing of sensor arrays introduced by wang and kaveh led to the development of high performance and computationally efficient algorithms for wideband direction finding and beamforming nonetheless the quality of focusing depends on the understanding and the proper exploitation of specific array manifold properties circular arrays exhibit uniform isotropic performance over the entire azimuthal range and allow the use of fast algorithms originally developed for uniform linear arrays by decomposing the manifold into circular harmonics coherent wideband focusing of circular arrays suffers from ambiguities noise warping and numerical ill conditioning in this work it is shown that a fast orthonormal beamspace transformation combining the responses of two concentric rings can perfectly focus wideband sources at all azimuth angles in the circular harmonic domain in the limit of infinite number of sensors the information loss after focusing is minimized through an analytical approach the proposed focusing scheme is computationally very efficient and can be directly extended to multiring circular arrays that are arranged into a set of nested two ring subarrays to cover very large bandwidths

design selection and classification for hadamard matrices using generalized minimum aberration criteria deng and tang 1999 and tang and deng 1999 proposed and justified two criteria of generalized minimum aberration for general two level fractional factorial designs the criteria are defined using a set of values called j characteristics in this article we examine the practical use of the criteria in design selection specifically we consider the problem of classifying and ranking designs that are based on hadamard matrices a theoretical result on j characteristics is developed to facilitate the computation the issue of design selection is further studied by linking generalized aberration with the criteria of efficiency and estimation capacity our studies reveal that generalized aberration performs quite well under these familiar criteria

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

transient survival probability of a particle diffusing in a disordered system of perfectly absorbing spherical sinks abstract the transient survival probability of a particle diffusing in a disordered system of perfectly absorbing non overlapping spherical sinks is studied by use of a self consistent cluster expansion for its laplace transform the self consistent cluster expansion which in principle is exact is formulated in two alternative versions corresponding to different ways of handling the instantaneous absorption of particles created initially inside a sink in each version of the theory the cluster expansion is truncated at either the singlet or the pair level so that four different approximations to the exact result are obtained an approximation on the pair level constitutes an improvement to the corresponding singlet approximation it is shown that at moderate volume fraction of the sink system the two pair approximations yield almost identical results for the survival probability all four approximations lead to a band gap in the spectrum of relaxation rates followed by a continuum extending to infinity

escape by diffusion from a parabolic well across a parabolic barrier abstract the problem of escape of a particle by diffusion from a parabolic potential well across a parabolic barrier adjacent to free space is studied on the basis of the one dimensional smoluchowski equation for the space and time dependent probability distribution for the model potential the smoluchowski equation is solved exactly by a laplace transform with respect to time for the initial condition that at time zero the probability distribution is given by a thermal equilibrium distribution in the well in the limit of a high barrier the rate of escape is given by an asymptotic result due to kramers for a potential barrier of moderate height there are significant corrections to the asymptotic result the probability that the particle resides in the well barrier region at time t decays with a 1 t long time tail

nonregular designs with desirable projection properties in many industrial applications the experimenter is interested in estimating some of the main effects and two factor interactions in this article we rank two level orthogonal designs based on the number of estimable models containing a subset of main effects and their associated two factor interactions by ranking designs in this way the experimenter can directly assess the usefulness of the experimental plan for the purpose in mind we apply the new ranking criterion to the class of all non isomorphic two level orthogonal designs with 16 and 20 runs and introduce a computationally efficient algorithm based on two theoretical results which will aid in finding designs with larger run sizes catalogs of useful designs with 16 20 24 and 28 runs are presented

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

performance analysis of spatial smoothing with interpolated arrays the interpolated spatial smoothing algorithm is a computationally efficient method for estimating the directions of arrival doas of signals some of which may be perfectly correlated it extends the spatial smoothing method to arbitrary array geometries a statistical performance analysis of the algorithm is presented closed form expressions for the covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluating these expressions for specific cases and comparing them to the cramer rao lower bound for the doa estimates provides insight into the statistical efficiency of this algorithm the formulas for the error covariance are quite general and can be specialized to provide results for other doa estimation algorithms as well

direction finding for wide band signals using an interpolated array the authors derive a new direction finding algorithm for multiple wideband signals received by an arbitrary array and analyze its performance using an interpolation technique they generate a set of virtual arrays each for a different frequency band having the same array manifold the convergence matrices of these arrays are added to produce a composite covariance matrix direction of arrival doa estimates are obtained by eigendecomposition of this composite covariance matrix using the narrowband music algorithm or its variants closed form expressions for the asymptotic covariance matrix of the doa estimation errors are derived using a perturbation analysis evaluated for specific cases and compared with the cramer rao lower bound special attention is given to correlated and coherent signals the formulas for the error covariance are quite general and can be modified to provide results for other wideband doa estimation algorithms

moment aberration projection for nonregular fractional factorial designs nonregular fractional factorial designs such as plackett burman designs are widely used in industrial experiments for run size economy and flexibility a novel criterion called moment aberration projection is proposed to rank and classify nonregular designs it measures the goodness of a design through moments of the number of coincidences between the rows of its projection designs the new criterion is used to rank and classify designs of 16 20 and 27 runs examples are given to illustrate that the ranking of designs is supported by other design criteria

a generalization of weighted subspace fitting to full rank models the idea of subspace fitting provides a popular framework for different applications of parameter estimation and system identification previously some algorithms have been suggested based on similar ideas for a sensor array processing problem where the underlying data model is not low rank we show that two of these algorithms dspe and dispare fail to give consistent estimates and introduce a general class of subspace fitting like algorithms for consistent estimation of parameters from a possibly full rank data model the asymptotic performance is analyzed and an optimally weighted algorithm is derived the result gives a lower bound on the estimation performance for any estimator based on a low rank approximation of the linear space spanned by the sample data we show that in general for full rank data models no subspace based method can reach the cramer rao lower bound crb

performance analysis of root music the authors analyze the performance of root music a variation of the music algorithm for estimating the direction of arrival doa of plane waves in white noise in the case of a linear equispaced sensor array the performance of the method is analyzed by examining the perturbation in the roots of the polynomial formed in the intermediate step of root music in particular asymptotic results for the mean squared error in the estimates of the direction of arrival are derived simplified expressions are presented for the one and two source case and compared to those obtained for least squares esprit computer simulations are also presented and they are in close agreement with the theory an important outcome of this analysis is the fact that the error in the signal zeros has a largely radial component this provides an explanation as to why the root music is superior to the spectral music algorithm

self diffusion of spherical brownian particles with hard core interaction abstract the n particle smoluchowski equation is solved exactly for a system of spherical brownian particles interacting through hard core potentials to first order in the volume concentration the self diffusion coefficient is found to be given by d s d 0 1 2 where d 0 is the free diffusion constant the hydrodynamic interaction is then taken into account in a perturbative way using the oseen approximation d s d 0 1 0 09 is found whereas the improved form for the hydrodynamic interaction due to felderhof gives d s d 0 1 1 89

projective properties of certain orthogonal arrays summary a question of importance in factor screening is when a two level orthogonal design for a multifactor experiment can be projected into lower dimension typically p 2 or 3 new results relate to the projectivity p of saturated designs in which n 1 factors are tested in n runs it is shown that a design obtained by doubling an n x n orthogonal array is always of projectivity p 2 a twolevel cyclic design is either a factorial array and hence has p 2 or it has p 3 a two level orthogonal design with 4m runs m odd has p 3 in particular these results allow the designs derived by plackett burman 1946 to be categorised in terms of these projective properties

array interpolation and bias reduction interpolation mapping of data from a given antenna array onto the output of a virtual array of more suitable configuration is well known in array signal processing this operation allows arrays of any geometry to be used with fast direction of arrival doa estimators designed for linear arrays conditions for preserving doa error variance under such mappings have been derived by several authors however in many cases such as omnidirectional signal surveillance over multiple octaves systematic mapping errors will dominate over noise effects and cause significant bias in the doa estimates to prevent mapping errors from unduly affecting the doa estimates this paper uses a geometrical interpretation of a taylor series expansion of the doa estimator criterion function to derive an alternative design of the mapping matrix verifying simulations show significant bias reduction in the doa estimates compared with previous designs the key feature of the proposed design is that it takes into account the orthogonality between the manifold mapping errors and certain gradients of the estimator criterion function with the new design mapping of narrowband signals between dissimilar array geometries over wide sectors and large frequency ranges becomes feasible

projection properties of plackett and burman designs the projection properties of the 2 r q p fractional factorials are well known and have been used effectively in a number of published examples of experimental investigations the plackett and burman designs also have interesting projective properties knowledge of which allows the experimenter to follow up an initial plackett and burman design with runs that increase the initial resolution for the factors that appear to matter and thus permit efficient separation of effects of interest projections of designs into 2 5 dimensions are discussed and the 12 run case is given in detail a numerical example illustrates the practical uses of these projections

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

the cramer rao bound on frequency estimates of signals closely spaced in frequency unconditional case the paper analyzes the cramer rao cr bound on frequency estimation covariance for the unconditional or stochastic signal model it addresses the problem of n signals closely spaced in temporal or spatial frequency the main result is that for this regime the cr bound decomposes into a product of simple scalar factors that individually reflect frequency separation signal powers and covariances data sampling grid and sample size the factored expression provides useful insight into the behavior of the bound for closely spaced frequencies the result also leads to a new formula for the signal to noise snr threshold at which an unbiased frequency estimator can resolve signals closely spaced in frequency interestingly with a simple modification the formulae are identical to those recently obtained for the conditional or deterministic signal model

hidden projection properties of some nonregular fractional factorial designs and their applications in factor screening often only a few factors among a large pool of potential factors are active under such assumption of effect sparsity in choosing a design for factor screening it is important to consider projections of the design onto small subsets of factors cheng showed that as long as the run size of a two level orthogonal array of strength two is not a multiple of 8 its projection onto any four factors allows the estimation of all the main effects and two factor interactions when the higher order interactions are negligible this result applies for example to all plackett burman designs whose run sizes are not multiples of 8 it is shown here that the same hidden projection property also holds for paley designs of sizes greater than 8 even when their run sizes are multiples of 8 a key result is that such designs do not have defining words of length three or four applications of this result to the construction of e s 2 optimal supersaturated designs are also discussed in particular certain designs constructed by using wu s method are shown to be e s 2 optimal the article concludes with some three level designs with good projection properties

dynamic computer simulation of concentrated hard sphere suspensions ii re analysis of mean square displacement data in view of recent theoretical results by cichocki and felderhof we reevaluate previously published simulation data for the mean square displacement of a particle in a hard sphere suspension without hydrodynamic interactions this new evaluation is consistent with the theoretically predicted algebraic long time tails we observe better agreement for dense systems and obtain values for the relaxation time almost twice as large as previously

projective three level main effects designs robust to model uncertainty this paper is concerned with designing experiments under the assumption that an analysis strategy is used that considers interactions in addition to main effects a criterion which averages an approximation to as efficiency over lower dimensional projections of the design is introduced to compare designs a columnwise design procedure is used to construct three level designs for six factors in 18 runs the projection efficiencies of these designs are explored and compared with designs obtained from the l 18 orthogonal array results are also given for designs with 14 and 17 runs

rotational velocity autocorrelation function of interacting brownian particles recently hagen frenkel and lowe physica a 272 1999 376 have obtained interesting simulation data for the rotational velocity autocorrelation function of a selected particle in a dense suspension of interacting spherical brownian particles although a wide time interval was studied it was found that the correlation function had not yet settled down to its t 5 2 long time tail at the longest time considered in the following analysis the method of pade approximants is applied to the laplace transform of the correlation function a dierent value for the coecient of the long time tail is obtained than found by hagen et al by extrapolation a prediction is made for the behavior of the correlation function outside the range of presently available data c 2001 elsevier science b v all rights reserved

on the cramer rao bound for direction finding of correlated signals in this paper we present compact closed form formulas for the cramer rao bound corresponding to the joint estimation of the directions of arrival the signal covariance matrix and the noise variance using these formulas we investigate the effect of signal correlation on the achievable accuracy of direction finding system in a correlated signal environment as expected estimation accuracy decreases with increasing correlation magnitude we observe that under certain conditions small aperture high correlation magnitude correlation phase has a strong effect on doa estimation accuracy

a new optimization technique for adaptive antenna arrays an adaptive nulling algorithm for adjusting the array weights under the soft constraint of the weight norm being very much less than 1 or equal to 1 based on the measured correlations between the array and element outputs is described the algorithm can be regarded as an extension of the constrained least mean square algorithm it is derived from the same concept of signal and noise subspaces defined in the multiple signal classification music algorithm one of the unique features of the present algorithm is that the number of the iterations required to adapt the array weights to form nulls is exactly equal to the number of interferers

linear kinetic theory of a suspension of interacting brownian particles i enskog renormalization abstract time dependent equilibrium correlation functions for interacting brownian particles are analyzed to this end the kinetic theory method recently proposed by blawzdziewicz and cichocki is used the elementary processes i e single particle diffusion and many particle interactions contributing to the evolution of the time correlation functions are renormalized by the equilibrium correlations the final result which corresponds to the enskog renormalization in the kinetic theory of fluids is a convenient tool for an analysis of dynamical properties of dense suspensions

dynamic equivalence between soft and hard core brownian fluids in this work we demonstrate the dynamic equivalence between the members of the family of brownian fluids whose particles interact through strongly repulsive radially symmetric soft core potentials we specifically consider pair potentials proportional to inverse powers of r sigma this equivalence is the dynamic extension of the static equivalence between all these pair potentials and the hard sphere fluid assumed in the treatment of soft core reference potentials in the classical weeks chandler andersen or barker henderson perturbation theories of simple liquids in contrast with the strict hard sphere brownian system in the case of soft sphere potentials the conventional brownian dynamics algorithm is indeed well defined we find that except for small values of nu and or very short times the dynamic properties of all these systems collapse into a single universal curve upon a well defined rescaling of the time and distance variables this family of systems includes the hard sphere limit this observation permits a conceptually simple new and accurate brownian dynamics algorithm to simulate the dynamic properties of the hard sphere model dispersion without hydrodynamic interactions such an algorithm consists of the straightforward rescaling of the brownian dynamics simulated properties of any of the dynamically equivalent soft sphere systems

slow dynamics of linear relaxation systems abstract linear relaxation occurring in dielectrics viscoelastic fluids and many other systems is often characterized by a broad continuous spectrum we show that the relaxation behavior may be analyzed effectively by means of n point pade approximants applied in the complex plane of the square root of frequency the method leads to a compact analytic expression for the laplace transform of the relaxation function characterized by a small number of poles and their residues in the square root of frequency plane we study the method in detail for a model of diffusion in three dimensions with a single or double radial potential barrier and demonstrate its use in the analysis of the viscoelastic relaxation spectrum of polyisobutylene

tracking an unknown time varying number of speakers using tdoa measurements a random finite set approach speaker location estimation techniques based on time difference of arrival measurements have attracted much attention recently many existing localization ideas assume that only one speaker is active at a time in this paper we focus on a more realistic assumption that the number of active speakers is unknown and time varying such an assumption results in a more complex localization problem and we employ the random finite set rfs theory to deal with that problem the rfs concepts provide us with an effective solid foundation where the multispeaker locations and the number of speakers are integrated to form a single set valued variable by applying a sequential monte carlo implementation we develop a bayesian rfs filter that simultaneously tracks the time varying speaker locations and number of speakers the tracking capability of the proposed filter is demonstrated in simulated reverberant environments

reduced complexity maximum likelihood direction of arrival estimation based on spatial aliasing spatial aliasing is an undesirable phenomenon that prevents the unique determination of the direction of arrival doa of impinging signals in array signal processing however the characteristics of spatial aliasing that generates ambiguous doas can be also used to reduce the computational complexity in maximum likelihood ml doa estimation this paper proposes a structural method to dramatically reduce the computational complexity of the ml doa estimation using the spatial aliasing generated by a nested array structure with a doubly scaled aper ture an ml full grid search is computationally simplified by the highly compressed searching range and the small number of candidate values to be searched which are derived based on spatial aliasing performance analyses based on the theoretical bounds and computational complexity with computer simulations show that the proposed method requires an extremely reduced computational load compared to the conventional ml doa estimation with a uniform linear array ula while achieving the performance enhancement in the estimation accuracy due to the enlarged array aperture

wavefield modeling and array processing ii algorithms for pt i see ibid vol 42 no 10 p 2549 1994 we present several novel algorithms for array processing as well as extensions of existing methods based on this approach we first consider the problem of localization of wideband sources via coherent processing and show how wavefield modeling enables us to derive expressions for the frequency transformation focusing matrices this method is extended to three dimensions and to sector processing we then develop computationally efficient implementations of music and root music for the narrowband and the coherent and incoherent wideband cases as well as a natural extension of root music to any 2 d array in addition wavefield modeling allows us for the first time to extend root music to 3 d arrays and wavefields we also present a low complexity variant of root music for direction finding within a limited angular sector finally we derive a low dimensional sufficient statistic and reduced rank processing schemes for the case of oversampled arrays and or limited angular sector scenarios

performance analysis of multi dimensional esprit type algorithms for arbitrary and strictly non circular sources with spatial smoothing spatial smoothing is a widely used preprocessing scheme to improve the performance of high resolution parameter estimation algorithms in case of coherent signals or if only a small number of snapshots is available in this paper we present a first order performance analysis of the spatially smoothed versions of r d standard esprit and r d unitary esprit for sources with arbitrary signal constellations as well as r d nc standard esprit and r d nc unitary esprit for strictly second order so non circular nc sources the derived expressions are asymptotic in the effective signal to noise ratio snr i e the approximations become exact for either high snrs or a large sample size moreover no assumptions on the noise statistics are required apart from a zero mean and finite so moments we show that both r d nc esprit type algorithms with spatial smoothing perform asymptotically identical in the high effective snr regime generally the performance of spatial smoothing based algorithms depends on the number of subarrays which is a design parameter that needs to be chosen beforehand in order to gain more insights into the optimal choice of the number of subarrays we simplify the derived analytical r d mean square error mse expressions for the special case of a single source the obtained mse expression explicitly depends on the number of subarrays in each dimension which allows us to analytically find the optimal number of subarrays for spatial smoothing based on this result we additionally derive the maximum asymptotic gain from spatial smoothing and compute the asymptotic efficiency for the single source case in closed form all the analytical results are verified by simulations

blocking in compound dispersion experiments in quality design a dispersion experiment attempts to estimate the effects of control factors on the dispersion introduced by error factors that is the effect of product design on the stability of the performance of the product as its operating environment changes in conducting a dispersion experiment it is important to distinguish the sources of dispersion that one wishes to control from extraneous sources of dispersion so blocking is often necessary this is especially true when the quality or utility of a product is appraised subjectively as in conjoint analysis compound designs for dispersion experiments are orthogonal array designs that generalize taguchi s direct product designs compared to direct product designs compound designs are often stronger for a given size or smaller for a given strength this article discusses blocked compound dispersion experiments providing that blocks form an orthogonal array of strength 1 for the error factors dispersion within blocks may be pooled to estima

optimal fractions of two level factorials under a baseline parameterization two level fractional factorial designs are considered under a baseline parameterization the criterion of minimum aberration is formulated in this context and optimal designs under this criterion are investigated the underlying theory and the concept of isomorphism turn out to be significantly different from their counterparts under orthogonal parameterization and this is reflected in the optimal designs obtained copyright 2012 oxford university press

estimation of multicomponent polynomial phase signals impinging on a multisensor array using state space modeling this contribution addresses the problem of estimating the parameters of multicomponent polynomial phase signals when impinging on a multisensor array an original approach is proposed based on a state space modelization of the signal and the application of an extended kalman filter for the state estimation the use of a multisensor array allows the exploitation of a spatial information and leads to the consideration of multiple filters with different observation equations computer simulations are used to demonstrate the effectiveness of the proposed algorithm

optimal foldover plans for two level nonregular orthogonal designs this article considers optimal foldover plans for nonregular designs by using the indicator function we define words with fractional lengths the extended word length pattern is then used to select among nonregular foldover designs some general properties of foldover designs are obtained using the indicator function we prove that the full foldover plan that reverses the signs of all factors is optimal for all 12 run and 20 run orthogonal designs the optimal foldover plans for all 16 run regular and nonregular orthogonal designs are constructed and tabulated for practical use optimal foldover plans for higher order orthogonal designs can be constructed in a similar manner

transitions between wells and escape by diffusion in a one dimensional potential landscape abstract the time dependence of the occupation probabilities of neighboring wells due to diffusion in one dimension is formulated in terms of a set of generalized rate equations describing transitions between neighboring wells and escape across a final barrier the equations contain rate coefficients memory coefficients and a long time coefficient characterizing the amplitude of long time decay on a more microscopic level the stochastic process is described by a smoluchowski equation for the one dimensional probability distribution a numerical procedure is presented which allows calculation of the transport coefficients in the set of generalized rate equations on the basis of the smoluchowski equation