relating continuous and discrete pepa models of signalling pathways pepa and its semantics have recently been extended to model biological systems in order to cope with massive quantities of processes as is usually the case when considering biological reactions the model is interpreted in terms of a small set of coupled ordinary differential equations odes instead of a large state space continuous time markov chain ctmc so far the relationship between these two semantics of pepa had not been established this is the goal of the present paper after introducing a new extension of pepa denoted email protected that allows models to capture both mass action law and bounded capacity law cooperations the relationship between these two semantics is demonstrated the result relies on kurtz s theorem that expresses that a set of odes can be in some sense considered as the limit of pure jump markov processes

fluid computation of passage time distributions in large markov models recent developments in the analysis of large markov models facilitate the fast approximation of transient characteristics of the underlying stochastic process fluid analysis makes it possible to consider previously intractable models whose underlying discrete state space grows exponentially as model components are added in this work we show how fluid approximation techniques may be used to extract passage time measures from performance models we focus on two types of passage measure passage times involving individual components as well as passage times which capture the time taken for a population of components to evolve specifically we show that for models of sufficient scale global passage time distributions can be well approximated by a deterministic fluid derived passage time measure where models are not of sufficient scale we are able to generate upper and lower approximations for the entire cumulative distribution function of these passage time random variables using moment based techniques additionally we show that for passage time measures involving individual components the cumulative distribution function can be directly approximated by fluid techniques finally using the gpa tool we take advantage of the rapid fluid computation of passage times to show how a multi class client server system can be optimised to satisfy multiple service level agreements

a fluid analysis framework for a markovian process algebra markovian process algebras such as pepa and stochastic p calculus bring a powerful compositional approach to the performance modelling of complex systems however the models generated by process algebras as with other interleaving formalisms are susceptible to the state space explosion problem models with only a modest number of process algebra terms can easily generate so many states that they are all but intractable to traditional solution techniques previous work aimed at addressing this problem has presented a fluid flow approximation allowing the analysis of systems which would otherwise be inaccessible to achieve this systems of ordinary differential equations describing the fluid flow of the stochastic process algebra model are generated informally in this paper we show formally that for a large class of models this fluid flow analysis can be directly derived from the stochastic process algebra model as an approximation to the mean number of component types within the model the nature of the fluid approximation is derived and characterised by direct comparison with the chapman kolmogorov equations underlying the markov model furthermore we compare the fluid approximation with the exact solution using stochastic simulation and we are able to demonstrate that it is a very accurate approximation in many cases for the first time we also show how to extend these techniques naturally to generate systems of differential equations approximating higher order moments of model component counts these are important performance characteristics for estimating for instance the variance of the component counts this is very necessary if we are to understand how precise the fluid flow calculation is in a given modelling situation

direction of arrival estimation using parametric signal models we consider the problem of estimating the directions of arrival doas of narrowband sources with known center frequency the paper evaluates the potential improvement in estimation accuracy by using spatial temporal processing for signals obeying a deterministic parametric model one would expect that prior information about the temporal structure of the signals will yield some gain in performance by deriving the cramer rao bound crb on the doa estimates we quantify this gain and identify the cases for which the gain is significant we show that for the single source case spatial temporal processing does not yield any gain in performance relative to conventional spatial processing for multiple noncoherent signals incorporating temporal processing can achieve the single source performance yielding a significant gain for the case of multiple sources with small spatial separation relative to the beamwidth of the array however spatial temporal processing cannot yield any gain in performance for multiple coherent signals

noisy input output system identification using cumulants and the steiglitz mcbride algorithm we consider the problem of identifying a linear time invariant system from its noisy input output data the input and output are assumed to be non gaussian while the input and output noises are assumed to be mutually correlated colored and gaussian using third order cross and auto cumulants we extend the well known steiglitz mcbride 1965 identification method to cumulant domains and show that it is consistent under a certain third order persistency of excitation condition by comparison the steiglitz mcbride method is not consistent when either input noise is present or when the output noise is colored for an empirical assessment we provide simulations that demonstrate the proposed method s usefulness

the steiglitz mcbride identification algorithm revisited convergence analysis and accuracy aspects the convergence and accuracy properties of the steiglitz and mcbride identification method are examined the analysis is valid for a sufficiently large number of data it is shown that the method can converge to the true parameter vector only when the additive output noise is white in that case the method is proved to be locally convergent to the true parameters the global convergence properties are also investigated it is pointed out that the method is not always globally convergent some sufficient conditions guaranteeing global convergence are given assuming convergence takes place the estimates are shown to be asymptotically gaussian distributed an explicit expression is given for their asymptotic covariance matrix

linear prediction approach to direction estimation of cyclostationary signals in multipath environment we investigate the estimation of the directions of arrival doa of closely spaced narrowband cyclostationary signals in the presence of multipath propagation by exploiting the spatial and temporal properties of most communication signals we propose a new cyclic forward backward linear prediction fblp approach for coherent signals impinging on a uniform linear array ula in the proposed algorithm the evaluation of the cyclic array covariance matrix is avoided and the difficulty of choosing the optimal time lag parameter is alleviated as a result the proposed approach has two advantages 1 the computational load is relatively reduced and 2 the robustness of estimation is significantly improved the performance of the proposed approach is confirmed through numerical examples and it is shown that this approach is superior in resolving the closely spaced coherent signals with a small length of array data and at relatively low signal to noise ratio snr

decentralized control design for large scale systems with strong interconnections using neural networks we propose a decentralized neural network nn controller for a class of large scale nonlinear systems with the strong interconnections the nns are used to approximate the unknown subsystems and interconnections due to the functional approximation capabilities of nns the additional precautions are not required to be made for avoiding the possible control singularity problems semiglobal asymptotic stability results are obtained and the tracking error converges to zero furthermore the issue of transient performance of the subsystems is also addressed under an analytical framework

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

decentralized state feedback stabilization and robust control of uncertain large scale systems with integrally constrained interconnections abstract this paper is concerned with a problem of stabilization and robust control design for interconnected uncertain systems a new class of uncertain large scale systems is considered in which interconnections between subsystems as well as uncertainties in each subsystem are described by integral quadratic constraints the problem is to design a set of local decentralized controllers which stabilize the overall system and guarantee robust disturbance attenuation in the presence of the uncertainty in interconnections between subsystems as well as in each subsystem the paper presents necessary and sufficient conditions for the existence of such a controller the proposed design is based on recent absolute stabilization and minimax optimal control results and employs solutions of a set of game type riccati algebraic equations arising in h control

analysis of joint angle frequency estimation using esprit high resolution parameter estimation techniques have been applied to jointly estimate multiple signal parameters we consider the problem of determining the directions and center frequencies of a number of narrowband sources in a band of interest we present a joint angle frequency estimation method based on the multidimensional esprit algorithm a perturbation error analysis gives bounds on the parameter estimates and provides optimal values for the temporal and spatial smoothing parameters the analysis is shown to be consistent with simulation results

design of nonlinear interconnections guaranteeing the absence of periodic solutions abstract in this paper a novel methodology for scheming interconnection structure for a class of nonlinearly interconnected systems is proposed to guarantee the absence of a specific kind of periodic solutions those types of systems can be viewed as an interconnection of single input single output isolated subsystems with the interconnection structure specified by a square matrix frequency domain inequalities conditions as well as linear matrix inequalities lmis conditions for nonexistence of limit cycles of the second kind in the entire interconnected system are established the main results also define the frequency range on which cycles of the second kind of the system cannot exist based on this lmi approach an estimate of the largest bound of the frequency of cycles of the second kind can be explicitly computed by solving a generalized eigenvalue minimization problem numerical results show the effect of the nonlinear interaction on system behavior and the applicability and validity of the proposed method

h spl infin decentralized fuzzy model reference tracking control design for nonlinear interconnected systems in general due to the interactions among subsystems it is difficult to design an h sub spl infin decentralized controller for nonlinear interconnected systems the model reference tracking control problem of nonlinear interconnected systems is studied via h sub spl infin decentralized fuzzy control method first the nonlinear interconnected system is represented by an equivalent takagi sugeno type fuzzy model a state feedback decentralized fuzzy control scheme is developed to override the external disturbances such that the h spl infin model reference tracking performance is achieved furthermore the stability of the nonlinear interconnected systems is also guaranteed if states are not all available a decentralized fuzzy observer is proposed to estimate the states of each subsystem for decentralized control consequently a fuzzy observer based state feedback decentralized fuzzy controller is proposed to solve the h sub spl infin tracking control design problem for nonlinear interconnected systems the problem of h sub spl infin decentralized fuzzy tracking control design for nonlinear interconnected systems is characterized in terms of solving an eigenvalue problem evp the evp can be solved very efficiently using convex optimization techniques finally simulation examples are given to illustrate the tracking performance of the proposed methods

on the number of signals resolvable by a uniform linear array an algebraic limitation on the maximum number of directions of arrival of plane waves that can be resolved by a uniform linear sensor array is studied achievable lower and upper bounds are derived on that number as a function of the number of elements in the array number of snapshots and the rank of the source sample correlation matrix the signals are assumed narrow band and of identical and known center frequency the results are also applicable in the coherent signal case and when directions of arrival are estimated from few snapshots while in the multiple snapshot case the lower bounds coincide with known asymptotic results the upper bounds indicate the potential for resolving more signals than by present methods of array processing

turning back time in markovian process algebra product form solutions in markovian process algebra mpa are constructed using properties of reversed processes the compositionality of mpas is directly exploited allowing a large class of hierarchically constructed systems to be solved for their state probabilities at equilibrium the paper contains new results on both reversed stationary markov processes as well as mpa itself and includes a mechanisable proof in mpa notation of jackson s theorem for product form queueing networks several examples are used to illustrate the approach

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

a new state space approach for direction finding direction of arrival estimation using state space models in sensor array processing with a uniform linear array can be reduced to finding a solution to the equation u spl tilde sub 1 f spl ap u spl tilde sub 2 for f where noises in both sides of the equation are highly correlated least squares or even total least squares solutions are not optimal and the complicated covariance structure in u spl tilde sub 1 and u spl tilde sub 2 does not allow a weighted total least squares procedure to be carried out the approach presented in this correspondence is to first solve a least squares problem to get an estimate of the underlying subspace represented by the noisy basis vectors in u spl tilde sub 1 and u spl tilde sub 2 an approximate error covariance matrix for the least squares problem is obtained using a first order perturbation expansion this covariance matrix is used to solve for the underlying subspace in a weighted least squares sense parameters are then extracted from the estimated subspace numerical examples show that the performance of the proposed method is very close to the cramer rao bound

decorrelation performance of deese and spatial smoothing techniques for direction of arrival problems second order spatial analysis methods for array signal processing have been shown to yield high resolution by exploiting specific eigenstructure properties of the array output covariance matrix however when some of the signals are coherent these covariance based methods face serious difficulties produced by smaller rank in this correspondence a theoretical expression is derived for the effective correlation coefficient between sources after processing when using spatial smoothing and a new scheme of space diversity called deese decomposition de l espace source estime monte carlo simulations have been used to compare deese and spatial smoothing and to show the advantages of using deese when noise is present

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

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

doa estimation for mixed signals in the presence of mutual coupling in this paper a new direction of arrival doa estimation method is proposed in the presence of unknown mutual coupling the impinging signals are a mixture of signals in different correlation degrees which are uncorrelated partially correlated or coherent with each other the method proceeds in three steps the noncoherent uncorrelated or partially correlated signals are firstly estimated with unknown mutual coupling then these estimates are utilized to get the mutual coupling coefficients finally by eliminating the contributions of the noncoherent signals and compensating the mutual coupling effect only coherent signals remain to be estimated this method is simple but effective and does not need iterative processing simulation results demonstrate the effectiveness and performance of the proposed method

efficient maximum likelihood doa estimation for signals with known waveforms in the presence of multipath we present a large sample maximum likelihood ml algorithm for estimating the directions of arrival doa s and signal amplitudes of known possibly coherent signals impinging on an array of sensors the algorithm is an extension of the deml method of li et al that handles coherent multipath that may be present in the signals the algorithm is computationally efficient because the nonlinear minimization step decouples into a set of minimizations of smaller dimension

doa estimation by exploiting the symmetric configuration of uniform linear array a new direction of arrival doa estimation method is proposed for uniform linear array in this paper when both uncorrelated and coherent sources are present the uncorrelated and coherent sources are estimated at two different stages the uncorrelated sources are first estimated using conventional subspace methods and then they are eliminated by exploiting the symmetric configuration of the array finally the remaining coherent sources are estimated by reconstructing a non toeplitz matrix the number of sources resolved by our method can exceed the number of array elements simulation results demonstrate the effectiveness and efficiency of our proposed method

a modified cumulant matrix for doa estimation presents a modification of the fourth order cumulant matrix c sub g proposed by one source the modification consists of taking certain submatrices of c sub g and using them to apply the esprit principle with general arrays which may not be composed of matched sensor doublets or to perform spatial smoothing to deal with the coherent sources in the cumulant domain computer simulations are carried out to illustrate the effectiveness of the modified cumulant matrix

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

on information theoretic criteria for determining the number of signals in high resolution array processing an important problem in high resolution array processing is the determination of the number of signals arriving at the array information theoretic criteria provide a means to achieve this two commonly used criteria are the akaike information criterion aic and minimum descriptive length mdl criterion while the aic tends to overestimate even at a high signal to noise ratio snr the mdl criterion tends to underestimate at low or moderate snr by excluding irrelevant parameters a new log likelihood function has been chosen utilizing this new log likelihood function gives a set of more accurate estimates of the eigenvalues and in the establishment of modified information theoretic criteria which moderate the performance of the aic and the mdl criterion computer simulations confirm that the modified criteria have superior performance

complex amplitude estimation in the known steering matrix and generalized waveform case we consider a special growth curve sgc model with a known steering matrix and generalized waveform in the presence of unknown interference and noise several estimators of the complex amplitude based on this model are derived including the methods of approximate maximum likelihood aml minimum variance distortionless response mvdr and amplitude and phase estimation apes we analyze the statistical properties of these estimators and show that in the presence of temporally white but spatially correlated noise and interference aml is asymptotically statistically efficient for a large snapshot number while mvdr and apes are asymptotically equivalent but not statistically efficient via several numerical examples we also show that when the noise and interference are both spatially and temporally correlated the apes estimator can achieve better estimation accuracy and exhibit greater robustness than the other methods

efficient estimation of a narrow band polynomial phase signal impinging on a sensor array the parameters of interest of a polynomial phase signal observed by a sensor array include the direction of arrival and the polynomial coefficients the direct maximum likelihood estimation of these parameters requires a nonlinear multidimensional search in this paper we present a two step estimation approach the estimation requires only a one dimensional search in the direction of arrival space and involves a simple least squares solution for the polynomial coefficients the efficiency of the estimates is corroborated by monte carlo simulations

efficient direction finding methods employing forward backward averaging in this paper we develop a general approach for reducing the computational complexity of any direction finding method implemented with forward backward fb averaging we develop simplified fb data matrices in a manner paralleling previous work related to centrohermitian correlation matrices based on these simplified data matrices efficient construction and updating of the fb correlation matrix is developed in addition efficient fb fft fb beamspace fb evd updating fb svd and fb svd updating methods are derived in most cases fb based direction finding methods can be simplified so that the computational complexity is reduced below that of an analogous forward only implementation thus effectively twice the amount of data is processed with less total computation

a tree structure one dimensional based algorithm for estimating the two dimensional direction of arrivals and its performance analysis a tree structure algorithm using one dimensional 1d multiple signal classification music algorithm is proposed to estimate the two dimensional direction of arrivals 2d doas of coherent signals impinging on a uniform rectangular array the basic idea of the proposed algorithm is to successively apply several times of the 1d spatial smoothing music algorithm in tree structure to estimate the azimuth and the elevation angles independently to optimally separate the receive signal constrained spatial beamformers with adjustable null width are exploited in conjunction with the 1d spatial smoothing music algorithm to decompose the received signal into several signals each lead by its own 2d doa performance analysis is provided to investigate the estimation bias caused by the residue signal propagating in the tree structure

performance analysis for finite sample mvdr beamformer with forward backward processing the employment of forward backward fb processing to both batch and adaptive beamformers provides a superior performance than the forward only fo algorithm based on the finite sample minimum variance distortionless response mvdr beamformer a set of closed form expressions for the variance of the weight vector the output signal to interference plus noise ratio sinr and the mean square error mse is derived for both fb and fo algorithms as shown in our analysis all errors of the fb algorithm are only approximately half of the fo case

array signal processing in the known waveform and steering vector case the amplitude estimation of a signal that is known only up to an unknown scaling factor with interference and noise present is of interest in several applications including using the emerging quadrupole resonance qr technology for explosive detection in such applications a sensor array is often deployed for interference suppression this paper considers the complex amplitude estimation of a known waveform signal whose array response is also known a priori two approaches viz the capon and the maximum likelihood ml methods are considered for the signal amplitude estimation in the presence of temporally white but spatially colored interference and noise we derive closed form expressions for the expected values and mean squared errors mses of the two estimators a comparative study shows that the ml estimate is unbiased whereas the capon estimate is biased downwards for finite data sample lengths we show that both methods are asymptotically statistically efficient when the number of data samples is large but not when the signal to noise ratio snr is high furthermore we consider a more general scenario where the interference and noise are both spatially and temporally correlated we model the interference and noise vector as a multichannel autoregressive ar random process an alternating least squares als method for parameter estimation is presented we show that in most cases the als method is superior to the model mismatched ml m sup 3 l method which ignores the temporal correlation of the interference and noise

semidefinite programming duality and linear time invariant systems several important problems in control theory can be reformulated as semidefinite programming problems i e minimization of a linear objective subject to linear matrix inequality lmi constraints from convex optimization duality theory conditions for infeasibility of the lmis as well as dual optimization problems can be formulated these can in turn be reinterpreted in control or system theoretic terms often yielding new results or new proofs for existing results from control theory we explore such connections for a few problems associated with linear time invariant systems

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

exact fluid lumpability in markovian process algebra quantitative analysis by means of discrete state stochastic processes is hindered by the well known phenomenon of state space explosion whereby the size of the state space may have an exponential growth with the number of agents of the system under scrutiny when the stochastic process underlies a markovian process algebra model this problem may be alleviated by suitable notions of behavioural equivalence that induce lumping at the underlying continuous time markov chain establishing an exact relation between a potentially much smaller aggregated chain and the original one for the analysis of massively parallel systems however lumping techniques may not be sufficient to yield a computationally tractable problem recently much work has been directed towards forms of fluid techniques that provide a set of ordinary differential equations odes approximating the expected path of the stochastic process unfortunately even fluid models of realistic systems may be too large for feasible analysis this paper studies a behavioural relation for process algebra with fluid semantics called projected label equivalence which is shown to yield an exactly fluid lumpable model i e an aggregated ode system which can be related to the original one without any loss of information project label equivalence relates sequential components of a process term in general for any two sequential components that are related in the fluid sense nothing can be said about their relationship from the stochastic viewpoint we define and study a notion of well posedness which allows us to relate fluid lumpability to the stochastic notion of semi isomorphism which is a weaker version of the common notion of isomorphism between the doubly labelled transition systems at the basis of the markovian interpretation

a diagonal growth curve model and some signal processing applications we consider a variation of the growth curve gc model referred to as the diagonal growth curve dgc model where the steering vectors and waveforms are both known and the complex amplitude matrix is constrained to be diagonal a closed form approximate maximum likelihood aml estimator for this model is derived based on the maximum likelihood principle we analyze the statistical properties of this method theoretically and show that the aml estimate is unbiased and asymptotically statistically efficient for a large snapshot number via several numerical examples in array signal processing and spectral analysis we also show that the proposed aml estimator can achieve better estimation accuracy and exhibit greater robustness than the best existing methods

two dimensional direction estimation for a mixture of noncoherent and coherent signals this paper deals with the two dimensional 2 d direction of arrival doa estimation of a mixture of noncoherent including uncorrelated and partially correlated and coherent i e fully correlated narrowband signals impinging on a planar sensor array composed of two parallel uniform linear arrays ulas an oblique projection based approach for 2 d direction estimation opade is proposed by using some cross correlations between the received array data in the proposed opade the oblique projection is utilized to isolate the coherent signals from the noncoherent ones and the effect of additive noise is alleviated while the computationally intensive eigendecomposition is avoided and the estimated elevation and azimuth angles are paired automatically further an iterative alternating scheme is presented to improve the estimation accuracy of the oblique projector and hence that of the doas of coherent signals the cramer rao lower bound crb for the mixture of noncoherent and coherent signals is also derived explicitly where the prior knowledge of the signal correlation is incorporated into the 2 d doa estimation of noncoherent signals finally the effectiveness of the opade and the theoretical analysis are substantiated through 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

spatial spectrum estimation in a coherent signal environment using an array in motion spatial spectrum estimation utilizing an array in motion is here investigated for dealing with coherent arrivals in a multiple signal environment the effect of estimating the spatial correlations while the array is moving is studied in terms of the decorrelation it produces the change it causes in the eigenvalues of the correlation matrix and the improvements obtained in the measured spectrum cases of both fixed and varying angle of arrival are investigated the former arises with distant sources and will with a sufficiently long estimation interval emulate uncorrelated sources and given correspondingly sharp spectra the latter arises with nearby sources and will allow them to be distinguished but will be attended by spectral shift and broadening and loss of resolution it is shown that meaningful estimates of the arrival angles can nevertheless be made specific illustrations are worked out using a seven element sparse nonuniformly spaced linear array utilizing the well known superresolution spectral estimators the maximum likelihood ml method the method of linear prediction lp and the method of multiple signal classification music

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

a low complexity blind estimator of narrowband polynomial phase signals consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array in practice it is difficult to maintain a precisely calibrated array the array manifold is then assumed to be unknown and the estimation is referred to as blind estimation to date only an approximated maximum likelihood estimator amle was suggested for blindly estimating the polynomial coefficients of each signal however this estimator requires a multidimensional search over the entire coefficient space instead we propose an estimation approach which is based on two steps first the signals are separated using a blind source separation technique which exploits the constant modulus property of the signals then the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal this estimator does not involve any search in the coefficient spaces the computational complexity of the proposed estimator increases linearly with respect to the polynomial order whereas that of the amle increases exponentially simulation results show that the proposed estimator achieves the cramer rao lower bound at moderate or high signal to noise ratio

a new simultaneous estimation of directions of arrival and channel parameters in a multipath environment we present two new blind techniques for simultaneous estimation of the direction of arrival doa and the channel parameters for a uniform linear array in a multipath environment the first method is based on the sum of weighted complex exponentials and pade spl acute approximation and the second method determines the transfer function of a linear time invariant system given its impulse response for each method we introduce a rational function whose complex poles contain the desired doa the magnitude of its residues are the channel gains and the phase of its residues are in terms of the channel delays we also derive and numerically evaluate the pertinent crame spl acute r rao lower bound crlb for the estimation process our error analysis based on a perturbation series formulation of the parameter estimation reveals that doa and the channel parameters are extracted from a gaussian signal dependent noise for both methods the amount of computations are also determined some simulations are provided to assess the capabilities of the new methods

a unitary transformation method for angle of arrival estimation eigenstructure methods for estimating angles of arrival of radiation sources generally require complex computations in computing eigencomponents of the covariance matrix and calculating the search function a unitary transformation method that transforms the complex covariance matrix of an equally spaced linear array which is hermitian persymmetric and the complex search vector into a real symmetric matrix and a real vector respectively is presented both tasks can be accomplished by real computations the sampled covariance matrix available is not persymmetric to suit the unitary transformation method a persymmetrized estimator of the sampled covariance matrix which is optimal in the sense of euclidean distance is proposed

unitary esprit how to obtain increased estimation accuracy with a reduced computational burden esprit is a high resolution signal parameter estimation technique based on the translational invariance structure of a sensor array previous esprit algorithms do not use the fact that the operator representing the phase delays between the two subarrays is unitary the authors present a simple and efficient method to constrain the estimated phase factors to the unit circle if centro symmetric array configurations are used unitary esprit the resulting closed form algorithm has an esprit like structure except for the fact that it is formulated in terms of real valued computations throughout since the dimension of the matrices is not increased this completely real valued algorithm achieves a substantial reduction of the computational complexity furthermore unitary esprit incorporates forward backward averaging leading to an improved performance compared to the standard esprit algorithm especially for correlated source signals like standard esprit unitary esprit offers an inexpensive possibility to reconstruct the impinging wavefronts signal copy these signal estimates are more accurate since unitary esprit improves the underlying signal subspace estimates simulations confirm that even for uncorrelated signals the standard esprit algorithm needs twice the number of snapshots to achieve a precision comparable to that of unitary esprit thus unitary esprit provides increased estimation accuracy with a reduced computational burden

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

estimation of fading coefficients in the presence of multipath propagation in order to get the information about multipath propagation this communication presents two estimation methods for slowly varying fading coefficients with known numbers of the far field sources and multipaths from each far field source the fading coefficients in multipath propagation can be well estimated the methods not only have low complexity but also have high performance and the fading coefficients can be resolved directly without a searching procedure afterwards we make an extension to further improve the estimation accuracy of both direction of arrival doa and fading coefficients after obtaining their estimations the cramer rao bound crb for this problem is also deduced simulation results demonstrate the effectiveness and efficiency of the proposed methods

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

frequency domain cramer rao bound for gaussian processes an expression is derived for the asymptotic frequency domain cramer rao bound crb on the parameters of gaussian processes with information in their means the general result extends whittle s 1953 formula which is applicable to gaussian processes with information in their covariance matrices or spectra it is useful in many fields such as system identification radar and sonar examples of its application to system deconvolution and time delay estimation in colored noise are given

the effect of spatial averaging on spatial correlation matrices in the presence of coherent signals two types of spatial averaging are considered subaperture averaging and redundancy averaging the reduction of coherence due to subaperture averaging is shown to depend on the separation between the sources highly coherent closely spaced sources remain highly coherent after subaperture averaging in finite averaging situations this remaining high degree of coherence will prevent adaptive direction finding methods such as music or ev from resolving the two signals in contrast redundancy averaging greatly reduces intersignal coherence regardless of source spacing but bias may be introduced into the source bearing estimates

maximum likelihood angle estimation for signals with known waveforms maximum likelihood estimation mle of the arrival angles of narrowband plane waves when one or all signals have known waveforms is considered computationally efficient and rapidly converging algorithms that iteratively maximize the likelihood functions are presented cramer rao bounds for these estimators are obtained the conditions under which incorporating knowledge of one or all of the signal waveforms in the estimators improves the accuracy of the angle estimates are described

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

nested arrays in two dimensions part ii application in two dimensional array processing this paper explores the practical application of a new class of two dimensional arrays namely the two dimensional nested arrays in array processing problems like two dimensional direction of arrival estimation nested arrays constitute a class of two dimensional arrays with physical sensors on lattice s whose difference co array gives rise to a virtual two dimensional array with o mn elements although the number of physical sensors used is m n the structure of the two dimensional nested array was proposed in a companion paper and several issues related to the geometrical orientation of the difference co array in the two dimensional space were addressed in this paper the practical aspects of the application of the nested array in two dimensional array processing are considered which can enable us to exploit the increased degrees of freedom offered by the co array under the constraint of a fixed total number of physical sensors the optimal structure of the 2d nested array is solved which maximizes the number of elements in the virtual co array this provides closed form expressions for the sensor locations and the exact degrees of freedom obtainable from the proposed array as a function of the total number of sensors it is shown that one can obtain o n2 virtual elements in the co array using only n physical sensors to exploit the increased degrees of freedom large number of virtual sensors offered by the virtual array for two dimensional doa estimation of more sources than sensors a novel algorithm based on the concept of two dimensional spatial smoothing is proposed and several issues related to identifiability in two dimensional doa estimation problem which is a fundamental issue in two dimensions are addressed the validity of the proposed methods is verified through several numerical examples

performance analysis of multivariate complex amplitude estimators we consider multivariate complex amplitude estimation in the presence of unknown interference and noise two multivariate approaches maximum likelihood ml and capon are provided we derive the closed form expression of the crame spl acute r rao bound crb for the unknown complex amplitudes we also analyze the bias properties and mean squared errors mse of the two estimators a comparative study shows that the multivariate ml estimator is unbiased whereas the multivariate capon estimator is biased downward for finite snapshots both estimators are asymptotically statistically efficient when the number of snapshots is large

theory and application of covariance matrix tapers for robust adaptive beamforming we unify several seemingly disparate approaches to robust adaptive beamforming through the introduction of the concept of a covariance matrix taper cmt this is accomplished by recognizing that an important class of adapted pattern modification techniques are realized by the application of a conformal matrix taper to the original sample covariance matrix from the schur product theorem for positive semi definite matrices and kolmogorov s existence theorem we further establish that cmts are in fact the solution to a minimum variance optimum beamformer associated with an auxiliary stochastic process that is related to the original by a hadamard schur product this allows us to gain deeper insight into the design of both existing pattern modification techniques and new cmts that can for example simultaneously address several different design constraints such as pattern distortion due to insufficient sample support and weights mismatch due to nonstationary interference a new two dimensional 2 d cmt for space time adaptive radar applications designed to provide more robust clutter cancellation is also introduced since the cmt approach only involves a single matrix haddamard product it is also inherently low complexity the practical utility of the cmt approach is illustrated through its application to both spatial and spatio temporal adaptive beamforming examples

grid free compressive beamforming the direction of arrival doa estimation problem involves the localization of a few sources from a limited number of observations on an array of sensors thus it can be formulated as a sparse signal reconstruction problem and solved efficiently with compressive sensing cs to achieve high resolution imaging on a discrete angular grid the cs reconstruction degrades due to basis mismatch when the doas do not coincide with the angular directions on the grid to overcome this limitation a continuous formulation of the doa problem is employed and an optimization procedure is introduced which promotes sparsity on a continuous optimization variable the doa estimation problem with infinitely many unknowns i e source locations and amplitudes is solved over a few optimization variables with semidefinite programming the grid free cs reconstruction provides high resolution imaging even with non uniform arrays single snapshot data and under noisy conditions as demonstrated on experimental towed array data

maximum likelihood separation of constant modulus signals in this correspondence we derive a newton scoring algorithm for the maximum likelihood separation and direction of arrival doa estimation of constant modulus cm signals using a sensor array we present a rapidly converging scheme for the joint estimation of the signals and their directions based on their cm property we discuss initialization and show that the complexity is moderate

time delay and spatial signature estimation using known asynchronous signals this paper considers the problem of estimating the parameters of known signals received asynchronously by an array of antennas the parameters of primary interest are the time delays of the signals and their spatial signatures at the array estimates of the signal directions of arrival are also considered but are of secondary importance in this work maximum likelihood algorithms and more computationally efficient approximations are developed for both the case where all received signals are identical the channel estimation overlapping echo problem and where they are all distinct conditions are also derived under which the standard matched filter approach yields consistent and statistically efficient parameter estimates the issue of solution uniqueness is addressed and in particular an upper bound on the number of signals whose parameters may be uniquely identified is derived for a number of different cases typically the bound is far greater than the number of sensors and is limited only by the number of data samples collected some representative simulation examples are also included to illustrate the algorithms performance relative to the cramer rao bound

interconnected nonlinear systems local and global stabilization a family of interconnected nonlinear systems including partially linear systems is studied no assumption on the stability of each uncontrolled subsystem is imposed but asymptotic stabilizability for each of them is assumed the objective of this work is the state feedback stabilization of the origin of such composite systems local and global results are derived using simple techniques such as coordinate and feedback transformations

doa estimation with enhanced dofs by exploiting cyclostationarity many modulated signals exhibit a cyclostationarity property which has been applied in direction of arrival estimation due to its immunity to interference and noise in this paper we focus on how this cyclostationarity can be effectively integrated with the spatial dimension to enhance both the degrees of freedom and the accuracy of doa estimation first for narrowband signal case by vectorizing the second order cyclic correlation matrix instead of the conventional zero lag covariance matrix one can directly generate an augmented virtual array with sensors at positions defined by the difference coarray of the physical array then for wideband signal case two additional fractional factors are introduced so that the vectorized cyclic correlation matrix can be viewed as a single snapshot received signal from an array with sensors at positions defined by the fractional weighted difference coarray due to the fact that cyclic correlation matrices as special second order statistics allow us to obtain more degrees of freedom the proposed two virtual array models can resolve o n 2 sources by using a sparse linear array consisting of only n physical sensors e g nested coprime array furthermore a scheme of multipseudosampling is proposed in order to reduce the sensitivity to noise and parameter the proposed models can be considered as an extension of difference coarray perspective via the combination of cyclic frequency and temporal lag in the end numerical simulation results validate the effectiveness of the proposed models

forward backward averaging in the presence of array manifold errors we investigate the use of forward backward f b averaging for estimating the covariance matrix used for adaptive beamforming and space time adaptive processing stap we demonstrate that the estimation loss is reduced by the use of f b averaging and for some stap cases f b averaging can even quadruple the available sample support we also show that unknown array manifold errors have little effect on the effectiveness of f b averaging the gain from f b averaging is demonstrated on data from the mountaintop database

subspace based direction of arrival estimation using nonparametric statistics the problem of subspace estimation using multivariate nonparametric statistics is addressed we introduce new high resolution direction of arrival doa estimation methods that have almost optimal performance in nominal conditions and are robust in the face of heavy tailed noise the extensions of the techniques for the case of coherent sources are considered as well the proposed techniques are based on spatial sign and rank concepts we show that spatial sign and rank covariance matrices can be used to obtain convergent estimates of the signal and noise subspaces in the proofs the noise is assumed to be spherically symmetric moreover we illustrate how the number of signals may be determined using the proposed covariance matrix estimates and a robust estimator of variance the performance of the algorithms is studied using simulations in a variety of noise conditions including noise that is not spherically symmetric the results show that the algorithms perform near optimally in the case of gaussian noise and highly reliably if the noise is non gaussian

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

on the structure of the signal subspace in a correlated signal environment this correspondence considers the problem of signal enumeration and direction finding with a uniform linear array in the presence of correlated wavefronts the principal contribution is to present the relationships between the physical model the array steering vectors the computational model the signal eigenvectors and the processed data the covariance matrices in a common mathematical framework

adaptive beamforming with conjugate symmetric weights the hermitian persymmetric maximum likelihood estimator mle is better than the conventional mle in estimating the covariance matrix of a symmetrically distributed antenna array though using the hermitian persymmetric mle improves the performance of adaptive beamforming it increases the computational load due to the forward backward averaging of array input sample data by observing that the weight vector obtained from the hermitian persymmetric mle is conjugate symmetric if the phase origin is chosen at the array geometry center methods are developed to reduce the computational load of the direct form beamformer and the generalized sidelobe canceler gsc the weights of both beamformers can be adapted with real computations with significant savings in computation time

generalized forward backward subaperture smoothing techniques for sample starved stap a major issue in space time adaptive processing stap for moving target indicator mti radar is the so called sample support problem often the available sample support for estimating the requisite interference covariance matrix is inadequate thereby precluding stap beamforming utilizing many adaptive degrees of freedom dofs although deterministic rank reduction methods can reduce sample support requirements they are invariably suboptimal from a signal to interference plus noise ratio sinr standpoint a new generalized subspatial and subtemporal aperture smoothing method employing forward and backward data vectors is introduced to overcome the data deficiency problem it is shown that multiplicative improvement in data samples can be obtained at the expense of negligible loss in space time aperture of the steering vector

improved spatial smoothing techniques for doa estimation of coherent signals in the context of coherent signal classification spatial smoothing is necessary for the application of the eigen based direction of arrival doa estimation methods however the currently known spatial smoothing algorithms not only reduce the effective aperture of the array but also do not consider the cross correlations of the subarray outputs an improved spatial smoothing algorithm which can fully utilize the correlations of the array outputs and produce a more stable estimate of the covariance matrix is presented simulation results are provided to verify the theoretical prediction the superiority of this method over the conventional methods is obvious especially when the sosr subarray to overall size ratio is small

some applications of small gain theorem to interconnected systems based on small gain theorem decentralized control of interconnected systems is studied linear matrix inequality conditions are given for stabilizability of interconnected systems interconnections can be used to improve system robustness in the sense of small gain theorem an example is given to illustrate the results finally interconnected systems composed of symmetric subsystems are studied

a note on redundancy averaging it is well known that the performance of direction of arrival estimation and beamforming algorithms degrades in the presence of correlated signals since techniques like spatial and weighted smoothing which were developed for decorrelating the signals suffer from reduced effective aperture several authors have recently proposed redundancy averaging as an alternative spatial averaging method considering a two source signal model and the asymptotic case the authors show analytically that this technique results in an eigenstructure which is inconsistent with that of the underlying signal model in particular the resulting signal subspace fills up the whole m dimensional space where m is the array size and the resulting covariance matrix is not guaranteed to be nonnegative definite it is shown that complete decorrelation is not possible with this method even if the array size is infinitely large

model checking single agent behaviours by fluid approximation in this paper we investigate a potential use of fluid approximation techniques in the context of stochastic model checking of csl formulae we focus on properties describing the behaviour of a single agent in a large population of agents exploiting a limit result known also as fast simulation in particular we will approximate the behaviour of a single agent with a time inhomogeneous ctmc which depends on the environment and on the other agents only through the solution of the fluid differential equation and model check this process we will prove the asymptotic correctness of our approach in terms of satisfiability of csl formulae we will also present a procedure to model check time inhomogeneous ctmc against csl formulae

subspace leakage analysis and improved doa estimation with small sample size classical methods of doa estimation such as the music algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix for a small number of samples such methods are exposed to performance breakdown as the sample covariance matrix can largely deviate from the true covariance matrix in this paper the problem of doa estimation performance breakdown is investigated we consider the structure of the sample covariance matrix and the dynamics of the root music algorithm the performance breakdown in the threshold region is associated with the subspace leakage where some portion of the true signal subspace resides in the estimated noise subspace in this paper the subspace leakage is theoretically derived we also propose a two step method that improves the performance by modifying the sample covariance matrix such that the amount of the subspace leakage is reduced furthermore we introduce a phenomenon named as root swap which occurs in the root music algorithm in the low sample size region and degrades the performance of the doa estimation a new method is then proposed to alleviate this problem numerical examples and simulation results are given for uncorrelated and correlated sources to illustrate the improvement achieved by the proposed methods moreover the proposed algorithms are combined with the pseudo noise resampling method to further improve the performance