performance analysis of the uca esprit algorithm for circular ring arrays statistical performance analysis of the uca uniform circular array esprit algorithm is the subject of the present paper the uca esprit arrival angle estimates are shown to be asymptotically unbiased and expressions for the asymptotic estimator variances have been obtained simulation results that verify the analysis are presented

the spectrum of the period doubling operator in terms of cycles the eigenvalue spectrum of the period doubling operator is evaluated both in terms of unstable periodic orbits and by a diagonalization at the operator cycles up to length ten yield the twelve leading eigenvalues direct diagonalization yields some 50 eigenvalues the feigenbaum 6 the hausdorff dimension and the escape rate for the period doubling repeller are evaluated to high accuracy in this letter we apply the technique for the extraction of correlation exponents of i to evaluation of the spectrum of the period doubling renormalization operator the basic idea of relating the feigenbaum constant 6 to the scaling or the presentation function is due to sullivan 2 and is implemented as an eigenvalue spectrum calcula tion in 3 51 we refer the reader to 3 41 for an introduction to the cycle expansions in general and their application to the evaluation of the stability the dimension and the escape rate of the period doubling repeller in particular the fredholm determinant evaluation method and the transfer operator diagonalization 11 used here are superior to the method of locating zeros of finite products of dynamical 6 functions 6 of 3 4 7 81 and in that sense the present letter supersedes the above references the repeller we study here is the non wandering set of the period doubling presenta tion function 9

expanding direction of the period doubling operator we prove that the period doubling operator has an expanding direction at the fixed point we use the induced operator a perron frobenius type operator to study the linearization of the period doubling operator at its fixed point we then use a sequence of linear operators with finite ranks to study this induced operator the proof is constructive one can calculate the expanding direction and the rate of expansion of the period doubling operator at the fixed point

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

a variational principle for free semigroup actions abstract in this paper we introduce a notion of measure theoretical entropy for a finitely generated free semigroup action and establish a variational principle when the semigroup is generated by continuous self maps on a compact metric space and has finite topological entropy in the case of semigroups generated by ruelle expanding maps we prove the existence of equilibrium states and describe some of their properties of independent interest are the different ways we will present to compute the metric entropy and a characterization of the stationary measures

annealed and quenched limit theorems for random expanding dynamical systems in this paper we investigate annealed and quenched limit theorems for random expanding dynamical systems making use of functional analytic techniques and more probabilistic arguments with martingales we prove annealed versions of a central limit theorem a large deviation principle a local limit theorem and an almost sure invariance principle we also discuss the quenched central limit theorem dynamical borel cantelli lemmas erdos renyi laws and concentration inequalities

consistency and mse performance of music based doa of a single source in white noise with randomly missing data music is a popular algorithm for estimating the direction of arrival doa in array signal processing applications in this paper we analyze the performance of the music algorithm for a single source system in the presence of noisy and missing data when only a random subset of the entries in the data matrix are observed we prove consistency of the doa estimate when signal from a single source is impinging on low coherence arrays and derive an analytic expression for the mean squared error mse performance of music for the case of uniform linear arrays in the large array and relatively large sample setting our analysis is mathematically justified in both the sample rich and deficient regimes the expression for the mse is a simple function of array geometry signal to noise ratio snr the fraction of entries observed and the ratio of the number of sensors to number of snapshots we derive a phase transition threshold which separates a regime where music is consistent from a regime where music is inconsistent this threshold depends upon the snr the probability of observing entries in the data matrix and number of sensors and snapshots in a simple manner which we make explicit

performance analysis of esprit and tam in determining the direction of arrival of plane waves in noise the authors evaluate two subspace based methods esprit and the toplitz approximation method tam for estimating the direction of arrival doa of plane waves in white noise in the case of linear equispaced sensor array it is shown that the least squares versions of esprit and tam result in the same estimate and are statistically equivalent it is also shown that asymptotically the estimates obtained using least squares esprit and total least squares esprit have the same mean squared error expressions for the asymptotic mean squared error in the estimates of the doa are derived for both methods simple closed form expressions are derived for the one and two source cases to get further insight computer simulation results are provided to substantiate the analysis

dynamic analysis of fractional order quaternion valued fuzzy memristive neural networks vector ordering approach abstract this paper addresses the problems of stabilization and synchronization control of the fractional order quaternion valued fuzzy memristive neural networks by means of the contraction mapping theorem the corresponding conditions are established for the existence and uniqueness of the equilibrium point ep subsequently the corresponding stability analysis are proposed by two suitable controllers what should be mentioned is that a vector ordering approach is developed to determine the magnitude of two different quaternions as a result the closed convex hull proposed by quaternion connections can be easily derived finally two simulation examples are utilized to illustrate the effectiveness of the proposed control method

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

iterative hos sos ihoss algorithm for direction of arrival estimation and sensor localization a new method for joint direction of arrival doa and sensor position estimation is introduced the sensors are assumed to be randomly deployed except two reference sensors the proposed method exploits the advantages of both higher order statistics hos and second order statistics sos with an iterative algorithm namely iterative higher order second order statistics ihoss a new cumulant matrix estimation technique is proposed for the hos approach by converting the multisource problem into a single source one ihoss performs well even in case of correlated source signals due to the effectiveness of the proposed cumulant matrix estimate a cost function is defined for the joint doa and position estimation the iterative procedure is guaranteed to converge the ambiguity problem in sensor position estimation is solved by observing the source signals at least in two different frequencies the conditions on these frequencies are presented closed form expressions are derived for the deterministic cramer rao bound crb for doa and unknown sensor positions for noncircular complex gaussian noise with unknown covariance matrix simulation results show that the performance of ihoss is significantly better than the hos approaches for doa estimation and closely follows the crb for both doa and sensor position estimations

exponential decay of correlations for random lasota yorke maps we consider random piecewise smooth piecewise invertible maps mainly on the interval but also in higher dimensions we assume that on the average and possibly without any stochastic uniformity i the maps expand distances ii do not have too many pieces iii do not have too large a distortion and iv are strongly mixing we assume it no markov property we prove that as in the classical case of the iteration of a fixed piecewise expanding map of the interval we have it exponential decay of random correlations our proof builds on the one given by c liverani for deterministic mixing and piecewise expanding interval maps

one dimensional gibbs states and axiom a diffeomorphisms on etudie la mecanique statistique en equilibre de systemes reticules classiques a une dimension a interactions a decroissance exponentielle pour de tels systemes les transformees de fourier des fonctions de correlation de paires sont meromorphes dans une bande et les residus des poles peuvent s exprimer en termes de distributions de gibbs on applique ces resultats aux diffeomorphismes de l axiome a de smale

correlation spectrum of quenched and annealed equilibrium states for random expanding maps we show that the integrated transfer operators for positively weighted independent identically distributed smooth expanding systems give rise to annealed equilibrium states for a new variational principle the unique annealed equilibrium state coincides with the unique annealed gibbs state using work of ruelle 1990 and fried 1995 on generalised fredholm determinants for transfer operators we prove that the discrete spectrum of the transfer operators coincides with the correlation spectrum of these invariant measures yielding exponential decay of correlations and with the poles of an annealed zeta function defined also for complex weights a modified integrated transfer operator is introduced which describes the relativised quenched states studied e g by kifer 1992 and conditions including srb ensuring coincidence of quenched and annealed states are given for small random perturbations we obtain stability results on the quenched and annealed measures and spectra by applying perturbative results of young and the author 1993

the thermodynamic formalism for expanding maps letf x x be an expanding map of a compact space small distances are increased by a factor 1 a generating function z is defined which countsf periodic points with a weight one can express in terms of nonstandard fredholm determinants of certain transfer operators which can be studied by methods borrowed from statistical mechanics in this paper we review the spectral properties of the transfer operators and the corresponding analytic properties of z gibbs distributions and applications to julia sets are also discussed some new results are proved and some natural conjectures are proposed

semigroup actions of expanding maps we consider semigroups of ruelle expanding maps parameterized by random walks on the free semigroup with the aim of examining their complexity and exploring the relation between intrinsic properties of the semigroup action and the thermodynamic formalism of the associated skew product in particular we clarify the connection between the topological entropy of the semigroup action and the growth rate of the periodic points establish the main properties of the dynamical zeta function of the semigroup action and relate these notions to recent research on annealed and quenched thermodynamic formalism meanwhile we examine how the choice of the random walk in the semigroup unsettles the ergodic properties of the action

direction finding algorithms based on high order statistics two direction finding algorithms are presented for nongaussian signals which are based on the fourth order cumulants of the data received by the array the first algorithm is similar to music while the second is asymptotically minimum variance in a certain sense the first algorithm requires singular value decomposition of the cumulant matrix while the second is based on nonlinear minimization of a certain cost function the performance of the minimum variance algorithm can be assessed by analytical means at least for the case of discrete probability distributions of the source signals and spatially uncorrelated gaussian noise the numerical experiments performed seem to confirm the insensitivity of these algorithms to the gaussian noise parameters

performance analysis of the total least squares esprit algorithm the asymptotic distribution of the estimation error for the total least squares tls version of esprit is derived the application to a uniform linear array is treated in some detail and a generalization of esprit to include row weighting is discussed the cramer rao bound crb for the esprit problem formulation is derived and found to coincide with the asymptotic variance of the tls esprit estimates through numerical examples a comparison of this method to least squares esprit music and root music as well as to the crb for a calibrated array is also presented tls esprit is found to be competitive with the other methods and the performance is close to the calibrated crb for many cases of practical interest for highly correlated signals however the performance deviates significantly from the calibrated crb simulations are included to illustrate the applicability of the theoretical results to a finite number of data

asymptotic performance analysis of esprit higher order esprit and virtual esprit algorithms in this paper we present an asymptotic performance analysis of three subspace based methods for direction of arrival doa estimation the esprit algorithm using second order statistics the higher order esprit algorithm using fourth order cumulants and the virtual esprit vespa algorithm using fourth order cumulants we examine the least squares version of these algorithms derive the expressions for the asymptotic variance of the estimated doas and use specific examples to compare the relative performance of the algorithms finally we present monte carlo simulations to validate the theoretical analysis