delay estimation by expected value the estimation of time delay between narrowband signals is discussed a minimum mean square error mmse estimator is used that utilizes the maximum likelihood ml window derived by knapp and carter in obtaining the required conditional probability density function from which the delay estimate is calculated the results of simulations using a narrowband signal are presented which evaluate and compare the mean square error of the mmse and ml processors the mmse estimator shows improvement over the ml estimator particularly in regions below the threshold signal to noise ratio conditions for application of the mmse processor are discussed as well as some important considerations for its implementation

quickest detection of a random pulse in white gaussian noise a class of stochastic processes characterized by rapid transitions in their structure is considered and the quickest detection of such transitions is studied in a bayesian framework the emphasis is on stochastic processes consisting of a randomly arrived causal pulse possibly with a set of random parameters such as amplitude and duration and an additive white gaussian noise in this model the pulse shape and the prior joint density of the arrival time and other random parameters are assumed known the task of quickest detection in this paper is described mathematically by minimizing the expected detection error the detection error is represented by a nonlinear function of the distance between the actual transition time and its associated detection time the assumptions on this function are fairly mild and allow to flexibly design its shape for a desired trade off between the detection delay and the false alarm rate two special cases of such design are well known error measures mean squared and mean absolute error the quickest detection problem a subclass of optimal stopping time problems is formulated as a stochastic optimal control problem and is resolved using dynamic programming the optimal detection rule is determined in terms of the solution of an integral equation that cannot be directly solved due to its complexity this equation is later used to develop a class of suboptimal detection rules and a lower bound on the minimum error using this lower bound it is shown for a numerical example that the suboptimal detector is nearly optimal

discrete time techniques for time delay estimation basic aspects of time delay estimation tde based on sampled signals are investigated the direct cross correlation method is analyzed and compared to the average square difference function asdf and the addition only based average magnitude difference function amdf estimators their relative accuracy is theoretically evaluated and previous empirical results are explained it is shown that both the asdf and the amdf based estimators outperform the direct cross correlation based estimator for medium high signal to noise ratios moreover the amdf based estimator which avoids any multiplications significantly reduces the computational complexity of the estimation procedure while offering only a moderate performance loss with respect to the asdf based estimator

around property t for quantum groups we study property t for locally compact quantum groups providing several new characterisations especially related to operator algebraic ergodic theory quantum property t is described in terms of the existence of various kazhdan type pairs and some earlier structural results of kyed chen and ng are strengthened and generalised for second countable discrete unimodular quantum groups with low duals property t is shown to be equivalent to property t 1 1 of bekka and valette this is used to extend to this class of quantum groups classical theorems on typical representations due to kerr and pichot and on connections of property t with spectral gaps due to li and ng and with strong ergodicity of weakly mixing actions on a particular von neumann algebra due to connes and weiss finally we discuss in the appendix equivalent characterisations of the notion of a quantum group morphism with dense image

an experimental comparison of optimum and sub optimum filters effectiveness in the generalized correlator abstract various optimum and sub optimum filters have been added to the basic cross correlator in order to enhance its detection and estimation capabilities in the presence of noise these pre detection filters include the hannan thomson the eckart the smoothed coherence transform some least squares and two optimum filters recently derived by the authors here a quantitative comparison of all six filters has been conducted by extensive simulation for various input signal to noise ratios and signal and noise bandwidths the results define the actual enhancement in time delay detection and estimation when using the optimum filters and the amount of performance degradation from the optimum for the other filters the rank ordering of the filters is carried out histograms of the time delay estimates their mean variance and probability of detection are presented wherever available comparison of analytical predictions with the experimental results is noted

lower bounds on worst case probability of large error for two channel time delay estimation a lower bound on the worst case probability of large error for two channel time delay estimation using random signals is developed the bound is based on the minimum probability of error m ary hypothesis test using a maximum likelihood estimator mle the bound can only be evaluated approximately however it can be determined arbitrarily well via simulation if the mle can be instrumented the bound is evaluated in detail for uniform lowpass signal and noise spectra and large bandwidth time product it is then compared with another lower bound based on a binary hypothesis test with computer simulation results for an approximate mle instrumentation and with an upper bound established via computer simulation for a correlator for a uniform lowpass spectrum the m ary bound is shown to be very nearly a greatest lower bound over the full range of input signal to noise ratio further the correlator is shown to be very nearly an optimal instrumentation in the sense of reaching the minimum probability of large error

robust adapative kalman filtering for systems with unknown step inputs and non gaussian measurement errors target tracking with kalman filters is hampered by target maneuvering and unknown process and measurement noises we show that moving data windows may be used to analyze state and measurement error sequences determining robust estimates of bias and covariance for steps in the system forcing functions and non gaussian measurement errors the robust estimators yield improvements over linear bias and covariance estimators extensive simulations compare conventional linear adaptive and robust adaptive average step responses of a first order system filter quantities examined are state estimate state error process and measurement covariance estimates kalman gain and input step estimate

delay estimation using narrow band processes array processing of narrow band gaussian signals is studied with emphasis on delay estimation the barankin bound is used to examine the effect of ambiguity on mean square measurement error when the bound is plotted as a function of signal to noise ratio one observes a distinct threshold above the critical signal to noise ratio the lower bound on mean square error is given by the cramer rao inequality which is approached by the barankin inequality under these conditions below the threshold the barankin bound can exceed the cramer rao bound by large factors the relative magnitude of the bounds in that region depends critically on the ratio of signal center frequency to signal bandwidth

application of generalized thermostatistics to fully developed turbulence abstract we apply the formalism of non extensive statistical mechanics to fully developed turbulent flows we obtain analytical formulas for probability density functions of velocity differences depending on distance r and reynolds number r which are in very good agreement with turbulence experiments the skewness is taken into account by analysing universal contributions due to higher order correlations of the chaotic dynamics we also calculate the moment scaling exponents m which also agree well with experimental data

quasi additivity of tsallis entropies and correlated subsystems abstract we use beck s quasi additivity of tsallis entropies for n independent subsystems to show that like the case of n 2 the entropic index q approaches 1 by increasing system size then we will generalize that concept to correlated subsystems to find that in the case of correlated subsystems when system size increases q also approaches a value corresponding to the additive case

nonlinear filters for bayesian estimation of pulse arrival time in additive white gaussian noise bayesian estimation of the arrival time of a single pulse is considered in the presence of a white noise the employed model is a stochastic process consisted of a randomly delayed causal pulse and an additive white gaussian noise where the prior density of the delay is known the history of this stochastic process is given at every point in time and the problem is to obtain the conditional expectation of an arbitrary function of the arrival time the paper adopts a stochastic differential equation approach to develop nonlinear filters to efficiently compute this estimation the filtering problem is resolved for a number of pulse shapes which allow for a finite dimensional solution these pulse shapes include step exponential and rectangular functions as well as a piecewise constant function which well approximates a broad class of waveforms the application of this filtering problem in real time pulse arrival detection is discussed the task of this operation is to report the event of pulse arrival as soon after occurrence as possible the performance of nonlinear filtering is numerically verified for this application

extended quasi additivity of tsallis entropies abstract we consider statistically independent non identical subsystems with different entropic indices q 1 and q 2 a relation between q 1 q 2 and q for the entire system extends a power law for entropic index as a function of distance r a few examples illustrate a role of the proposed constraint q min q 1 q 2 for the beck s concept of quasi additivity

a new generalized cross correlator a new generalized cross correlator gcc for the passive time delay estimation problem is presented the interpretation of this gcc is that of estimating the cross correlation function by cross correlating the least mean square estimates of the signal component in each of the observed waveforms the implementation is simply a gcc with the weighting filter equal to the magnitude coherency squared numerical evaluation of the performance of this processor and a robust version indicate that they compare favorably to some of the well known gcc procedures

property t and strong property t for unital c algebras in this paper we will give a thorough study of the notion of property t for c algebras as introduced by m b bekka as well as a slightly stronger version of it called strong property t which is also an analogue of the corresponding concept in the case of discrete groups and type ii1 factors more precisely we will give some interesting equivalent formulations as well as some permanence properties for both property t and strong property t we will also relate them to certain t type properties of the unitary group of the underlying c algebra

delay estimation simulations and a normalized comparison of published results three recent publications have reported delay estimate variances from simulations using the generalized cross correlator method on both stationary random signals with noise and deterministic signals with noise further simulations with finite energy signals are reported here a method of comparing the three reported data sets is developed and a remarkable consistency is observed even though the simulation parameters have varied widely

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

haagerup property for c algebras abstract we define the haagerup property for c algebras a and extend this to a notion of relative haagerup property for the inclusion b a where b is a c subalgebra of a let be a discrete group and a normal subgroup of we show that the inclusion a r a r has the relative haagerup property if and only if the quotient group has the haagerup property in particular the inclusion c r c r has the relative haagerup property if and only if has the haagerup property c r has the haagerup property if and only if has the haagerup property we also characterize the haagerup property for in terms of its fourier algebra a

time delay estimation via cross correlation in the presence of large estimation errors the estimate of the difference in time of arrival of a common random signal received at two sensors each of which also receives uncorrelated noise is examined for both small and large estimation errors it is shown that as the post integration signal to noise ratio decreases the correlator exhibits a thresholding effect that is the probability of a large error an anomalous estimate increases rapidly approximate theoretical results for the probability of an anomaly are presented and are verified experimentally the variance of the time delay estimate is examined for both a gated mode in which the time delay corresponding to the correlation peak closest to the true time delay is used as the estimate of time delay and an ungated mode in which the time delay corresponding to the largest peak over the full range of the correlator delay times is used as the estimate the observed variance for both modes is compared with the theoretical variance based on a small error analysis for the gated modes the signal to noise ratio below which the observed variance begins to differ significantly from the small error theory can be reliably predicted from a linearity criterion it is shown however that the expected variance for the ungated mode can depart from the small error theory at a higher signal to noise ratio than for the gated modes thus the variance due to anomalies can be the most important factor in determining the region of applicability of the small error analysis

nonparametric narrowband wavefront estimation from wavefront gradients the wavefield sampled by a two dimensional 2 d planar array can he characterized by a delayed signal this correspondence investigates the problem of the nonparametric estimation of the delay function or wavefront when the waveform is narrowband the wavefront is estimated by integrating the local estimates of the differential time of delay tod of the waveform between neighboring sensors the ambiguity of the tod estimator for the narrowband waveform can be conveniently limited by the a priori search interval for the cross correlation method the reconstruction of the wavefronts is formulated as a least squares problem that is solved iteratively errors of the solution are quantified and the contribution caused by noise is shown to be negligible

measuring nonextensitivity parameters in a turbulent couette taylor flow we investigate probability density functions of velocity differences at different distances r measured in a couette taylor flow for a range of reynolds numbers re there is good agreement with the predictions of a theoretical model based on nonextensive statistical mechanics where the entropies are nonadditive for independent subsystems we extract the scale dependent nonextensitivity parameter q r mathrm re from the laboratory data

asymptotically scale invariant occupancy of phase space makes the entropy sq extensive phase space can be constructed for n equal and distinguishable subsystems that could be probabilistically either weakly correlated or strongly correlated if they are locally correlated we expect the boltzmann gibbs entropy s bg k i p i ln p i to be extensive i e s bg n n for n in particular if they are independent s bg is strictly additive i e s bg n ns bg 1 n however if the subsystems are globally correlated we expect for a vast class of systems the entropy s q k 1 i p q i q 1 with s 1 s bg for some special value of q 1 to be the one which is extensive i e s q n n for n another concept which is relevant is strict or asymptotic scale freedom or scale invariance defined as the situation for which all marginal probabilities of the n system coincide or asymptotically approach for n the joint probabilities of the n 1 system if each subsystem is a binary one scale freedom is guaranteed by what we hereafter refer to as the leibnitz rule i e the sum of two successive joint probabilities of the n system coincides or asymptotically approaches the corresponding joint probability of the n 1 system the kinds of interplay of these various concepts are illustrated in several examples one of them justifies the title of this paper we conjecture that these mechanisms are deeply related to the very frequent emergence in natural and artificial complex systems of scale free structures and to their connections with nonextensive statistical mechanics summarizing we have shown that for asymptotically scale invariant systems it is s q with q 1 and not s bg the entropy which matches standard clausius like prescriptions of classical thermodynamics

on the determination of the position of extrema of sampled correlators the problem of determination of the position of the extremum of a continuous correlator function from its samples if the spectrum of the correlator is not bandlimited is discussed searching for the position of the extremum by fitting a parabola through three samples around that extremum leads to clustering of the estimates around values corresponding with the sampling moments

on the simulation of a class of time delay estimation algorithms the time delay between signals received at two or more sensors has proven to be a useful parameter in passive sonar for estimating the location of an acoustic source this paper presents the results of a simulation comparing the smoothed coherence transform and maximum likelihood estimation methods to the basic cross correlation technique for time delay estimation band limited random signals which are corrupted by white noise and received at two sensors are considered at various signal to noise ratios the variance of the time delay estimates are compared to the minimum variance obtainable in theory as given by the cramer rao lower bound

analysis of discrete implementation of generalized cross correlator a common discrete implementation of the cross correlator uses a parabolic fit to the peak when the delay is not an integral multiple of the sampling period this correspondence analyzes and assesses the pitfalls of this approach it is shown that this yields a biased estimate of the time delay with both the bias and variance of the estimate dependent on the location of the delay between samples snr signal and noise bandwidths and the prefilter or window used in the generalized correlator

robust eckart filters for time delay estimation minimax or robust filters which optimize worst case performance have been considered previously for matched and wiener filtering in this paper we show how similar ideas can be applied to obtain robust versions of one particular filter the eckart filter for time delay estimation the use of a robust filter can eliminate the requirement of estimation of the signal and noise power spectral densities psd s and cross psd s robust filters being less sensitive in their performance to variations of the input psd s within specified classes of psd s explicit solutions for specific classes of psd s are derived and several numerical examples and simulation results are given similar formulations for robust filters should also be possible for other types of filters used in time delay estimation

passive bearing estimation of a broad band source the variance on the bearing estimates of a wide band source has been given wide attention in the literature under the assumption of unbiased estimation process this paper relaxes such a condition and derives the resulting statistical measures those lower bound measures depend on the tangent of the true bearing pt to the source and the bearing variance 2 u as derived with an unbiased condition in the far field the resulting bias isgiven simply by a tan t 2 u where a is a constant the bias size can be in the order of the unbiased bearing variance 2 u the variance is the sum of the unbiased variance 2 u and a combination of the bias and 2 u the variance is contrasted against the cramer rao bound developed for the biased estimate such statistical results enable the sizing of the bias and its deteriorating effect on the estimation process for the specific case of interest when the bias is unacceptable averaging should be applied to the time delays rather than the bearings the bias impact is also of interest when noisy bearings are applied to estimate other functions such as passive source motion at long ranges

alignment blur in coherently averaged images blurring of coherently averaged images due to imperfect alignment is studied and two restoration methods are proposed and evaluated it is shown that iterative realignment is more powerful than post filtering in reducing blur the value of averaging and restoration is illustrated on human subjects in noisy video sequences