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

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

near optimal range and depth estimation using a vertical array in a correlated multipath environment this paper proposes a near optimal procedure to localize a single stationary source in a two path underwater acoustic environment the investigation is for an m element vertical array with omnidirectional sensors the range and depth estimators are developed using a linear least squares technique when a set of auto and cross correlators is used for time difference of arrival tdoa estimates a weighting matrix is derived to achieve the approximate maximum likelihood ml performance of the weighted least squares range and depth estimators the expressions for error variances and covariances of the range and depth estimates are derived with a small error analysis technique it is verified analytically that the error covariance matrix of the weighted least squares solutions reaches the cramer rao lower bound in the small error region the correlation of the range and depth estimation errors is investigated results show that the range and depth estimation errors are highly correlated in a multipath environment the accuracy properties of the proposed multipath localization procedure are analyzed using different array configurations the results show that the performances of the range and depth estimators are significantly improved if the linear dependent tdoa estimates are included for localizing and that the unweighted range and depth estimators using the entire set of tdoas are approximately optimal for most of the applications the theoretical development of error variance and covariance expressions of the range and depth estimates which incorporates the correlation in the tdoa estimates is corroborated with monte carlo simulations

fine estimators of two dimensional parameters and application to spatial shift estimation this paper presents a fast technique for fine estimation of two dimensional 2 d parameters based on a parabolic interpolation of the same ambiguity function samples and aimed at block oriented estimation of the spatial shift between pairs of images in video sequences expressions for the bias and variance of the position error and the prediction error are derived the method is tested using a synthetically generated autocorrelation function varying the directionality and the eccentricity factor in order to compare the performance of the proposed 2 d estimator to the case of two separate one dimensional 1 d estimators the method has also been applied in vision systems evidencing encouraging results for estimating the parameters of sophisticated global motion models from real images

determination of the number of errors in dft codes subject to low level quantization noise this paper analyzes the effects of quantization or other low level noise on the error correcting capability of a popular class of real number bose chaudhuri hocquenghem bch codes known as discrete fourier transform dft codes in the absence of low level noise a modified version of the peterson gorenstein zierler pgz algorithm allows the correction of up to corrupted entries in the real valued code vector of an dft code in this paper we analyze the performance of this modified pgz algorithm in the presence of low level quantization or other noise that might affect each entry of the code vector and not simply of them we focus on the part of the algorithm that determines the number of errors that have corrupted the real number codeword our approach for determining the number of errors is more effective than existing systematic approaches in the literature and results in an explicit lower bound on the precision needed to guarantee the correct determination of the number of errors our simulations suggest that this bound can be tight finally we prove that the optimal bit allocation for dft codes in terms of correctly determining the number of errors is the uniform one

the eigenvalues of matrices that occur in certain interpolation problems the eigenvalues of the matrices that occur in certain finite dimensional interpolation problems are directly related to their well posedness and strongly depend on the distribution of the interpolation knots that is on the sampling set we study this dependency as a function of the sampling set itself and give accurate bounds for the eigenvalues of the interpolation matrices the bounds can be evaluated in as few as four arithmetic operations and therefore they greatly simplify the assessment of sampling sets regarding numerical stability the accuracy and usefulness of the bounds are illustrated with examples

a fast local maximum likelihood estimator for time delay estimation a fast algorithm for the local maximum likelihood determination of the difference of arrival time of a common signal at two spatially separated sensors with uncorrelated noise is given the fast algorithm consists of locally maximizing the cross correlation function from the two wide band signals by using newton s method for finding the root of an equation the probability density function of one iteration of newton s method is explicitly computed in terms of exponential and error functions using a theorem by rice on the probability density of local maxima of gaussian processes the probability density of the local maxima of the cross correlator is obtained these results are new when both the signal and the noises have flat power spectral densities the mean square error mse of two iterates of newton s method is practically equal to the mse computed from the probability density of the local maxima of the cross correlator via rice s theorem the above holds if the starting point used in newton s method is within a quarter signal resolution binwidth from the true delay and the signal to noise ratio snr at the cross correlator output is 15 db or higher the mse of the local maximum estimator obtained from rice s theorem is almost equal to the cramer rao bound even for low snr i e 5 db

the statistical performance of the music and the minimum norm algorithms in resolving plane waves in noise this paper presents an asymptotic statistical analysis of the null spectra of two eigen assisted methods music 1 and minimum norm 2 for resolving independent closely spaced plane waves in noise particular attention is paid to the average deviation of the null spectra from zero at the true angles of arrival for the plane waves these deviations are expressed as functions of signal to noise ratios number of array elements angular separation of emitters and the number of snapshots in the case of music an approximate expression is derived for the resolution threshold of two plane waves with equal power in noise this result is validated by monte carlo simulations

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

statistical studies of infectious disease incidence summary methods for the analysis of data on the incidence of an infectious disease are reviewed with an emphasis on important objectives that such analyses should address and identifying areas where further work is required recent statistical work has adapted methods for constructing estimating functions from martingale theory methods of data augmentation and methods developed for studying the human immunodeficiency virus acquired immune deficiency syndrome epidemic infectious disease data seem particularly suited to analysis by markov chain monte carlo methods epidemic modellers have recently made substantial progress in allowing for community structure and heterogeneity among individuals when studying the requirements for preventing major epidemics this has stimulated interest in making statistical inferences about crucial parameters from infectious disease data for such community settings

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

subspace algorithms for error localization with quantized dft codes recently a class of real number bose chaudhuri hocquengem codes known as discrete fourier transform dft codes have been considered as joint source and channel codes for providing robustness to erasures and errors over wireless networks we propose three subspace algorithms for error localization with quantized dft codes the algorithms are similar to the music the minimum norm and the esprit algorithms used in array signal processing for direction of arrival estimation they provide different but related formulations of the error localizations by first partitioning a vector space into the channel error subspace and its orthogonal complement the noise subspace the locations of the errors are determined from either the error subspace eigenvectors or the noise subspace eigenvectors we also present a brief performance analysis of the localization error in terms of the perturbation of the error subspace due to quantization simulation results show that their localization performances are similar and they perform better than the coding theoretic approach over a broad range of channel error to quantization noise ratios

short pulse multi frequency phase based time delay estimation an approach for time delay estimation based on phase difference detection is presented a multiple frequency short continuous wave pulse is used to solve the well known phase ambiguity problem when the maximum distance exceeds a full wavelength within an unambiguous range defined with the lowest frequency difference between components the corresponding phase difference is unique and any distance within this range can be determined phase differences between higher frequency components are used to achieve a finer resolution the concept will be presented and the effectiveness of the approach will be investigated through theoretical and practical examples the method will be validated using underwater acoustic measurements simulating noisy environments demonstrating resolutions better than a 50th of a wavelength even in the presence of high levels 5db of additive gaussian noise furthermore the algorithm is simple to use and can be easily implemented being based on phase detection using the disc

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

systematic dft frames principle eigenvalues structure and applications motivated by a host of recent applications requiring some amount of redundancy frames are becoming a standard tool in the signal processing toolbox in this paper we study a specific class of frames known as discrete fourier transform dft codes and introduce the notion of systematic frames for this class this is encouraged by a new application of frames namely distributed source coding that uses dft codes for compression studying their extreme eigenvalues we show that unlike dft frames systematic dft frames are not necessarily tight then we come up with conditions for which these frames can be tight in either case the best and worst systematic frames are established in the minimum mean squared reconstruction error sense eigenvalues of dft frames and their subframes play a pivotal role in this work particularly we derive some bounds on the extreme eigenvalues dft subframes which are used to prove most of the results these bounds are valuable independently

hermitian symmetric dft codes a new class of complex dft codes we introduce a new class of real number codes derived from dft matrix hermitian symmetric dft hsdft codes we propose a new decoding algorithm based on coding theoretic as well as subspace based approach decoding of hsdft codes requires only real arithmetic operations and smaller dimension matrices compared to the decoding of the state of art real bch dft rbdft class of codes hsdft codes will also be shown to have more burst error correction capacity for a gauss markov source on a binary symmetric channel at lower to moderate bit error rates bers hsdft codes show better performance than rbdft codes and on a gilbert elliot channel hsdft codes consistently perform better than rbdft codes

distributed source channel coding based on real field bch codes we use real number codes to compress statistically dependent sources and establish a new framework for distributed lossy source coding in which we compress sources before rather than after quantization this change in the order of binning and quantization blocks makes it possible to model the correlation between continuous valued sources more realistically and compensate for the quantization error partially we then focus on the asymmetric case i e lossy source coding with side information at the decoder the encoding and decoding procedures are described in detail for a class of real number codes called discrete fourier transform dft codes both for the syndrome and parity based approaches we leverage subspace based decoding to improve the decoding and by extending it we are able to perform distributed source coding in a rate adaptive fashion to further improve the decoding performance when the statistical dependency between sources is unknown we also extend the parity based approach to the case where the transmission channel is noisy and thus we perform distributed joint source channel coding in this context the proposed system is well suited for low delay communications as the mean squared reconstruction error mse is shown to be reasonably low for very short block length

the infectiousness of a disease in a community of households summary procedures for making inference about both the mean potential that an infective has for infecting a given susceptible from the same household and the mean potential he has for infecting a given susceptible from another household are proposed these estimation procedures provide a check for the assumption that the disease spreads homogeneously through the community that is the assumption of homogeneous mixing they also provide a means of checking whether or not the spread of infection within each household is essentially independent of the spread of the disease in the rest of the community common cold epidemic data from tristan da cunha are used to illustrate the results

redundancy the discrete fourier transform and impulse noise cancellation the relationship between the discrete fourier transform and error control codes is examined under certain conditions we show that discrete time sequences carry redundant information which then allow for the detection and correction of errors an application of this technique to impulse noise cancellation for pulse amplitude modulation transmission is described

improved coding theoretic and subspace based decoding algorithms for a wider class of dct and dst codes the decoding of a class of discrete cosine transform dct and discrete sine transform dst codes that are maximum distance separable codes mds is considered in this paper these class of codes are considered for error correction over real fields all the existing algebraic decoding algorithms are capable of decoding only a subclass of these codes which can be characterized into the bose chaudhuri hocquenghem bch form and fails to decode the remaining even though they are mds in this paper we propose a new generic algorithm along the lines of coding theoretic and subspace methods to decode the entire class of mds dct and dst codes the proposed subspace approaches are similar to popular esprit and music algorithms the proposed algorithms also perform significantly better than the existing algorithms on the bch like subclass a perturbation analysis is also presented to study the effect of various parameters on the error localization due to the quantization noise simulation results are presented to demonstrate the capability of proposed algorithms to decode the entire class and to perform significantly better on the bch like subclass than the existing algorithm under the influence of quantization noise

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

fft pruning applied to time domain interpolation and peak localization the efficiency of the fast fourier transform may be increased by removing operations on input values which are zero and on output values which are not required this is applied to interpolation of complex and real valued time domain functions for real functions analytic signal concepts may be used to get the hilbert transform as a byproduct and applied to the cross correlation function this gives an efficient and accurate method for peak localization

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