E.C. Real et al. have presented an algorithm for fast tracking of a signal subspace or interference subspace for application in adaptive detection or estimation (see ICASSP '97; IEEE Trans. Sig. Processing, vol.47, p.1036-45, 1999). For cases in which the signal matrix is formed from a single-channel discrete-time signal, we show how one can further reduce computation in the fast approximate subspace tracking (FAST) algorithm by using the fast Fourier transform.

The thresholding of univariate test statistics for signal detection is considered for the case in which the pertinent probability distributions are not known but some training data is available. A distribution-free method for setting the threshold is derived. This threshold value maintains the average probability of false alarm (Pfa) at a fixed level and can be applied to noise/clutter data from any underlying probability distribution. Detection and false alarm performance are evaluated for the case in which the true, underlying univariate probability density is exponential for both noise and signal-plus-noise data. Performance is compared to the best adaptive detector, which is invariant to the exponential parameter governing the noise distribution, as well as the bounding case in which the exponential parameter is completely known. For this case, it is shown that the cost for a robust design is a small loss in the average probability of detection for a fixed average probability of false alarm. The study is of particular interest to radar and sonar.

We present a method for estimating threshold values for signal detection and classification systems in which a prescribed value of false alarm probability is needed. The threshold values are determined directly from observed test statistic data without knowledge of the probability distribution of the data. Our method uses the concept of tolerance intervals from nonparametric statistics.

We present a method for estimating threshold values for signal detection and classification systems in which a prescribed value of false alarm probability is needed. The threshold values are determined directly from observed test statistic data without knowledge of the probability distribution of the data. Our method uses the concept of tolerance intervals from nonparametric statistics.

This paper presents a review of the principal component inverse (PCI) method of rapid adaptive signal detection and contrasts the use of principal components with the cross spectral metric (CSM) method for the generalized sidelobe canceller. The CSM method is optimal with known statistics and has been shown to outperform the PCI method in many cases of unknown covariance. This paper describes a scenario which represents a class of covariances where the PCI method can be expected to outperform the CSM method. The choice of method is therefore more subtle than previously thought.

An efficient scheme for implementing a search of a likelihood function of known form at moderate to high SNR is constructed. Often, the original function to be searched is ill behaved with many local extreme points. By projecting the signal onto a subspace of replica waveforms we first find the maximum of a related function that is more well behaved, and then follow with a local search on the original function. The approach builds on a method of estimation of the time delay of a narrowband signal, and it can be used to improve the efficiency of fast maximum likelihood estimation.

In many estimation problems, the set of unknown parameters can be divided into a subset of desired parameters and a subset of nuisance parameters. Using a maximum a posteriori (MAP) approach to parameter estimation, these nuisance parameters are integrated out in the estimation process. This can result in an extremely computationally-intensive estimator. This paper proposes a method by which computationally-intensive integrations over the nuisance parameters required in Bayesian estimation may be avoided under certain conditions. The proposed method is an approximate MAP estimator which is much more computationally efficient than direct, or even Monte Carlo, integration of the joint posteriori distribution of the desired and nuisance parameters. As an example of its efficiency, we apply the fast algorithm to matched-field source localization in an uncertain environment.

A new fast and accurate algorithm for tracking singular values, singular vectors and the dimension of the signal subspace through an overlapping sequence of data matrices is presented. The accuracy of the algorithm approaches that of the Prony-Lanczos (PL) method with speed and accuracy superior to both the PAST and PASTd algorithms for moderate to large size problems. The algorithm is described for the special case of changes to two columns of the matrix prior to each update of principal singular vectors and values. Comparisons of speed and accuracy are made with the algorithms named above.

In many estimation problems, the set of unknown parameters can be divided into a subset of desired parameters and a subset of nuisance parameters. Using a maximum a posteriori (MAP) approach to parameter estimation, these nuisance parameters are integrated out in the estimation process. This can result in an extremely computationally intensive estimator. This letter proposes a method by which computationally intensive integration over the nuisance parameters required in Bayesian estimation can be avoided under certain conditions. The proposed method is an approximate MAP estimator, which is much more computationally efficient than direct, or even Monte Carlo, integration of the joint posteriori distribution of the desired and nuisance parameters. As an example, we apply the fast algorithm to matched-field source localization in an uncertain environment.

The concept, structures, and algorithms of principal feature classification (PFC) are presented in this paper. PFC is intended to solve complex classification problems with large data sets. A PFC network is designed by sequentially finding principal features and removing training data which has already been correctly classified. PFC combines advantages of statistical pattern recognition, decision trees, and artificial neural networks (ANNs) and provides fast learning with good performance and a simple network structure. For the real-world applications of this paper, PFC provides better performance than conventional statistical pattern recognition, avoids the long training times of backpropagation and other gradient-descent algorithms for ANNs, and provides a low-complexity structure for realization.

Matched-field source localization methods can be sensitive to environmental parameter mismatch. In this paper, a source localization method which is robust to environmental parameter uncertainty is presented. This method allows for a family of propagation models based on the uncertainty intervals of the environmental-parameters. It is a computationally efficient approximation to a full maximum-likelihood search which can be followed by a local exact maximum-likelihood search. The effectiveness of this method is demonstrated using experimental data from the Mediterranean Sea.

A modified linear discriminant analysis technique for speaker verification, referred to as normalized discriminant analysis (NDA), is presented. Using this technique it is possible to design an efficient linear classifier with very limited training data and to generate normalized discriminant scores with comparable magnitudes for different classifiers. The NDA technique is applied to a classifier for speaker verification based on speaker specific information obtained when utterances are processed with speaker independent models. In experiments conducted on a network based telephone database, the NDA technique provides an equal-error rate of 6.13% while the classifier using Fisher linear discriminant analysis has an equal-error rate of 18.18%. Furthermore, when the NDA combined with HMM approach in a hybrid speaker verification system, the rate was reduced from 5.30% (HMM with cohort normalization) to 4.32%.

We address the design of hardware-efficient digital implementations for the estimation of sinusoidal frequency from noisy data. We are motivated by the design of digital microwave receivers with high sample rates, which thus require simple processing to be cost-effective. By a controlled introduction of potential ambiguities and by use of formulas for the noise-free Prony (1795), or linear prediction coefficients, we provide several novel approaches to simple, effective frequency estimation.

Matched-field source localization methods attempt to estimate the range and depth of a source in an acoustic waveguide. These methods give good results when the waveguide parameters are known precisely; however, matched-field methods have been shown to be very sensitive to model mismatch resulting from errors in the assumed environmental parameters. In this paper, we describe an approach which minimizes model mismatch by estimating the environmental parameters and source location together. We propose an efficient way to initialize the maximum-likelihood search by projecting the received data onto subspaces corresponding to regions in parameter space.

Investigations of the design of a discriminant neural network (DNN) have shown the advantages of sequential design of hidden nodes and pruning of the training data for improved classification and fast training time. The performance can be further improved by adding the capability of a nonlinear, principal component discriminant node. This type of hidden node is useful for separating classes which have common mean vectors and are overlapped on one other.

We present an novel method of fast and accurate estimation of the frequencies of sinusoids from short data records of wide-band under-sampled data. By introducing properly chosen delay lines, and by using sparse linear prediction, our proposed method provides unambiguous frequency estimates using low A/D conversion rates. It provides a new way to implement a digital microwave receiver under these conditions.

The authors extend previous work on ambiguity resolution in sparse linear prediction to array signal processing. A non-uniformly spaced linear array with minimum number of sensors is introduced in order to obtain high resolution spatial frequency estimates at reduced computation and at minimum hardware cost. By properly choosing inter-element spacing, combining and processing subarray outputs in parallel, a computationally simple algorithm is proposed for unambiguously estimating spatial frequencies of the source signals.>

In this paper we present a nested sequence of hypothesis tests for determining the number of signals. The procedure is based on the interpretation of the sum of singular values, of the backward/forward-backward matrix as energy in a particular subspace. The threshold selected is based on a user-specified significance level. Using matrix perturbation ideas, we provide an approximation to the probability of overestimation.>

Presents a method for improving the signal-to-interference-ratio (SIR) for a desired digital signal in the presence of time-varying local multipath reception and interference from other signals. The singular value decomposition (SVD) based method identifies the channel by the aid of a known pilot signal. The method is applied to a multipath, cellular channel with a cochannel interference signal. The effectiveness of the method is demonstrated through simulations.>

Techniques based on linear prediction (LP) and the singular value decomposition (SVD) for the robust estimation of the parameters of closely spaced exponentially damped sinusoidal signals in additive noise are extended and improved. An iterative method of fitting lower-rank least squares approximations subject to a general choice of weights is used. The method is applied to data sequences consisting of one and two signals with impulsive noise or with missing data samples.>

Evaluation and improvement of a data-adaptive signal estimation algorithm are presented. Perturbation analysis of a rank-reduced data matrix is used to reveal its statistical properties. The obtained information is used for calculating the performance of the Toeplitz-restoration algorithm of D. Tufts et al. (1982). The analysis leads to improvements of the method, and the predicted improvements are demonstrated by simulation and comparison with Cramer-Rao bounds.>

The authors propose a multistage procedure to achieve good local resolution of significantly overlapping components in a transient signal. The received transient signal is assumed to be a superposition of modulated and time-shifted versions of a single one-sided exponential function whose damping coefficient is known. At each stage of the proposed procedure the authors coarsely identify (as compared to the next stage) broad regions in the time-frequency plane that have significant signal energy. These correspond to possible regions where signal components may be present. In each succeeding stage, they focus on these coarsely identified signal regions to further identify subregions in them that have significant energy. The detection of signal components in the subregions is done in the presence of possible interference from neighboring regions. Implementation of this method is based on the use of generalized eigenvectors of signal and interference correlation matrices. The detection statistics is a linear combination of the magnitude squared projections of the received data onto the individual generalized eigenvectors.>

A suboptimum, linear, minimum mean-squared error (MMSE) data communication receiver that is based on a parametric model for a linear, time-invariant, or slowly time-varying channel is shown to perform well at reasonable input signal-to-noise ratios (SNRs) and for short training periods. The receiver makes use of a fractionally spaced equalizer (FSE) design whose time span is a single symbol period. It is assumed that a parametric model, with parameter estimates that are obtainable from a training sequence prior to data acquisition, is adequate for representing the impulse response of the equivalent baseband channel.>

The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical fast Fourier transform (FFT) in terms of accuracy, complexity and speed. Theorems developed previously for the AFT algorithm are used to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A computationally balanced AFT algorithm for Fourier analysis and signal processing is developed. This algorithm does not require complex multiplications. A VLSI architecture is suggested for this amplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25% over that used by the direct method. This efficient AFT algorithm is shown to be identical to Brun's original AFT algorithm.>

A unified performance analysis of subspace-based algorithms for direction-of-arrival (DOA) estimation involving multiple signal arrivals in array signal processing is presented. Following previous analyses of MUSIC and Min-Norm, an analytical expression of the variance of the DOA estimation-error is developed for state-space realization and ESPRIT in a greatly simplified fashion. The tractable formulas provide insight for design. Simulation results verify the analysis.>

The computational complexity and the effects of quantization and sampling instant errors in the arithmetic Fourier transform (AFT) and the summation by parts discrete Fourier transform (SBP-DFT) algorithms are examined. The relative efficiency of the AFT and SBP-DFT algorithms is demonstrated by comparing the number of multiplications, additions, memory storage locations, and input signal samples as well as the latency time and level of parallelism of these two methods with that of more conventional single-output DFT and multiple-output fast Fourier transform (FFT) routines. The error response of the kth Fourier bin of these algorithms is analyzed as a function of increasing levels of input signal sampling errors in the AFT and coefficient quantization errors in the SBP-DFT. It is demonstrated that invalid assumptions on the bandwidth of the input signal will cause aliasing errors to occur in the AFT spectrum that are different from the aliasing errors that occur in the DFT.>

The authors present a min-norm algorithm for estimating the directions of arrival of signals impinging on a sensor array of arbitrary geometry. The algorithm is an extension of the min-norm algorithm derived by R. Kumaresan and D.W. Tufts (1983) for the case of a uniform line array. A perturbation analysis for this arbitrary array min-norm method is also presented, and analytical formulas that predict the variance of the estimated directions are given. Simulations with a circular array demonstrate the algorithm as well as verify the performance analysis.>

A greatly simplified calculation of the accuracy of estimates of the parameters of exponential signals is introduced. The authors assume that the estimates are obtained by first estimating the coefficients of a prediction-error filter (PEF) that arises in signal modeling by linear prediction. A simplified approach based on matrix approximation is used to calculate the statistics of the errors in the estimated signal parameters at high SNR. This approach provides insights for design and tractable formulas even for the case of multicomponent signals and Hankel or Toeplitz data matrices. The analyses are verified by simulation examples that include single- and multiple-component signals consisting of damped or undamped complex exponential signals in noise.>

The problem of analyzing the threshold effect of signal processing algorithms which use the singular-value decomposition (SVD) is addressed. The probability of obtaining an outlier is calculated and used to determine the threshold SNR at which the variance of parameter estimation errors depart from Cramer-Rao bound behavior. Simulation results using low rank approximation and linear prediction for frequency estimation verify the analysis. The same method of analysis can be applied to a broad class of parameter-estimation methods in which the principal-component technique or low rank approximations to matrices are used.>

Threshold computation is essential in comparing the statistical performance of algorithms when estimating signal parameters. The authors show that it is possible to extend the threshold effect of singular-value-decomposition (SVD)-based signal-processing algorithms by using the Prony-Lanczos (P-L) method to lower values of signal-to-noise ratio. The procedure is comprised of two steps. In the first step, a nonparametric spectrum analysis or beamforming is used to yield a good starting point. This is followed in the second step by the (P-L) algorithm, which performs a local search, a procedure relatively insensitive to outliers. Simulation results, based on the angles between the estimated and true subspaces using the SVD-based algorithm and the P-L method, provide valuable insight.>

This paper presents a statistical analysis of the state-variable balancing and Prony methods for estimating the parameters of exponential signals in the presence of additive noise. The case of frequency estimation for a single sinusoid is carried out in detail. Analytical expressions for the variances of the frequency estimates at high signal-to-noise ratios are derived. The calculated variances are compared to the Cramer-Rao bound. The results are validated by simulations over a wide range of signal-to-noise ratios. The analysis and simulations show that the state-variable balancing method can provide slightly more accurate frequency estimates while avoiding the problem of selecting the signal zeros of the Prony polynomial.

The analysis of signals that can be represented as a linear combination of exponentially damped sinusoids where the values of damping factors, frequencies, and the linear combination coefficients change at certain transition times is considered. These transitions represent the opening and closing of the glottis in the case of speech signals. Techniques are presented for the accurate estimation of the exponential parameters and the times of transition, from noise corrupted observations of the signal. The exponential parameters are obtained by improved linear prediction techniques using low-rank approximations, and further refined by an iterative least-squares technique with stability constraints imposed on the damping factors. Optimal estimates (in the least-squares sense) of the time of transition are presented. Our knowledge of the signal structure is used to obtain improved performance and also a computationally efficient estimation algorithm. Experiments with real, connected speech indicate that the speech waveforms can be accurately represented from a small number of parameters using the analysis presented here.

Two improvements are presented for adaptive equalization of communication channels for data transmission. One of them is designed to mitigate the effects of impulsive noise on the channel through data-adaptive nonlinear filtering. The other improvement uses low-rank approximation techniques to adaptively prefilter the received training waveform which is to be used for adaptive equalization. This permits successful equalization to be carried out with less received data and at lower values of signal-to-noise ratio (SNR).

Two previously proposed methods of Tufts and Kumaresan for estimating paired frequency-wavenumber values of multiple two-dimensional (2-D) sinusoids are evaluated in more detail using results of simulations.

Two previously proposed methods of Tufts and Kumaresan for estimating paired frequency-wavenumber values of multiple two-dimensional (2- D) sinusoids are evaluated in more detail using results of simulations. The results indicate that the use of singular value decomposition and low rank approximation, instead of the simplified method of [6], lowers the SNR threshold by roughly 8dB and reduces the rms error in estimation by roughly a factor of one half for the case of the sum of two closely spaced 2-D sinusoids.

The main advantage of our previously presented [10] principal-component method of adaptive detection, in comparison with the method based on the inverse of the estimated covariance matrix, is that much less data is required to produce a given, needed level of SNR with high probability. In this paper we present an outline of the derivation of the approximate probability density of the SNR for this adaptive detector. To simplify the derivation we assume that the noise consists of a strong gaussian rank-one-covariance interference component plus a component of white gaussian background noise. The approximations and the final probability density are tested through simulation.

We present the results of a preliminary investigation of a method of Lanczos and the power method for simple computation of approximations to eigenvectors and eigenvalues. We concentrate on the application of high-resolution estimation of frequencies of multiple sinusoids. We find that the performance is similar to that of high-resolution estimates which are calculated using singular value decomposition of a data matrix or estimated covariance matrix. These methods are also suitable for VLSI implementation.

Maximum-likelihood estimates of the parameters of exponentially damped sinusoidal signals in noise can be found by using an iterative procedure based on Newton's method. The initial estimate is obtained by an improved linear-prediction method. The properties of the Newton estimates obtained from short data records is experimentally studied.

The detection of a constant signal in additive noise is considered for independent and correlated impulsive noise environments. Suboptimum detector structures which estimate the occurrences of impulses and eliminate those data points are shown, through example, to yield performance close to that of systems which are given the indices of the data contaminated by the impulses.

Estimates of frequencies of noise corrupted sinusoidal signals are often obtained from the zero locations of data adaptive or prediction error filters [1,2]. It is well known that the frequency estimation error decreases as the order of the prediction error filter is increased for a given data record length. In this paper, we explain this phenomenon, at high SNR by calculating the statistics of the estimation error.

Assuming that a short segment of observed speech signal can be modeled as the noisy impulse response of a linear system we obtain the pole locations of the system from the zeros of a polynomial. The coefficients of the polynomial are accurately determined by two methods using eigenvalue-eigenvector decomposition of an estimated correlation matrix. The speech-like signal is used in the reversed time direction to identify the signal related zeros of the Polynomial from the rest. Experimental results comparing the accuracy of the Pole parameters obtained by different methods are given.

We present more information about improved methods for estimation of the frequencies of sinusoids which are closely spaced in frequency and which are observed in the presence of noise using limited apertures in time and/or space. We compare our realization of maximum likelihood estimation of multiple frequencies with an improved version of Owsley's method and with the forward-backward prediction method advocated by Ulrych and Clayton and by Marple.

The application of linear prediction to frequency estimation for sinusoidal signals in noise is investigated. It is shown that improved performance is obtained by processing a complex-valued version of the real-valued input signal, with the corresponsing sampling rate reduced by one-half. The case of a single sinusoid in white noise is studied in detail, including the eigenvalues of the covariance matrix, zeros of the inverse filter polynomial, frequency bias, and frequency variance as a function of input SNR and prediction order.

An iterative procedure for optimally estimating the phase angle of a sinusoid of known frequency is presented. The sinusoid is observed in additive Gaussian noise, and the phase angle is assumed to be a Gaussian random variable. The maximum {\em a posteriori} probability (MAP) criterion is used. It is also shown how other signal parameters, such as amplitude and frequency, can be optimally estimated and tracked. Examples are given in which these techniques are used to perform optimum demodulation of angle-modulated signals. The results should dispel the commonly held belief that the best one can do in approaching optimum demodulation of angle-modulated signals is to use a phase-locked loop.

We present new techniques for the measurement of pitch period and formant frequencies. Individual pitch periods are estimated by finding local maxima in the power spectrum averaged over a frequency band that includes a formant. A spectral analysis is then performed for each pitch period over a data interval that is of shorter duration than the estimated pitch period. The pitch synchronous spectral analysis followed by post detection smoothing - preferably carried out over both time and frequency - leads to a spectrogram from which formant trajectories can be estimated by simple algorithms.

Intersymbol interference and additive noise are two common sources of distortion in data transmission systems. For pulse amplitude modulation (PAM) communication links, the combination of transmitter waveform and linear receiver that minimizes the mean-squared error arising from these sources is determined. An extension to include the effects of timing jitter is performed in a companion paper. Performance characteristics of the optimal PAM systems, showing the mean-squared error versus the signal-to-noise ratio, are determined explicitly for several examples. These characteristics are compared both with those of certain suboptimal systems and with the optimal performance theoretically attainable (OPTA), derived by combining Shannon's concepts of the capacity of a channel and the rate distortion function of a source. The optimal PAM systems are seen to perform very close to the OPTA for low signal-to-noise ratios. For high signal-to-noise ratios, however, the mean-squared error of optimal PAM systems decreases as the reciprocal of the signal-to-noise ratio, but the OPTA decreases more rapidly, except for band-limited channels. The performance of PAM systems can be improved at high signal-to-noise ratios by coding techniques. One such technique, called Shannon-Cantor coding, is discussed briefly.

Signal flow graph methods are applied to the problem of counting the number of allowable code words for certain classes of prefixed comma-free codes. This method can be applied whenever the distance between the prefix and otherA-tuples in the code word is a prescribed function of the position of theA-tuple. Such codes can have desirable synchronization properties without leading to very small code word sets.

A method is presented for specifying transmitter waveforms and receiver filters for pulse amplitude modulation (PAM) systems which are subject to distortion from additive noise, intersymbol interference, and timing jitter. A criterion of minimum mean-squared error is used. For the case of band-limited transmission, specific procedures are developed for computing optimum transmitters, optimum receivers, and jointly optimum transmitters and receivers. For two special jitter distributions the joint optimization problem is solved without a bandwidth limitation, and the resulting systems are found to be band-limited. In cases of localized timing jitter and high signal-to-noise ratio, we are led to system pulse responses of the form[\sin x/x]^{2}. A nonparametric method of reducing the effects of timing jitter is briefly discussed. In this approach the noise interference is minimized subject to the constraints that the intersymbol interference be zero and that the system pulse response have zero derivative at each nominal sampling point.

Using a criterion of minimum average error probability we derive a method for specifying an optimum linear, time invariant receiving filter for a digital data transmission system. The transmitted data are binary and coded into pulses of shape\pm s(t). The linear transmission medium introduces intersymbol interference and additive Gaussian noise. Because the intersymbol interference is not Gaussian and can be correlated with the binary digit being detected, our problem is one of deciding which of two waveforms is present in a special type of correlated, non-Gaussian noise. For signal-to-noise ratios in a range of practical interest, the optimum filter is found to be representable as a matched filter followed by a tapped delay line--the same form as that of the least mean square estimator of the pulse amplitude. The performance (error probability vs.S/N) of the optimum filter is compared with that of a matched-filter receiver in an example.