Delay Estimation Method Research Articles

Performance of time delay estimation methods for small time shifts in ultrasonic signals.

In this study several time delay estimation (TDE) methods were investigated for estimation of time shifts of less than 10 ns at a frequency of 30 MHz. Using simulated and experimental echosignals we investigated the performance of five methods: two phase related methods (phase shift and phase difference method); two correlation methods (cross-correlation and correlation interpolation method); and a demodulation method. The results showed that the correlation interpolation method is by far the most accurate for all time delays. With this method, estimation errors of about 200 ps are achievable with an signal-to-noise ratio (SNR) of 40 dB (f0 = 30 MHz, bandwidth = 20 MHz) for time shifts of up to 10 ns.

A new cepstral prefiltering technique for estimating time delay under reverberant conditions

A microphone array can be used for hands-free acquisition of speech under reverberant conditions. This requires knowledge about the desired talker location, which can be obtained by estimating the time delays between the signals received by one or more pairs of spatially separated microphones. However, in a typical audio-conference room, strong reverberation is usually present and can have disastrous effects on the performance of conventional time delay estimation (TDE) methods. In this article, we present and evaluate a new cepstral prefiltering technique which can be applied on the received signals before the actual TDE in order to obtain a more accurate estimate of the delay in a typical reverberant environment. The technique is based on the estimation and the subtraction of the minimum-phase component (MPC) of the channel cepstrum from the total cepstrum of each microphone signal. So, in the same way that it is necessary in certain TDE methods to estimate the power spectral densities of the signals of interest from the received data, the new method requires the estimation of the channel MPC in the cepstral domain. The performances of a TDE system with and without cepstral prefiltering are compared via Monte-Carlo simulations for fixed random and speech sources as well as for a moving random source. The results clearly demonstrate the beneficial effects of the new cepstral prefiltering technique on TDE performance when the source is fixed or slowly moving.

An Eckart-weighted adaptive time delay estimation method

A new proposal for the Eckart-weighted adaptive time delay estimation is reported. The performance is analyzed, and the results of computer simulation are given. The theoretical analysis and computer simulation show that this method is highly precise in time delay estimation, and it does not depend on the knowledge of input signal and noises.

Joint estimation of time delay and frequency delay in impulsive noise using fractional lower order statistics

New methods for time delay estimation and joint estimation of time delay and frequency delay in the presence of impulsive noise are introduced. First, degradation of the conventional approaches based on second-order statistics is shown both theoretically and experimentally. Then, a new class of robust algorithms are developed using the theory of alpha-stable distributions, including the fractional lower order covariance (FLOC) method, which is formulated for the time delay estimation problem and the fractional lower order ambiguity function (FLOAF), which is defined for the joint estimation of time delay and frequency delay. It is shown that these new methods are robust for both Gaussian and non-Gaussian impulsive noise environments. The improved performance is clearly demonstrated through detailed analysis and comprehensive simulations with computer-generated data as well as actual radar and sonar clutter data.

Accuracy of a time delay estimator with unknown sampled signals

Time delay estimation methods from sampled base-band signals were recently devised and their performance provided in the Gaussian case. The accuracy of a sampled-time method is here evaluated for estimating the time delay between unknown band-pass Gaussian signals (represented by their complex envelopes), working on cross-correlation magnitude estimates.

LMS adaptive time delay estimation with two windows

An LMS adaptive time delay estimation method with two windows is presented. This method can reduce the superfluous calculation greatly when the time of correlation is long. It is suitable for the time delay estimation of white band-limited random signals. The feasibility and the performances of this method are also studied.

Practical issues in the use of a frequency-domain delay estimator for microphone-array applications

A frequency-domain delay estimator has been used as the basis of a microphone-array talker location and beamforming system [M. S. Brandstein and H. F. Silverman, Techn. Rep. LEMS-116 (1993)]. While the estimator has advantages over previously employed correlation-based delay estimation methods [H. F. Silverman and S. E. Kirtman, Comput. Speech Lang. 6, 129–152 (1990)], including a shorter analysis window and greater accuracy at lower computational cost, it has the disadvantage that since delays between microphone pairs are estimated independently of one another, there is nothing to ensure that a set of estimated delays corresponds to a single location. This not only introduces errors in talker location but degrades the performance of the beamformer. A method for delay estimation and talker location with a microphone array is described that preserves the low computational complexity and rapid tracking ability of the frequency-domain delay estimator, while improving the coherence and stability of the estimated delays and derived source locations. Experimental results using data from a real 16-element array are presented to demonstrate the performance of the algorithms. [Early work principally funded by DARPA/NSF Grant IRI-8901882, and current work by NSF Grant No. 9314625.]

An adaptive time delay estimation with direct computation formula

The problem of estimating and tracking time delay between signals received at two spatially separated sensors is essential in varied fields. For example, in the sonar system, the information of time delay can be used to localize the radiating source. In real-time processing, an adaptive time delay estimation (TDE) method with desired performance and less computational time is preferred. In this short paper, a simple and efficient method is suggested for TDE. This is done by employing a direct formula coupled with the adaptive LMS TDE algorithm. The advantage of the presented method, in terms of the accuracy as well as execution time, over the conventional lookup table method and interpolation formula method is shown in both the stationary and nonstationary time delay environments. Moreover, the capability of estimating time delay in an environment with multipath propagations is investigated.

A New Indirect Adaptive Time-Delay Estimation Method

Structures and parameter domains of discrete-time equivalent models of continuous-time linear processes play important role in advanced modeling and control methodologies. A simple technique is introduced how to represent fractional time delay with different discrete-continuous transformations. A new indirect adaptive time delay estimation method is shown based on these relationships.

A time delay estimator based on the signal integral: theoretical performance and testing on ECG signals

We present a theoretical and experimental performance study of a method for time delay estimation (TDE), based on the signal integral (TDE-SI). The TDE-SI method considers the delay between two transient signals as the difference between the center of mass of these signals. The method has three special cases: In the first, time is the mass coordinate and the signal sit) is the mass distribution (estimate D/spl circ//sub s/); in the second case, the squared signal s/sup 2/(t) is the mass distribution (estimate D/spl circ/(s/sup 2/)); and the last is a variant of the second. The bias and the standard deviation to) of the estimate have been evaluated when the signal is contaminated by Gaussian white noise. D/spl circ//sub s/ is not biased but the /spl sigma/ of the TDE is higher than that obtained when working with D/spl circ/(s/sup 2/). Moreover, the D/spl circ/(s/sup 2/) estimate is biased. The special case of a bias-corrected estimate (D/spl circ/'(s/sup 2/)) is presented; this D/spl circ/'(s/sup 2/) yields a /spl sigma/ of its TDE lower than the estimate D/spl circ//sub s/. Hence, D/spl circ/'(s/sup 2/) is the most suitable of the three TDE-SI options for TDE. Theoretical estimations are validated by simulation results with artificially generated signals and by real so-called QRS complex waves (ventricular activity) from an electrocardiographic (ECG) signal.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Time delay estimation with unknown spatially correlated Gaussian noise

The problem of estimating the difference in arrival times of a non-Gaussian signal at two spatially separated sensors is considered. The signal is assumed to be corrupted by spatially correlated Gaussian noises of unknown cross-correlation. The author proposes and analyzes two new classes of methods for time delay estimation based on higher order statistics. The proposed methods are conceptually very similar to the traditional cross-correlation-based techniques in that the proposed criteria peak at a lag value equalizing true delay. Since the proposed methods are based upon higher order cumulant statistics of the data, they result in estimators that remain unbiased in the presence of Gaussian noise. >

A new method for adaptive time delay estimation for non-Gaussian signals

A novel adaptive scheme for time delay estimation is introduced for signal environments where the signal is non-Gaussian and the additive noise sources are spatially correlated Gaussian with unknown power spectrum characteristics. This scheme is based on parametric modeling between two sensor measurements and employs higher-order statistics (third- or fourth-order) of the data. It is demonstrated by means of extensive simulations that this scheme works well for both stationary and nonstationary cases. As expected, it outperforms the cross-correlation-based gradient method for time-delay adaptation in spatially correlated Gaussian noises. The proposed scheme is compared to the overdetermined recursive instrumental variable method and is shown to exhibit substantially less computational complexity. >

Time delay estimation of signals with uncertain spectra

The performance of generalized correlation (GC) methods for time-delay estimation when a priori knowledge of the received source spectrum is limited is improved. The treatment is restricted to finite-time observation of a single low-pass source, where the uncertainty in its autospectrum is characterized by a single unknown parameter. The constrained processor (CP) selects an optimum postcorrelator filter from a finite set of alternatives that are designed to span the expected range of source spectra. An approach proposed previously for this situation is the LMS adaptive filtering method for time delay estimation (LMSTDE). For purposes of comparison, both the theoretical and simulation performance of the LMSTDE method are examined. Simulation experiments indicate that LMSTDE offers performance comparable to conventional GC methods without a priori knowledge of the source spectrum. The CP in the same setting, however, can yield significantly lower variance time delay estimates than either the LMSTDE or conventional GC methods, with performance approaching the Cramer-Rao lower bound. >

High resolution ECG analysis by an improved signal averaging method and comparison with a beat-to-beat approach

The aim of this paper is to describe the analysis of a high resolution ECG recorded from the body surface. Standard signal averaging techniques are improved by using a new time delay estimation method which leads to a better alignment accuracy of P and T waves. A second method uses adaptive identification to achieve a beat by beat fine ECG estimation. Information provided by the two methods allows a better interpretation of low and very low level signals.

Phase comparison time delay estimation using wideband signals

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Comparison of various time delay estimation methods by computer simulation

This correspondence provides qualitative estimates of the magnitude of the error in the measured delay time resulting from the error on the observed cross-correlation curve. The variances of five time delay estimators have been obtained by computer simulation to demonstrate the accuracy of all five methods. The comparison of the different correlation techniques shows that the average magnitude difference function gives results almost as accurate as direct correlation.

The least squares estimation of time delay between two signals with unknown relative phase shift

This correspondence addresses the problem of time delay estimation between two signals with an unknown constant relative phase shift. The method of time delay estimation for the pure delay case of Chan et al. [1] is applied here to derive the least squares estimator (LSE). An explicit expression for the LSE of the delay is obtained which is computationally less complex than the maximum likelihood estimator (MLE) [2]. It is shown that the LSE is unbiased, and that the mean-square error or the LSE is asymptotically equivalent to that of the pertinent MLE.

Comparison of two methods for time delay estimation of sinusoids

This note concerns the time delay estimation of a sinusoid in the absence of noise. It is shown that the smoothed coherence transform (SCOT) method performs much better than the standard cross-correlation (SCC) method, in that the former greatly reduces the ambiguity in determining the peak of the related cross-correlation function.

Delay estimation and the estimation of coherence and phase

The method of delay estimation given in Hamon and Hannan [1] is reviewed and a modification involving autoregressive model fitting is proposed. It is shown how numerical problems associated with the optimization of the criterion used in both the original and modified procedures can be circumvented. The modified procedure and a procedure due to Chan, Riley, and Plant [2] are compared to the Hamon-Hannan procedure by simulations. For moderate to large signal-to-noise ratios, the modified Hamon-Hannan procedure appears to provide better estimates. In the case of low signal-to-noise ratios, with the smaller size, the Chan, Riley, and Plant procedure performed best.