This paper presents a tutorial review of work in coherence and time delay estimation. A review of coherence research and development is presented. A derivation of the ML estimator for time delay is presented together with an interpretation of that estimator as a special member of a class of generalized cross correlators. The performance of the estimator is given for both high and low signal-to-noise ratio cases. The proposed correlator is implemented and stimulated with synthetic data. The results are compared with performance predictions and found to be in good agreement.

Coherence and time delay estimation

An overview of applied research in passive sonar signal processing estimation techniques for naval systems is presented. The naval problem that motivates time delay estimation is the source state estimation problem. A discussion of this problem in terms of estimating the position and velocity of a moving acoustic source is presented. Optimum bearing and range estimators are presented for the planar problem and related to the optimum time delay vector estimator. Suboptimum realizations are considered together with the effects of source motion and receiver positional uncertainty.

Time delay estimation for passive sonar signal processing

This paper introduces a new velocity estimator, referred to as the 2D autocorrelator, which differs from conventional Doppler techniques in two respects: the derivation of axial velocity values by evaluating the Doppler equation using explicit estimates of both the mean Doppler and the mean RF frequency at each range gate location; and, the 2D nature (depth samples versus pulse transmissions) of processing within the range gate. The estimator's output can be calculated by evaluating the 2D autocorrelation function of the demodulated (baseband) backscattered echoes at two lags. A full derivation and mathematical description of the estimator is presented, based on the framework of the 2D Fourier transform. The same framework is adopted to analyze two other established velocity estimators (the conventional 1D autocorrelator and the crosscorrelator) in a unifying manner, and theoretical arguments as well as experimental results are used to highlight the common aspects of all three estimators. In addition, a thorough performance evaluation is carried out by means of extensive simulations, which document the effect of a number of factors (velocity spread, range gate length, ensemble length, noise level, transmitted bandwidth) and provide an insight into the optimum parameters and trade-offs associated with individual algorithms. Overall, the 2D autocorrelator is shown to offer the best performance in the context of the specific simulation conditions considered here. Its superiority over the crosscorrelator is restricted to cases of low signal-to-noise ratios. However, the 2D autocorrelator always outperforms the conventional 1D autocorrelator by a significant margin. These comparisons, when linked to the computational requirements of the proposed estimator, suggest that it combines the generally higher performance of 2D broadband time-domain techniques with the relatively modest complexity of 1D narrowband phase-domain velocity estimators. >

/pdf/an-axial-velocity-estimator-for-ultrasound-blood-flow-11yyhdaxbj.pdf

An axial velocity estimator for ultrasound blood flow imaging, based on a full evaluation of the Doppler equation by means of a two-dimensional autocorrelation approach

To find the position of an acoustic source in a room, the relative delay between two (or more) microphone signals for the direct sound must be determined. The generalized cross-correlation method is the most popular technique to do so and is well explained in a landmark paper by Knapp and Carter. In this paper, a new approach is proposed that is based on eigenvalue decomposition. Indeed, the eigenvector corresponding to the minimum eigenvalue of the covariance matrix of the microphone signals contains the impulse responses between the source and the microphone signals (and therefore all the information we need for time delay estimation). In experiments, the proposed algorithm performs well and is very accurate.

Adaptive eigenvalue decomposition algorithm for passive acoustic source localization

Time delay estimation has been a research topic of significant practical importance in many fields (radar, sonar, seismology, geophysics, ultrasonics, hands-free communications, etc.). It is a first stage that feeds into subsequent processing blocks for identifying, localizing, and tracking radiating sources. This area has made remarkable advances in the past few decades, and is continuing to progress, with an aim to create processors that are tolerant to both noise and reverberation. This paper presents a systematic overview of the state-of-the-art of time-delay-estimation algorithms ranging from the simple cross-correlation method to the advanced blind channel identification based techniques. We discuss the pros and cons of each individual algorithm, and outline their inherent relationships. We also provide experimental results to illustrate their performance differences in room acoustic environments where reverberation and noise are commonly encountered.

/pdf/time-delay-estimation-in-room-acoustic-environments-an-2y9s0s5kf2.pdf

Time delay estimation in room acoustic environments: an overview

This paper concerns the use of Widrow's least-mean-square (LMS) algorithm for implementing a time delay estimation algorithm for fixed and moving passive sonar sources. Digital simulation results are included for evaluating the related performance of the LMS algorithm.

On using the LMS algorithm for time delay estimation

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.

On the simulation of a class of time delay estimation algorithms

This paper concerns an adaptive approach for estimating the magnitude-squared coherence (MSC) function via Widrow's least-mean-square (LMS) algorithm. Analytical expressions for the bias and variance of the estimate so obtained are derived for the case when the input signals are stationary. Some computer simulation results are also included for both stationary and nonstationary signals.

http://ieeexplore.ieee.org/iel6/29/26175/01164055.pdf

Magnitude-squared conherence function estimation: An adaptive approach

This correspondence concerns the use of the Widrow's adaptive least-mean-square (LMS) adaptive filter algorithm [1] for estimating the time delay between two-sensor outputs. Theoretical bias and estimation error are discussed. This analytical study provides a clue for determining the most effective way of processing the received signals through the adaptive filter. Computer simulation results are also included.

An adaptive approach for time delay estimation of band-limited signals

A method for generating a delayed version of a given bandlimited signal is presented, where the delay could be time-varying. Simulation results which illustrate the performance of this method are also included.

G. Carter

Papers

On using the LMS algorithm for time delay estimation

On the simulation of a class of time delay estimation algorithms

Magnitude-squared conherence function estimation: An adaptive approach

An adaptive approach for time delay estimation of band-limited signals

A method for generating a class of time-delayed signals