Subsample Time Delay Estimation Research Articles

A New Subsample Time Delay Estimation Algorithm for LFM-Based Detection

This paper investigated a Subsample Time delay Estimation (STE) algorithm based on the amplitude of cross-correlation function to improve the estimation accuracy. In this paper, a rough time delay estimation is applied based on traditional cross correlator, and a fine estimation is achieved by approximating the sampled cross-correlation sequence to the amplitude of the theoretical cross-correlation function for linear frequency modulation (LFM) signal. Simulation results show that the proposed algorithm outperforms existing methods and can effectively improve time delay estimation accuracy with the complexity comparable to the traditional cross-correlation method. The theoretical Cramér-Rao Bound (CRB) is derived, and simulations demonstrate that the performance of STE can approach the boundary. Eventually, four important parameters discussed in the simulation to explore the impact on Mean Squared Error (MSE).

Временные корреляционные методы оценки задержки комплексных сигналов, некратной периоду дискретизации, на основе полиномиальной интерполяции.

This paper deals with the problem of subsample time delay estimation of complex signal based on polynomial interpolation. Time delay estimation is performed by cross-correlation time approach. Three polynomial interpolation techniques applied to the discrete complex cross-correlation function in the neighborhood of its maximum are proposed. These methods show high processing speed and allow obtaining accurate real-valued time delay estimation when digital complex signals are processed. The comparative analysis between these methods is performed. A rigorous analytical solution for the correction of time delay estimation for one of the proposed methods is obtained for the case of the third-order polynomial interpolation. This solution is applied for an equidistant grid of discrete cross-correlation function samples. One can improve the accuracy of time delay estimates by using aforementioned correction. A numerical simulation is performed to quantify the accuracy of the time delay estimates when using the proposed methods for the case where a stationary random process described by the first-order autoregressive mode is chosen as a model of original signal. The main results were presented and discussed at XIV All-Russian conference “Radar and telecommunication”.

Subsample time delay estimation of chirp signals using FrFT

A new subsample time delay estimator is proposed in this paper. It is evaluated based on the time delay property of the fractional Fourier transform and is suitable for processing chirp signals. The theoretic derivation of the algorithm is also presented. The validity and superiority to the fractional time delay estimator (FRTDE), the conventional direct correlator (DC) and the average magnitude squared fractional difference function (AMSFDF) estimator of this new time delay estimator are demonstrated via computer simulations.

MUlti-Dimensional Spline-Based Estimator (MUSE) for Motion Estimation: Algorithm Development and Initial Results

Image registration and motion estimation play central roles in many fields, including RADAR, SONAR, light microscopy, and medical imaging. Because of its central significance, estimator accuracy, precision, and computational cost are of critical importance. We have previously presented a highly accurate, spline-based time delay estimator that directly determines sub-sample time delay estimates from sampled data. The algorithm uses cubic splines to produce a continuous representation of a reference signal and then computes an analytical matching function between this reference and a delayed signal. The location of the minima of this function yields estimates of the time delay. In this paper we describe the MUlti-dimensional Spline-based Estimator (MUSE) that allows accurate and precise estimation of multi-dimensional displacements/strain components from multi-dimensional data sets. We describe the mathematical formulation for two- and three-dimensional motion/strain estimation and present simulation results to assess the intrinsic bias and standard deviation of this algorithm and compare it to currently available multi-dimensional estimators. In 1000 noise-free simulations of ultrasound data we found that 2D MUSE exhibits maximum bias of 2.6 x 10(-4) samples in range and 2.2 x 10(-3) samples in azimuth (corresponding to 4.8 and 297 nm, respectively). The maximum simulated standard deviation of estimates in both dimensions was comparable at roughly 2.8 x 10(-3) samples (corresponding to 54 nm axially and 378 nm laterally). These results are between two and three orders of magnitude better than currently used 2D tracking methods. Simulation of performance in 3D yielded similar results to those observed in 2D. We also present experimental results obtained using 2D MUSE on data acquired by an Ultrasonix Sonix RP imaging system with an L14-5/38 linear array transducer operating at 6.6 MHz. While our validation of the algorithm was performed using ultrasound data, MUSE is broadly applicable across imaging applications.

Computationally efficient spline- based time delay estimation

We previously presented a highly accurate, spline-based time delay estimator that directly determines subsample time delay estimates from sampled data. The algorithm uses cubic splines to produce a continuous time representation of a reference signal, and then computes an analytical matching function between this reference and a delayed signal. The location of the minima of this function yields estimates of the time delay. In this paper we present more computationally efficient formulations of this algorithm. We present the results of computer simulations and ultrasound experiments which indicate that the bias and the standard deviation of the proposed algorithms are comparable to those of the original method, and thus superior to other published algorithms.

Bayesian regularization and nonnegative deconvolution for room impulse response estimation

This paper proposes Bayesian Regularization And Nonnegative Deconvolution (BRAND) for accurately and robustly estimating acoustic room impulse responses for applications such as time-delay estimation and echo cancellation. Similar to conventional deconvolution methods, BRAND estimates the coefficients of convolutive finite-impulse-response (FIR) filters using least-square optimization. However, BRAND exploits the nonnegative, sparse structure of acoustic room impulse responses with nonnegativity constraints and L/sub 1/-norm sparsity regularization on the filter coefficients. The optimization problem is modeled within the context of a probabilistic Bayesian framework, and expectation-maximization (EM) is used to derive efficient update rules for estimating the optimal regularization parameters. BRAND is demonstrated on two representative examples, subsample time-delay estimation in reverberant environments and acoustic echo cancellation. The results presented in this paper show the advantages of BRAND in high temporal resolution and robustness to ambient noise compared with other conventional techniques.

A new time delay estimator based on ETDE

In this paper, we address the problem of online subsample time delay estimation of narrowband signals of known center frequency. We propose a new so-called mixed modulated Lagrange explicit time delay estimation (MMLETDE) algorithm and study its performance through computer simulations. The MMLETDE is a modulated Lagrange ETDE, but the delay estimate adaptation process is based on the truncated sinc fractional delay filter algorithm. We provide theoretical derivations for our proposed estimator, a proof of its convergence performance, learning characteristics of its error performance surface, and an expression for its delay variance. Using simulations, we show that MMLETDE requires only a small filter order and has no noticeable estimation bias over a wide frequency range.

Model-based estimation of ultrasonic echoes. Part II: Nondestructive evaluation applications.

Accurate estimation of the ultrasonic echo pattern leading to the physical property of the object is desirable for ultrasonic NDE (nondestructive evaluation) applications. In Part I of this study, we have presented a generalized parametric ultrasonic echo model, composed of a number of Gaussian echoes corrupted by noise, and algorithms for accurately estimating the parameters. In Part II of this study, we explore the merits of this model-based estimation method in ultrasonic applications. This method produces high resolution and accurate estimates for ultrasonic echo parameters, i.e., time of flight (TOF) amplitude, center frequency, bandwidth, and phase. Furthermore, it offers a solution to the deconvolution problem for restoration of the target response, i.e., ultrasonic reflection and transmission properties of materials, from the backscattered echoes. The model-based estimation method makes deconvolution possible in the presence of significant noise. It can also restore closely spaced overlapping echoes beyond the resolution of the measuring system. These properties of the estimation method are investigated in various ultrasonic applications such as transducer pulse-echo wavelet estimation, subsample time delay estimation, and thickness sizing of thin layers.

Adaptive subsample time delay estimation using Lagrange interpolators

This letter addresses the problem of on-line sub-sample time delay estimation of narrowband signals of known center frequency. A new form of the Lagrange interpolator filter is presented in this letter, which is incorporated into the explicit time delay estimator (ETDE) method. Simulations show that ETDE with the filter modulated to the signal center frequency significantly outperforms conventional ETDE.

Comparison of discrete subsample time delay estimation methods applied to narrowband signals

The problem of estimating the subsample time delay between two noise-corrupted narrowband signals is considered. Significant improvements to two previously proposed estimators, the MXS and MSX, are made. The performance of the revised estimators is assessed through simulation over a range from -10 to 20 dB, with four well known estimators, two of which are asymptotically maximum likelihood (the direct correlator and the average square difference function) and the other two are windowed versions of them (the generalized cross-correlator and generalized least squares). Also, the estimators are applied to ultrasonic experimental data at three different SNRs. At low SNR, the MXS/MSX estimators are shown to exhibit a significant reduction in the variance of the estimates.

Noise reduction in elastograms using temporal stretching with multicompression averaging

Elastography uses estimates of the time delay (obtained by cross-correlation) to compute strain estimates in tissue due to quasistatic compression. Because the time delay estimates do not generally occur at the sampling intervals, the location of the cross-correlation peak does not give and accurate estimate of the time delay. Sampling errors in the time-delay estimate are reduced using signal interpolation techniques to obtain subsample time-delay estimates. Distortions of the echo signals due to tissue compression introduce correlation artifacts in the elastogram. These artifacts are reduced by a combination of small compressions and temporal stretching of the postcompression signal. Random noise effects in the resulting elastograms are reduced by averaging several elastograms, obtained from successive small compressions (assuming that the errors are uncorrelated). Multicompression averaging with temporal stretching is shown to increase the signal-to-noise ratio in the elastogram by an order of magnitude, without sacrificing sensitivity, resolution or dynamic range. The strain filter concept is extended in this article to theoretically characterize the performance of multicompression averaging with temporal stretching.

On the subsample time delay estimation of narrowband ultrasonic echoes

Correlation based time delay estimators, optimal under certain conditions, exhibit the well-known threshold effect of poor performance at low signal-to-noise ratio (SNR). This sudden reduction in performance of the correlation based time delay estimators at low SNR arises from the misidentification of one unique extremum in very noisy conditions and from the peak fitting procedure in the case of the subsample time delay estimation. In this paper, two new estimators-the MSX and MXS-for the estimation of subsample time delays in narrow-band signals are proposed. In these estimators, cross-correlations and autocorrelations are matched at a number of different lags to yield a number of time delay estimates which are subsequently combined to obtain one robust time delay estimate. They seem to perform adequately over the SNR range used in simulations of -5 to 20 dB. Their performances are compared to those of two cross-correlation based estimators. Using simulated data, it is demonstrated that all four estimators perform well at high SNR, but at low SNR the proposed MSX and MXS estimators offer significant improvements in the bias and variance of the estimates. Additionally, these findings are verified using ultrasonic experimental data at three different SNR.