Accurate Time Delay Estimation Research Articles

A D-norm cross-correlation method for particle velocity measurement through electrostatic sensing

The cross-correlation (CC) method is conventionally used for measuring the velocity of gas–solid flows using electrostatic sensors, wherein velocity measurement is transformed into a time-delay estimation problem. However, owing to the intricacies of signals in gas–solid flows, the cross-correlation function may exhibit multiple peaks, resulting in peak misjudgment and time-delay estimation bias. To address these issues, this paper proposes a D-norm cross-correlation (DCC) velocity measurement method and applies it to flow velocity measurements in pneumatic conveying. Such a technique leverages the sensitivity of D-norm to pulses, highlighting the pulse characteristics of measurement signals. This approach increases the accuracy of time-delay estimation for upstream and downstream signals, mitigating the issues caused by multi-peaks and fake peaks in the cross-correlation function. Compared to conventional CC, the DCC can eliminate the problem of multiple and fake peaks in cross-correlation functions more effectively, thereby increasing the reliability of velocity measurements.

The Combination of Spectrum Subtraction and Cross-power Spectrum Phase Method for Time Delay Estimation

In order to solve the problem of large error of delay estimation in low SNR environment, a new delay estimation method based on cross power spectral frequency domain weighting and spectrum subtraction is proposed. Through theoretical analysis and MATLAB simulation, among the four common weighting functions, it is proved that the cross-power spectral phase weighting method has a good sharpening effect on the peak value of the cross-correlation function, and it is verified that the improved spectral subtraction method generally has a good noise reduction effect under different SNR environments. Finally, the joint simulation results of the whole algorithm show that the combination of spectrum subtraction and crosspower spectrum phase method can effectively sharpen the peak value of cross-correlation function and improve the accuracy of time delay estimation in the low SNR environment. The results of this paper can provide useful help for sound source localization in complex environments.

USE OF SIMILARITY METRICS IN ROBUST TIME DELAY ESTIMATION

This paper addresses the task of time delay and direction of arrival estimation for a source of the wideband signal using two sensors with fixed displacement. The peculiarity of the task statement is that a limited time of signal observation is supposed and additive noise is assumed non-Gaussian with a heavy-tail distribution. This leads to a high probability of abnormal estimates for the conventional signal processing method based on cross-correlation. To decrease this probability, it is proposed to reformulate the task of cross-correlation processing to the task of similarity estimation between two data arrays. This allows using different similarity metrics, particularly those that have less sensitivity to outliers in data (impulse noise), and, thus, provide better robustness for non-Gaussian environments typical for several applications of time delay estimation. More than ten different similarity metrics are considered for the model of the symmetric α-stable distribution describing noise properties. It is shown that some metrics including cosine distance, Hellinger, and some others are able to provide sufficiently better accuracy of time delay estimation both in the sense of less RMSE of normal estimates and probability of abnormal estimates for typical values of α and a wide range of γ values for symmetric α-stable distribution.

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).

A sound source localization method based on improved second correlation time delay estimation

The sound source localization (SSL) system based on the microphone array has important applications in audio and video conference, security monitoring and intelligent cockpit. However, the SSL method based on time difference of arrival is susceptible to ambient noise. Therefore, an improved second correlation delay estimation algorithm is proposed in this paper. The pure source signal is obtained by wavelet denoising, and then the time delay is calculated by the second correlation time delay estimation algorithm with the weighting functions of the smoothed coherence transform and the Roth processor. The position of the sound target is calculated from the time delay. Aiming at the moving target, an extended Kalman filter is introduced to track the moving trajectory of the sound source. The static and moving SSL simulations are conducted and the results of the proposed algorithm are compared with those of the single-weighted quadratic correlation (SQC) algorithm and the high-power quadratic correlation algorithm. The static sound source positioning errors of the proposed algorithm under −10 dB SNR are respectively 3.97 m and 5.86 m smaller than those of the HQC algorithm and the SQC algorithm. The moving SSL trajectory based on the proposed algorithm is still closest to the real track under −10 dB SNR. This indicates that the proposed algorithm has high precision and strong robustness for sound source location in the low signal-to-noise ratio (SNR) environment. In the experiment, the proposed algorithm can accurately calculate the direction of arrival (DOA) of static sound source and stably track DOA of moving sound source. This is consistent with the simulation results, which further verifies the effectiveness and practicability of the algorithm. This novel algorithm with high time delay estimation accuracy is of great significance for SSL in low SNR environment.

Improved High-Order Cumulant TDE Parameter Accumulation Algorithm for Locating UHF Signals of Pulsed Electromagnetic Source

Ultra-high frequency (UHF) signal detection is one of the most effective methods for spatial orientation and partial discharge fault diagnosis. However, when the background noise, especially Gaussian white noise and narrow-band interference, is very high, or the detection region is remote, location accuracy may decrease. To improve this, a location system based on the improved higher-order cumulant time delay estimation (TDE) method combined with energy accumulation is proposed. In the system, the UHF waves are received by a four-antenna array. Improved fourth-order cumulants with a smoothed coherence transform (SCOT) window are used in the TDE, by which Gaussian white noise and narrow-band interference can be efficiently suppressed. The energy accumulation algorithm is applied to the cross-correlation results, by which the accuracy of TDE can be enhanced. The applicability of the proposed localization algorithm is evaluated by simulation and experiment. The simulation results show that the improved fourth-order cumulant TDE-parameter accumulation algorithm is superior in accuracy to traditional location methods. In the experimental measurements, two partial discharge measurement points located in a complex electromagnetic environment are tested. The results illustrate that the proposed method can effectively suppress Gaussian white and narrow-band noise, and the location results can satisfy accuracy requirements when the measurement point is within 70 m.

Investigation on leakage detection and localization in gas-liquid stratified flow pipelines based on acoustic method

Leakage detection technology is of vital importance to the safe operation and flow insurance of multiphase flow pipelines. This paper for the first time applies acoustic based leakage detection method to stratified flow pipelines and verifies the feasibility of this method in multiphase flow pipelines. Gas-liquid stratified flow pipeline leakage detection and localization experiment is conducted to investigate the effectiveness of different filtering methods when calculating the time difference (delay) between arrival times of leakage acoustic signals at different sensors using cross-correlation algorithm. Propagation characteristics of the leakage acoustic wave in stratified flow are also investigated. The results show that the 5-level Symlets wavelet filter can effectively improve the accuracy of time delay estimation. Moreover, the value of sound speed can be set as 346 m/s when carrying out leakage localization in stratified flow pipelines, which is nearly irrelevant with pressure, void fraction, superficial velocity of gas phase and the structure of pipe. The research in this paper lays a foundation for the application of acoustic based leakage detection technology in multiphase flow pipelines.

Research on Underwater Sound Source Localization Based on NLM-EEMD and FCM-Generalized Quadratic Correlation

The accuracy of underwater sound source localization depends on the preprocessing effect of signal denoising and delay estimation performance. In order to meet the needs of high-precision underwater positioning, this article studies a time delay estimation method based on nonlocal mean-enforced mean empirical mode decomposition (NLM-EEMD) autocorrelation denoising preprocessing and fuzzy C-means clustering (FCM)-generalized quadratic for underwater sound source localization technology. The theories such as NLM, EEMD, FCM, and generalized quadratic correlation delay estimation are studied in detail, and the speech signal of the test library in the TIMIT standard library is selected for simulation analysis, which verifies the correctness of the delay estimation method. Experiments were carried out in a larger outdoor pool. The analysis results show that the NLM-EEMD adaptive denoising method effectively reduces noise interference and improves the quality of EEMD decomposition and the FCM-generalized quadratic correlation method increases the correlation between two signals. The time delay estimation accuracy is improved, and the positioning accuracy is 48.66% higher than that of the direct generalized cross-correlation method.

Optimization Algorithm for Delay Estimation Based on Singular Value Decomposition and Improved GCC-PHAT Weighting.

The accuracy of time delay estimation seriously affects the accuracy of sound source localization. In order to improve the accuracy of time delay estimation under the condition of low SNR, a delay estimation optimization algorithm based on singular value decomposition and improved GCC-PHAT weighting (GCC-PHAT- weighting) is proposed. Firstly, the acoustic signal collected by the acoustic sensor array is subjected to singular value decomposition and noise reduction processing to improve the signal-to-noise ratio of the signal; then, the cross-correlation operation is performed, and the cross-correlation function is processed by the GCC-PHAT- weighting method to obtain the cross-power spectrum; finally, the inverse transformation is performed to obtain the generalized correlation time domain function, and the peak detection is performed to obtain the delay difference. The experiment was carried out in a large outdoor pool, and the experimental data were processed to compare the time delay estimation performance of three methods: GCC-PHAT weighting, SVD-GCC-PHAT weighting (meaning: GCC-PHAT weighting based on singular value decomposition) and SVD-GCC-PHAT- weighting (meaning: GCC-PHAT- weighting based on singular value decomposition). The results show that the delay estimation optimization algorithm based on SVD-GCC-PHAT- improves the delay estimation accuracy by at least 37.95% compared with the other two methods. The new optimization algorithm has good delay estimation performance.

Noise Reduction Based on CEEMDAN-ICA and Cross-Spectral Analysis for Leak Location in Water-Supply Pipelines

Due to the leakage vibration signal of the water-supply pipeline is easily interfered with by background noise, which leads to a significant leakage location error of time delay estimation. The complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and independent component analysis (ICA) combined noise reduction method based on cross-spectral analysis is proposed and applied to leak location of water supply pipelines. Firstly, determine the frequency band range of the source leakage signal by cross-spectral analysis of the leakage vibration signal. At the same time, the leakage vibration signal is decomposed into a finite number of intrinsic mode functions (IMFs) using CEEMDAN. Then, the IMF components are filtered according to the effective amplitude ratio criterion, and the filtered components are reconstructed into a virtual noise channel. Finally, the leakage vibration signal and virtual noise channel are unmixed using FastICA to obtain the best estimate of the source leakage signal, which is used to estimate time delay using cross-correlation for determining the leak location. Simulation and experimental results show that the proposed method effectively improves the signal-to-noise ratio (SNR) and time delay estimation accuracy, and reduces leak location error. Compared with cross-correlation, CEEMDAN-ICA based on correlation coefficients, and CEEMDAN based on cross-spectral analysis, the average relative positioning error of the proposed method is respectively reduced by 11.07%, 9.7%, and 1.8%. In addition, the superiority of the proposed method compared with other state-of-the-art noise reduction methods is verified by comparative experiments.

Application of the Differential Evolutionary Algorithm to the Estimation of Pipe Embedding Parameters.

The time-delay estimation (TDE) method is the primary method for predicting leakage locations in buried water distribution pipelines. The accuracy of TDE depends on the acoustic speed and attenuation of the leakage signal propagating along the pipeline. The analytical prediction model is the typical approach for obtaining the propagation speed and attenuation of leakage waves. However, the embedding parameters of the buried pipe in this model must be measured using soil tests, which are very difficult, costly, and time-consuming. These factors restrict the application of the TDE method in pinpointing pipeline leakage. A method for inverse identification of pipe embedding parameters using discrete wavenumbers obtained in field testing is presented in this paper, and the differential evolution algorithm is introduced as an optimization solution. A field experiment is conducted to validate the method, and the test wavenumbers are measured in a cast-iron pipeline. The estimated sensitive parameters in the analytical model using the method are soil elastic modulus, Poisson’s ratio, and pipe–soil contact coefficient, while the conventional soil test is used to measure the soil density due to the character of the optimization algorithm and the soil properties. The application effects show that the estimated parameters are close to those measured from a conventional soil test. The wave speed based on the estimated parameters was an excellent match for the on-site test in the engineering application. This work provides a less costly and more straightforward way to apply the TDE method for leak localization in buried pipelines.

An LBL positioning algorithm based on an EMD\u2013ML hybrid method

Autonomous underwater vehicles (AUVs) are essential assets for ocean exploration requiring reliable underwater positioning technology. Aiming to improve the latter technology in a low SNR and reverberation environment, the Chan–Taylor hybrid positioning algorithm establishes a long-baseline system (LBL) based on the time difference of arrival (TDOA) by reducing the number of sensors required while preserving the positioning accuracy. However, the traditional LBL algorithm’s accuracy is reduced due to the critical time delay estimation under such environmental conditions. Hence, this paper suggests a new LBL positioning technology relying on an empirical mode decomposition (EMD) to construct a filter function combined with the maximum likelihood (ML) estimation method. MATLAB/Simulink is applied to establish the simulation environment of LBL localization system, simulating the AUV motion under 5–30 dB SNR. This paper analyzes the accuracy of TDOA by generalizing the cross-correlation method (GCC), phase transform (PHAT), ML, and EMD–ML. Based on the TDOA value obtained by the EMD–ML filtering algorithm, the positioning errors of the Chan–Taylor hybrid positioning algorithm and the Chan algorithm are compared. The results show that comparative synthetic evaluations against the traditional GCC demonstrate that the proposed method has a higher time delay estimation accuracy within a reverberation environment with SNR less than 15 dB. The Chan–Taylor hybrid positioning algorithm limits the errors of the CHAN algorithm and improves the overall positioning system accuracy.

Variable Step Normalized LMS Adaptive Filter for Leak Localization in Water-Filled Plastic Pipes

Acoustic waves induced by leakage attenuate as they propagate in the piping system. Difficulties are generally encountered in leak localization in plastic pipes since these waves are heavily attenuated than in metallic pipes. This study presents a leak localization method based on the variable step normalized least mean square (VS-LMS) adaptive filter. In the method, the optimal weight vector of the filter is determined for time delay estimation (TDE) without requirement of the prior knowledge of statistical characteristics of leak and noise signals. It has a desirable feature of sharpening the main peak of TDE curve through adaptive iterative learning process, thus improving the accuracy of TDE for leak localization. By adjusting the update mode of iteration step, the convergence speed of the VS-LMS algorithm can be greatly improved. A simulation model of leak wave propagation is established and is subsequently analyzed for leak localization with respects to the TDE accuracy. Experimental work is further carried out on a plastic pipe to verify the effectiveness of the proposed method. The simulation sand experimental results demonstrate that the proposed method outperforms the original LMS and basic cross-correlation methods for the leak localization in a water-filled plastic pipe.

A Fuzzy Interpolation Cross-Correlation Method for Time-Delay Estimation of Partial Discharge UHF Pulse Signals

Time-delay estimation of partial discharge (PD) ultrahigh-frequency (UHF) pulse signals is one of the effective means to diagnose the local defect of electrical equipment. In order to improve the time-delay estimation accuracy of a multielement PD UHF pulse signal sensor array and reduce the cost of the PD detection system, a fuzzy interpolation cross-correlation method for time-delay estimation of PD UHF pulse signals was proposed in this paper. Improving the signal sampling rate is an effective way to improve the time-delay estimation accuracy. In this work, the fuzzy interpolation inference method was applied to interpolate intermediate values into the feature area of the PD UHF signal to improve the sampling rate, and then the cross-correlation method was used to estimate the time delay. This method not only improves the system sampling rate by fuzzy interpolation inference, which can make up for the deficiency of system equipment sampling performance, but also reduces the estimation error caused by noninteger multiple sampling intervals of signal time delay. The comparative experiment results demonstrate the power of the proposed method in improving the accuracy of the time-delay estimation of PD UHF pulse signals.

A Novel Synchronization Method in Terahertz Large‐Scale Antenna Array System

We focus on the problems of the accurate time delay estimation, the design of training pilots, and hybrid matrix optimization within the large-scale antenna array Terahertz (THz) broadband communication system. In contrast to the existing researches based on narrow-band arrays, we hereby shed light on the time delay estimation of broadband arrays. In THz broadband communication systems, the data symbol duration is relatively short when comparing with the dimension of the antenna array. In large-scale antenna systems, signals received in each antenna are no longer different phase-shifted copies of the same symbol, but completely different symbols in which occasion traditional narrow-band structure is no longer suitable. Based on the above conclusion, firstly, we put forward a system model based on large-scale antenna arrays and Time delay line (TDL) structure. Secondly, we deduce the Cramer-Rao lower bound (CRLB) of the time delay estimation, and present a time delay estimation algorithm that could reach the CRLB. Thirdly, by minimizing the CRLB, we address the design of the training pilot and optimized TDL structure under the condition of constant envelope training pilot and modulus TDL structure. Finally, we disclose the numerical simulation results. According to the simulation results, the aforementioned method is workable in reaching the CRLB, the TDL structure can significantly surpass that of the traditional model, and the optimal pilot design method outperforms the pseudo-random pilot structure.

Application of the denoising technique based on improved FastICA algorithm in cross-correlation time delay estimation

Cross-correlation is a common time delay estimation method. However, in the actual measurement environment, the near-end and far-end sensors are often disturbed by the correlated noise, which seriously affects the accuracy of time delay estimation and even leads algorithm is proposed, and the steepest descent is introduced to reduce the sensitivity of FastICA algorithm to initial values. The useful acoustic data and disturbing acoustic data were measured respectively in a simulated granary. From these data, the signals contaminated by noise were generated by a mixing matrix and used for testing the performance of the proposed method. The testing results show that the proposed method can effectively suppress the influence of correlated noise on cross-correlation time delay estimation, and improve the accuracy of estimation.

Generalized Weighted Adaptive Time Delay Estimation Algorithm Based on Minimum Average P Norm

The time delay estimation algorithm is one of the important factors of sound source localization. The generalized weighted adaptive time delay estimation algorithm is limited by the environmental conditions of signal and noise, and has great limitations in non-Gaussian environments. In order to make the algorithm suitable for non-Gaussian environments, and to retain the advantages of the algorithm in effectively suppressing harmonics, this paper combines the minimum average P norm (LMP) with the generalized weighting function, and proposes a method based on the minimum average P norm. The generalized weighted adaptive time delay estimation algorithm of the number can make the algorithm suitable for non-Gaussian environments, and for the shortcomings of slow iteration speed and large calculation amount for the minimum average P norm, the Sigmoid function is introduced to further improve the parameter selection in the algorithm. MATLAB simulation experiments show that the algorithm in this paper can effectively suppress the existence of harmonics in a non-Gaussian environment, and has strong convergence, high accuracy of time delay estimation, and fast iteration speed. It can be based on time delay estimation in a non-Gaussian environment. The positioning plays a certain role.

Prefiltering Approach of Adaptive Eigenvalue Decomposition Method for an Improved Time Delay Estimation in Room Environment

Time delay estimation is an essential step in sound source localization and beamforming systems, and an extensive amount of research has been performed on this subject. This task entails the accurate estimation of the relative time delay between two microphone signals originating from the same source. To overcome the limitations of the existing methods, the adaptive eigenvalue decomposition (AED) algorithm was developed for time delay estimation in reverberant acoustic environments in the early 2000s. This paper attempts to improve delay estimation performance using autoregressive model-based prefiltering for the AED algorithm. The proposed method establishes an autoregressive model of the room impulse response beforehand. Then, the model is utilized as a linear prediction filter to remove the reverberation component from the microphone signals, which improves the estimation capability of the algorithm. Monte Carlo experiments are performed to demonstrate the improved performance for various reverberation levels and signal-to-noise ratios. Provided that the noise level is moderate, the proposed method is shown to greatly increase the accuracy of the conventional approach in a highly reverberant room.

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”.

High accuracy phase‐matching delay estimation method based on phase correction

In the integrated system of underwater single-node detection and communication, active self-interference cancellation requires high accuracy of time delay estimation. To solve this problem, this Letter proposes a high accuracy delay estimation method based on phase correction. Initially, the normalised frequency correction is calculated according to the phase difference and time delay of the signal. Then, the discrete spectrum is reconstructed, and the phase is obtained by the least square method. Finally, the time delay is estimated by the phase difference between the received signal and the reference signal. This method corrects the phase and frequency errors caused by the Fourier transform and improves the accuracy of time delay estimation. Simulation results confirm the efficacy of the proposed method and achieve the accuracy requirement of the active self-interference cancellation.