Time Delay Estimation Method Research Articles

A high-order time-delay difference estimation method for signal enhancement in the distorted towed hydrophone array.

In passive sonar systems, deviations from an ideal linear configuration can significantly impair the beamforming performance of towed hydrophone arrays. This paper presents a method aimed at improving the underwater acoustic signals in the presence of array distortion. The method is centered on a high-order time-delay difference estimation technique utilizing time-frequency autofocus. Initially, a detailed signal model is established that captures the distinctive characteristics of distorted arrays. Subsequently, an algorithm is introduced for high-order time-delay difference estimation to enhance signal fidelity by leveraging phase information within narrowband components originating from incidental acoustic sources. Additionally, a quality metric to evaluate these components is introduced, facilitating the practical implementation of the method. The effectiveness of the proposed approach is validated through both simulation and experimental results, demonstrating its superiority over existing techniques. Importantly, this method does not require prior knowledge of the distortion pattern, making it adaptable to various non-linear array configurations.

TDITI: A time-delay information transfer index algorithm for corticomuscular coupling

Time delay (TD) across corticomuscular coupling (CMC) is a significant index to assess the information transmission between brain and muscle during movement execution. Larger methods have been widely used to calculate the time delay by estimating phase information, but fail to account for both linear and nonlinear characteristics in the bidirectional coupled systems. For this, this study proposed a novel time-delay estimation method, defined as time-delay information transfer index (TDITI), to explore the TD characteristics between two signal deriving from one system with time-delay coupling. To verify this, we introduced two models to generate a series of simulation signal with linearly unidirectional/ bidirectional coupling or nonlinearly unidirectional/ bidirectional coupling. Simulation results manifested that the TDITI method, compared with the information transfer index (ITI) and coherence methods, can not only describe the TD in the linearly or nonlinearly unidirectional systems, but was also suitable for the bidirectional coupled systems. We also found its robustness to data length, coupling strength and signal-noise ratio. After that, we applied it to explore the TD of CMC by synchronizing the electroencephalogram (EEG) and electromyogram (EMG) signal during steady-state task. Experimental results showed that the CMC between cortex and muscle were direction-dependent, and the average delay time from EEG to EMG (∼25 ms) was shorter than that in the opposition (∼30 ms). Both simulation and experimental data expound the effectiveness of the TDITI method to describe the time delay in the unidirectional or bidirectional coupled systems, and this study extends our perspective to the mechanism of motor control.

Nearest advocate: a novel event-based time delay estimation algorithm for multi-sensor time-series data synchronization

Estimating time delays in event-based time-series is a crucial task in signal processing as it affects the data quality and is a prerequisite for many subsequent analyses. In particular, data acquired from wearable devices often suffer from a low timestamp precision or clock drift. Current state-of-the-art methods such as Pearson Cross-Correlation are sensitive to typical data quality issues, e.g. misdetected events, and Dynamic Time Warping is computationally expensive. To overcome these limitations, we propose Nearest Advocate, a novel event-based time delay estimation method for multi-sensor time-series data synchronisation. We evaluate its performance using three independent datasets acquired from wearable sensor systems, demonstrating its superior precision, particularly for short, noisy time-series with missing events. Additionally, we introduce a sparse variant that balances precision and runtime. Finally, we demonstrate how Nearest Advocate can be used to solve the problem of linear as well as non-linear clock drifts. Thus, Nearest Advocate offers a promising opportunity for time delay estimation and post-hoc synchronization for challenging datasets across various applications.

High-Precision Time Difference of Arrival Estimation Method Based on Phase Measurement

In unmanned aerial vehicle (UAV)-based time difference of arrival (TDOA) positioning technique, baselines are limited due to communication constraints. In this case, the accuracy is highly sensitive to the TDOA measurements’ error. This article primarily addresses the problem of short-baseline high-precision time synchronization and TDOA measurement. We conducted a detailed analysis of error models in TDOA systems, considering both the time and phase measurement. We utilize the frequency division wireless phase synchronization technique in TDOA systems. Building upon this synchronization scheme, we propose a novel time delay estimation method that relies on phase measurements based on the integer least squares method. The performance of this method is demonstrated through Monte Carlo simulations and outdoor experiments. The standard deviations of synchronization and TDOA measurements in experiments are 1.12 ps and 1.66 ps, respectively. Furthermore, the circular error probable (CEP) accuracy is improved from 0.33%R to 0.02%R, offering support for the practical application of distributed short-baseline high-precision passive location techniques.

Multipoint leak localization for pipelines via acoustic wave amplitude ratio

Pipeline leak localization is significant for maintaining the regular operation of pipelines. This paper proposes a multipoint leak localization method for pipelines via the acoustic wave amplitude ratio, which addresses the issue of the traditional time delay estimation method (TDE) not being able to locate multiple leaks simultaneously. Firstly, a multipoint leak localization method for pipelines is established without time delay estimation and acoustic velocity. This method merely needs to determine the amplitude of the leakage acoustic wave propagating to both ends of the pipeline to achieve leakage localization. Secondly, the improved empirical wavelet transform (IEWT) method denoises the leakage acoustic wave, which can obtain an accurate acoustic amplitude to reduce the localization error. Finally, the trouble that the mutation factor and crossover probability cannot be adaptively selected in the differential evolution (DE) algorithm is improved, and the improved differential evolution (IDE) algorithm is used to solve the objective function to obtain the position of each leakage point. Field experiments show that the multipoint leak localization method proposed in this paper has perfect accuracy, and the minimum localization error is 11 m.

Development of a 2D spatial displacement estimation method for turbulence velocimetry of the gas puff imaging system on EAST

A gas puff imaging (GPI) diagnostic has been developed and operated on EAST since 2012, and the time-delay estimation (TDE) method is used to derive the propagation velocity of fluctuations from the two-dimensional GPI data. However, with the TDE method it is difficult to analyze the data with fast transient events, such as edge-localized mode (ELM). Consequently, a method called the spatial displacement estimation (SDE) algorithm is developed to estimate the turbulence velocity with high temporal resolution. Based on the SDE algorithm, we make some improvements, including an adaptive median filter and super-resolution technology. After the development of the algorithm, a straight-line movement and a curved-line movement are used to test the accuracy of the algorithm, and the calculated speed agrees well with preset speed. This SDE algorithm is applied to the EAST GPI data analysis, and the derived propagation velocity of turbulence is consistent with that from the TDE method, but with much higher temporal resolution.

Deep learning‐based time delay estimation for motion compensation in synthetic aperture sonars

AbstractAccurate and robust time delay estimation is crucial for synthetic aperture sonar (SAS) imaging. A two‐step time delay estimation method based on displaced phase centre antenna (DPCA) micronavigation has been widely applied in motion estimation and compensation of SASs. However, the existing methods for time delay estimation are not sufficiently robust, which reduces the performance of SAS motion estimation. Deep learning is currently one of the cutting‐edge techniques and has brought about a remarkable progress in the field of underwater acoustic signal processing. In this study, a deep learning‐based time delay estimation method is introduced to SAS motion estimation and compensation. The subband processing is first applied to obtain ambiguous time delays between adjacent pings from phases of SAS echoes. Then, a lightweight neural network is utilised to construct phase unwrapping. The model of the employed neural network is trained with simulation data and applied to real SAS data. The results of time delay estimation and motion compensation demonstrate that the proposed neural network‐based method has much better performance than the two‐step and joint‐subband methods.

Fault localization on power cables using time delay estimation of partial discharge signals

Precise localization of partial discharge (PD) sources on power cables is vital to prevent power line failures that can lead to significant economic losses for electrical suppliers. This study proposes four methods to estimate the time delay of PD signals under electromagnetic interference, including white Gaussian noise (WGN) and discrete sinusoidal interference (DSI), using denoised PD signals with signal-to-noise ratios ranging from 10.6 to -7.02 dB. The maximum peak detection (MPD) and cross-correlation (CC) approaches, as well as two new techniques, interpolation cross-correlation (ICC) and envelope cross-correlation (ECC), are evaluated for their effectiveness in PD source localization. The researchers employ the time difference of arrival (TDoA) algorithm to compute PD location using the double-end PD location algorithm, where the PD location precision serves as an indicator of the accuracy of the time delay estimation methods. The study concludes that CC and ICC are the most suitable methods for estimating the time delay of PD signals in the PD location algorithm, as they exhibit the lowest error rates. These results suggest that CC and ICC can be used effectively for precise PD source localization under electromagnetic interference on power cables.

Fiber Optic Sensor Based on Linear Sagnac Interferometer for Branch Localization

One of the challenges of distributed fiber optic sensors is to monitor objects that have multiple branches, such as pipelines or power grids. Existing sensors require multiple sensing systems to cover each branch, which increases the cost and complexity of the monitoring. We propose a fiber optic sensor based on linear Sagnac interferometer for branch localization for practical environments where branch paths exist. The system is based on a dual-wavelength single-core Sagnac interferometer, which can extend multiple branches in the sensing cable part. The phase difference signals caused by external disturbances are demodulated and go through different signal processing. By using time delay estimation and null frequency method, we can determine the exact location of the disturbance on the main or branch path. Moreover, we propose a new method to reduce interference with null frequencies of the spectrum by subtracting the phase difference signal at one wavelength from the other. We demonstrate the feasibility and performance of our proposed system through theoretical analysis and experimental results. Our proposed system offers a simple and effective solution for branch localization in distributed fiber optic sensing applications.

Research on Time Delay Estimation Method of Partial Discharges Signal with Improved Weighted Function

Positioning systems based on the Time Difference of Arrival (TDOA) often struggle to accurately estimate time delays for partial discharge signals in complex electromagnetic environments. To address this, we introduce an improved joint-weighted generalized cross-correlation (GCC) time delay estimation algorithm. Traditional GCC time delay estimations, when reliant on conventional weighted functions, significantly underperform in situations characterized by low signal–noise ratios (SNRs). Our proposed improved joint weighted function combines the advantages of both phase transform (PHAT) and correlation transform (SCOT) weightings, resulting in a composite function. Compared to the conventional weighted GCC, the improved joint weighted GCC displays a more distinct peak in cross-correlation functions and ensures more robust delay estimations, especially under low SNR conditions. Experimental results indicate that the improved joint-weighted GCC algorithm achieves an error margin below 1 ns in challenging outdoor electromagnetic scenarios, demonstrating its aptitude for detecting and localizing partial discharge signals in practical engineering applications.

Multipath time delay estimation based on the improved Wigner-ville distribution

The accuracy of underwater multipath channel time delay is crucial in underwater acoustic signal processing. The temporal resolution of the traditional matched filter is restricted by the transmitted signal bandwidth. Wigner-Ville distribution (WVD) which has excellent energy concentration characteristics and effectively avoids the interaction between temporal and frequency resolutions, and is widely used in non-stationary signal processing. However, considering the multipath signal processing, the cross-term in echo WVD would cause inaccurate time delay estimation. Therefore, in this paper, a novel multipath signal time delay estimation method based on the improved WVD is proposed. By utilizing the difference in the continuity of energy changes between auto-term and cross-term in the time-frequency domain, the Seeded Region Growing algorithm is applied and improved to extract auto-term in the WVD. The simulation results show that the method removes cross-term and maintains high concentration characteristics of auto-term, compared with pseudo-WVD and smooth pseudo-WVD, etc. In addition, it improves the accuracy of multipath signal delay estimation and has some anti-noise ability.

Improved variable step adaptive filtering algorithm and its application in time delay estimation for continuous wave dual-sensor pulse signals

Continuous wave mud pulse transmission is crucial for wireless logging, but surface pump noise disrupts upstream mud pulses, hindering downhole information extraction. At a theoretical level, the dual-sensor differential denoising approach is an excellent technology for suppressing pump noise, but precisely identifying the time delay, which has a considerable impact on the denoising effect, remains a challenge. This paper provides an improved variable step-size adaptive time delay estimation method TVSS-LMSTDE to address this issue. Iteration time regulates the change in step size. The preset adjustment principle states that modifying parameters ζ and γ controls the learning features of step size. A series of stable and erratic dual-sensor continuous wave mud pulse signals interfered by various noise intensities are created in the simulation, and the performance of three different variable step-size technologies—error-oriented, nonlinear relationship, and iterative time regulation—in terms of convergence speed, estimation stability, and calculation amount are compared and analyzed. The results show that the iterative time regulation technique produces a minimal mean square error in time delay estimate, with generally steady estimation and excellent accuracy. When applied to hydraulic cycle tests, the technique accurately gets the time delay value of dual-sensor signals, giving critical support for the successful recovery of mud pulse data severely disrupted by pump noise.

Deep Learning-Based Time Delay Estimation Using Ground Penetrating Radar

Time delay estimation (TDE) is of great interest for the thickness estimation of pavement using ground penetrating radar (a non-destructive testing tool that uses electromagnetic waves to probe civil engineering material), which determines the difference between the times of arrival of two incoming signals or backscattered echoes. However, conventional TDE methods suffer performance degradation because of limited resolution for thin layers and highly correlated backscattered echoes. In this paper, a deep neural network (DNN)-based TDE method is proposed. Firstly, a new DNN is constructed to classify and train the backscattered echoes; then, the time delays of the backscattered echoes can be estimated through the proposed DNN. The proposed method is based on the data processing of the backscattered echoes, which is more robust to the noise than conventional subspace-based methods (MUSIC, ESPRIT) and compressive sensing-based methods (OMP). The proposed method can directly process coherent backscattered echoes without decorrelation procedures, compared with MUSIC and ESPRIT. In addition, the proposed method is more powerful in resolving the close backscattered echoes than that of OMP. Simulation results show the efficiency of the proposed method in terms of signal-to-noise ratio (SNR) and BΔτ products. (The BΔτ products indicate the resolution of GPR, B is the frequency bandwidth of GPR and Δτ is the time delay between two incoming signals or backscattered echoes).

Error Analysis on Ultra-Short Baseline Positioning System

Aiming at the problem of low accuracy of ultrashort baseline positioning system in practical applications, this paper introduces hydroacoustic channel response error and transducer distortion error, and analyses the influence of each factor on positioning accuracy in the positioning process according to the time delay estimation method. Finally, the major and minor factors are distinguished according to the influence mechanism and the degree of influence of the error factors. The results show that the ship attitude error and hydroacoustic channel error are the main factors affecting the positioning accuracy.

Pipeline Leakage Detection Based on Secondary Phase Transform Cross-Correlation.

Leaks from pipes and valves are a reputational issue in industry. Maintenance of pipeline integrity is becoming a growing challenge due to the serious socioeconomic consequences. This paper presents a secondary phase transform (PHAT) cross-correlation method to improve the performance of the acoustic methods based on cross-correlation for pipeline leakage detection. Acoustic emission signals generated by pipe leakage are first captured by the sensors at different locations, and are subsequently analyzed using the cross-correlation curve to determine whether leakage is occurring. When leakage occurs, time delay estimation (TDE) is further carried out by peak search in the cross-correlation curve between the two sensor signals. In the analysis, the proposed method calculates the secondary cross-correlation function before the PHAT operation. A sinc interpolation method is then introduced for automatic searching the peak value of the cross-correlation curve. Numerical simulations and experimental results confirm the improved performance of the proposed method for noise suppression and accurate TDE compared to the basic cross-correlation method, which may be beneficial in engineering applications.

Enhanced Reaching-Law-Based Discrete-Time Terminal Sliding Mode Current Control of a Six-Phase Induction Motor

This paper develops an inner stator current controller based on an enhanced reaching-law-based discrete-time terminal sliding mode. The problem of tracking stator currents with high accuracy while ensuring the robustness of a six-phase induction motor in the presence of uncertain electrical parameters and unmeasurable states is tackled. The unknown dynamics are approximated by using a time delay estimation method. Then, an enhanced power-reaching law is used to make each stage of the convergence faster. A stability analysis and the system controller’s finite-time convergence are demonstrated in detail. Practical work was conducted on an asymmetrical six-phase induction machine to illustrate the developed discrete approach’s robustness and effectiveness.

A Target Detection Method of Distributed Passive Radar without Direct-Path Signal

At present, there are many technical methods in the field of target detection, but the detection methods are greatly affected by direct-path signals and need technical support such as extracting pure direct-path signals, so they cannot be used under the condition of without-direct-path signals. In this paper, a distributed target detection method is studied under a without-direct-path signals system. In the case of without-direct-path signals, target detection is achieved by the generalized likelihood ratio test (GLRT). At the same time, the input echo signals in target detection need time synchronization, so the impact of time delay should be eliminated. However, the traditional time delay estimation method is realized through coherent processing between echoes, which requires a high signal-to-noise ratio (SNR). Therefore, a time delay estimation method is proposed in this paper. Finally, the experimental results show that the accuracy of target detection by GLRT is improved, and the signal-to-noise ratio is also improved under the condition of without-direct-path signals. Moreover, the accuracy of delay detection is improved.

Variational Bayesian Inference Time Delay Estimation for Passive Sonars

In passive sonars, distance and depth estimation of underwater targets is often limited by the accuracy of time delay estimations. The estimation accuracy of the existing methods of time delay estimation is limited by the uniform discrete grid (signal sampling rate). When a true time delay is out of the grid, the estimation accuracy deteriorates due to the mismatch between the real-time delay and the discrete grid. This paper proposes a new method for time delay estimation, which realizes the time delay estimation under the framework of variational Bayesian inference. The proposed method is grid-less, that is, continuous in the time domain. Unlike the popular grid-less compressive time delay estimation method, this method does not require parameter adjustment, and can automatically estimate the number of time delays, noise variance, and amplitude variance. The simulation results showed that the performance of the proposed method was superior to the reference state-of-the-art time delay estimation methods.

High-Precision Time Delay Estimation Based on Closed-Form Offset Compensation

To improve the estimation accuracy, a novel time delay estimation (TDE) method based on the closed-form offset compensation is proposed. Firstly, we use the generalized cross-correlation with phase transform (GCC-PHAT) method to obtain the initial TDE. Secondly, a signal model using normalized cross spectrum is established, and the noise subspace is extracted by eigenvalue decomposition (EVD) of covariance matrix. Using the orthogonal relation between the steering vector and the noise subspace, the first-order Taylor expansion is carried out on the steering vector reconstructed by the initial TDE. Finally, the offsets are compensated via simple least squares (LS). Compared to other state-of-the-art methods, the proposed method significantly reduces the computational complexity and achieves better estimation performance. Experiments on both simulation and real-world data verify the efficiency of the proposed approach.

Time delay estimation of traffic congestion propagation due to accidents based on statistical causality

<abstract><p>The accurate estimation of time delays is crucial in traffic congestion analysis, as this information can be used to address fundamental questions regarding the origin and propagation of traffic congestion. However, the exact measurement of time delays during congestion remains a challenge owing to the complex propagation process between roads and high uncertainty regarding future behavior. To overcome this challenge, we propose a novel time delay estimation method for the propagation of traffic congestion due to accidents using lag-specific transfer entropy (TE). The proposed method adopts Markov bootstrap techniques to quantify uncertainty in the time delay estimator. To the best of our knowledge, our proposed method is the first to estimate time delays based on causal relationships between adjacent roads. We validated the method's efficacy using simulated data, as well as real user trajectory data obtained from a major GPS navigation system in South Korea.</p></abstract>