Time Delay Estimation Algorithm Research Articles

Research on pipeline leakage localization method based on CZIM algorithm

The time difference of arrival is a common method to find the leakage point of water pipeline. The leakage point localization is achieved by calculating the time delay between the signals reaching different sensors. Mainstream time delay estimation algorithms based on signal correlation analysis are susceptible to the introduction of noise signals, low sampling rates, and signal clipping, resulting in inaccurate localization results. The article analyzed the impact of different interference factors and proposed a new time delay estimation algorithm based on signal cross-zero information modulation (CZIM) to address these problems. By normalizing the amplitude of the two signals at the detection points on both sides of the pipeline leakage position, two sets of sparse signal sequences with only two eigenvalues of 0 and 1 are obtained. The error coefficient function is calculated by a similar traversal method to finally index the time delay. In this paper, the principle and characteristics of the algorithm are analyzed and compared with the most commonly used GCC method. In both numerical simulations and actual pipe leakage localization experiments, the CZIM algorithm has shown its wide applicability, low impact by low sampling rate, and adaptability to low signal-to-noise ratios, etc. At the same time, the algorithm is simple in design and has a small amount of calculation and can meet the demand for real-time data processing, providing a new idea for the development of acoustic localization technology.

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.

Робастное обнаружение и оценивание широкополосных сигналов

An asymptotically robust invariant (ARI) algorithm for signal detection and time delay estimation is proposed. It is based on the q-point model of noise distributions. The algorithm is based on calculating the correlation statistics of the nonlinear transformation of the observed sample with the vector of reference signal samples. Time delay estimate is determined by special processing of the obtained statistics, taking into account the presence of mirror interference in the observed process. The algorithm is implemented in the frequency domain, which allows the use of the fast Fourier transform to reduce computational costs. The simulation results show that in the case of heavy-tailed noise distributions, ARI algorithm provides an energy gain compared to the classical correlation algorithm, and it has similar performance in the case of Gaussian noise.

Precise disturbance localization of long distance fiber interferometer vibration senor based on an improved time–frequency variation feature extraction scheme

Locating intrusions with high accuracy is crucial for prompting long distance distributed optical fiber vibration sensing systems to practical applications in engineering filed. To achieve the high measurement accuracy and real-time performance simultaneously, in this paper, an intensity-modulated ultra-long distance distributed optical fiber vibration sensing system using an asymmetric dual Mach-Zehnder interferometer is experimentally established. More importantly, a positioning approach based on an ameliorated time–frequency feature extraction scheme is proposed with both theoretically analysis and experimental demonstration. In particular, an endpoint detection algorithm based on differential operation is firstly utilized to rapidly and accurately locate the endpoints of the received vibration signals. Thus the large-band width signals can be successfully acquired by setting an approximate window. Then, the ameliorated time–frequency feature extraction scheme based on a maximal overlap discrete wavelet packet transform is applied to eliminate the asymmetry of the large-band width signals, as it could lead to an erroneous positioning result when directly using a cross-correlation time delay estimation algorithm. Finally, the vibration positions along the sensing fiber link of the established sensing system can be successfully demodulated with the help of the extracted time–frequency features. To validate the effectiveness of the proposed scheme, vibration positioning tests were conducted in a real perimeter security scenario. And the results show that a mean positioning error of 11.12 m and a mean processing time of 0.276 s have been realized in a sensing length of 101 km. Thus, it is believed that through continuous technological advancements and refine algorithm optimization, the long distance distributed optical fiber vibration sensor founded on the proposed positioning strategy is poised to play an important role in the practical engineering 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.

Time delay estimation using cascaded LMS filters fused by correlation coefficient for pipeline leak localization

Water leaks are commonly detected using acoustic/vibration sensors, which are sensitive to sounds and vibrations caused by leakage. In practical surveys, the degree of success for leak detection and localization depends on the operating conditions and construction materials of the pipeline in question. In particular, under the condition of low signal-to-noise ratios (SNRs) and small leaks, the traditional localization method based on time delay estimation (TDE) tends to give pseudo peaks, which may lead to appreciable errors in the estimate of the leak position. In this paper, TDE is carried out based on cascaded least mean square (LMS) filters fused by correlation coefficient. Combined with the propagation theory of leak signals in the pipeline, the TDE algorithms using the LMS adaptive filters are introduced for leak localization. It is found that the single LMS filter is replaced by cascaded architectures, further improving its performance for TDE in a low SNR environment. Numerical simulations are presented to demonstrate the best performance for TDE by using the cascaded LMS filters in comparison with the basic cross-correlation, the phase transform generalized cross-correlation and the single LMS filter. This is further verified using some measurements made in the laboratory and field tests.

A Sound Source Localization Method Based on Frequency Divider and Time Difference of Arrival

In recent years, sound source localization, as a passive localization technique with higher safety and convenience compared with other localization techniques such as active emission of electromagnetic waves, has received more and more attention in academia. This paper researches and improves the far-field sound source localization algorithm based on the generalized cross-correlation method (GCC) Time Difference of Arrival (TDOA) estimation algorithm and completes the design and implementation of the microphone array sound source localization system. This paper adds a frequency divider to the traditional generalized correlation time delay estimation algorithm for pre-processing, sampling, and localization of sound source acoustic waves and adopts a low-cost microphone array deployment scheme as far as possible to improve the flexibility and practicality of the localization system; at the same time, the “Minimum Sphere Method” is used at the back end of the algorithm to classify the localization coordinates at different frequencies and, finally, output reasonable sound source coordinates. In the back-end of the algorithm, the “Minimum Sphere Method” is used to classify the localization coordinates at different frequencies and, finally, output the reasonable sound source coordinates. The experimental results show that the sound source localization system designed in this paper has good performance in terms of localization accuracy and cost-effectiveness and overcomes the failure of the generalized mutual correlation algorithm in the original application of high noise environment and multi-source environment localization.

Tracking Control of Robot Manipulator with Friction Compensation Using Time-Delay Control and an Adaptive Fuzzy Logic System

This paper aims to highlight the critical role of robot manipulators in industrial applications and elucidate the challenges associated with achieving high-precision control. In particular, the detrimental effects of nonlinear friction on manipulators are discussed. To overcome this challenge, a novel friction compensation controller (FCC) that combines time-delay estimation (TDE) and an adaptive fuzzy logic system (AFLS) is proposed in this paper. The friction compensation controller is designed to take advantage of the time-delay estimation algorithm’s strengths in eliminating and estimating unknown dynamic functions of the system using information from the previous sampling period. Simultaneously, the adaptive fuzzy logic system compensates for the hard nonlinearities in the system and suppresses the errors generated by time-delay estimation, thus improving the accuracy of the robotic arm’s tracking. The numerical experimental results demonstrate that the proposed friction compensation controller can significantly enhance the tracking accuracy of the robotic arm, with the addition of the adaptive fuzzy logic system improving time delay estimation’s performance by an average of 90.59%. Moreover, the proposed controller is more straightforward to implement than existing methods and performs exceptionally well in practical applications.

Ultra-short baseline positioning delay estimation based on signal preprocessing and fourth-order cumulant

To address the problem that the traditional generalized cross correlation (GCC) method in ultra-short baseline (USBL) positioning systems has a poor delay estimation accuracy in a low signal-to-noise ratio environment or complex noise background, a generalized quadratic cross correlation (GQCC) time delay estimation algorithm based on signal preprocessing and fourth-order cumulants is proposed. The noisy signal was first preprocessed using singular value decomposition and wavelet denoising. Then, the delay was calculated using an algorithm that combined the GQCC and the fourth-order cumulant. The results of the simulation and sea trial demonstrate that the proposed method is superior to the GCC method and the GQCC method and may significantly increase the positioning accuracy of the USBL system. This technique can offer a fresh technological perspective for weak signal detection and passive positioning of small targets in ocean detection.

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 time delay estimation approach with low computational complexity for speaker localization

Time delay estimation (TDE), which aims at estimating the time difference of arrival using the signals captured by an array of microphones, plays an essential role in hands-free speech communication systems for localizing and tracking speakers. The sparse linear prediction model, which is based on the l1-norm optimization with respect to the prediction-error vector and the coefficient vector of the linear predictor, can be effectively used to prefilter the microphone signals so as to establish a time delay estimator robust to background noise and reverberation. In the course to solve this model, however, a high-dimension cross-correlation matrix has to be inverted, indicating that the corresponding TDE algorithm has huge computational load. In this paper, we propose a new solution approach to this dual l1-norm optimization model. The original prediction-error filter is decomposed by Kronecker product into two short subpredictors. Accordingly, the size of the cross-correlation matrix in the TDE algorithm is degraded, which significantly reduces the computational complexity for prewhitening microphone signals. Simulation experiments in room acoustic environments demonstrate the computational efficiency of the proposed TDE algorithm as well as its estimation precision.

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.

Time-Delay Estimation of Microseismic DAS Data Using Band-Limited Phase-Only Correlation

Time-delay estimation is a critical step in many geophysical applications. Conventional approaches are mainly based on the cross correlation of waveforms in time domain but show strong distortions with multiple oscillations and side lobes. We propose a band-limited phase-only correlation (POC) algorithm for time-delay estimation. The algorithm involves the following key steps: 1) transforming 1-D waveform into 2-D time–frequency spectra using S-transform; 2) calculating the band-limited POC function of the transformed spectra; and 3) measuring time delays by analyzing POC coefficient. We demonstrate the effectiveness of the proposed algorithm using synthetic and real microseismic fiber-optic distributed acoustic sensing (DAS) datasets. Results show that POC can effectively and accurately estimate the time delays of waveforms. Compared with the performance of the conventional cross correlation method in time domain, the proposed method has three main advantages: 1) better identification of event and noise waveforms; 2) lower uncertainty of narrow correlation peaks; and 3) weaker distortions with small oscillations and side lobes.

Wind Speed and Direction Measurement Based on Three Mutually Transmitting Ultrasonic Sensors

The existing ultrasonic anemometer is influenced by the ambient temperature and humidity, shadow effect, and has weak suppression ability for fixed frequency interference, which directly affects the measurement accuracy of the ultrasonic anemometer. In this letter, we propose a three mutually transmitting ultrasonic sensors wind measurement method, which uses a three mutually transmitting ultrasonic sensors array structure combined with the cyclic correlation time delay estimation algorithm for ultrasonic transmission time estimation, and then obtains wind speed and direction values based on the relationship between ultrasonic transmission time and wind vector. The proposed method can effectively reduce the effects of temperature, humidity and shadowing effects on wind vector measurements, suppress interference at different frequencies, and reduce the computational complexity of the time delay estimation algorithm. Finally, we perform simulation experiments to verify the superiority of the proposed algorithm. At the same time, the validity of the proposed method is verified by actual measurement experiment of the three mutually transmitting ultrasonic wind measurement system built. The relative error of wind speed measurement is 3% and the error of wind direction measurement is 3° in the actual measurement environment.

Continuous Time-Delay Estimation From Sampled Measurements

An algorithm for continuous time-delay estimation from sampled output data and a known input of finite energy is presented. The continuous time-delay modeling allows for the estimation of subsample delays. The proposed estimation algorithm consists of two steps. First, the continuous Laguerre spectrum of the output (delayed) signal is estimated from discrete-time (sampled) noisy measurements. Second, an estimate of the delay value is obtained via a Laguerre domain model using a continuous-time description of the input. The second step of the algorithm is shown to be intrinsically biased, the bias sources are established, and the bias itself is modeled. The proposed delay estimation approach is compared in a Monte-Carlo simulation with state-of-the-art methods implemented in time, frequency, and Laguerre domain demonstrating comparable or higher accuracy in the considered scenario.

Sparse Reconstruction-Based Time-Delay Estimation Algorithm in the Exponential Correlation Domain

Sparse Reconstruction-Based Time-Delay Estimation Algorithm in the Exponential Correlation Domain

Weighting function modification used for phase transform-based time delay estimation

Generalized cross-correlation is considered as the most straightforward time delay estimation algorithm. Depending on various weighting function, different methods were derived and a straightforward method, named phase transform (PHAT) has been widely used. PHAT is well-known for its robustness to reverberation and its sensitivity to noise, which is partly due to the fact that PHAT distributes same weights to the frequencies dominated by signal or noise. To alleviate this problem, two weighting functions are proposed in this paper. By taking a posteriori signal-to-noise ratio (SNR) into account to classify reliable and unreliable frequencies, different weights could be assigned. The first proposed weighting function borrows the idea of binary mask and distributes same weights to frequencies in same set, whereas, the second one assigns weights based on coherence function. Experiments showed the robustness of proposed methods to reverberation and noise for improving the performance of time delay estimation through various criteria.

Leakage Detection and Localization of Water Pipeline Using Multi-features and Adaptive Time Delay Estimation

The leakage of water in pipelines severely affects the environment and economy. However, there are limitations in the effectiveness of existing leak detection and localization techniques and methodologies. In this paper, we propose a novel leakage detection and localization method based on the multiple time-frequency features, a neural network, and an adaptive time delay estimation algorithm. First, we use spectral subtraction and wavelet denoising to reduce the effects of noise. In addition, to ensure and improve the accuracy of leakage detection in complex realistic environments, we propose the use of multi time-frequency features that can comprehensively represent the leak signal and make the neural network more robust to train a radial basis function (RBF)neural network to detect the leak signal. Further, we extract multiple features of the leakage signal and input into the RBF neural network to train. Moreover, to prevent the impulsive components of environmental noise and improve localization accuracy, we further propose the use of a fractional lower-order statistics (FLOS) based adaptive time delay estimation algorithm to estimate the time delay and locate the leakage. The simulation results show that the detection and localization performance of the proposed method is superior to those of existing schemes.

Simultaneous multiple bands time delay and frequency component estimation based on expectation–maximization

Acoustic sensor systems often operate in complex environments containing multiple sound and noise sources. This paper proposes a new multi-band multi-source time delay estimation and frequency analysis algorithm based on the Expectation–Maximization (EM) method. The algorithm improves the multi-source signal superposition model and introduces the EM method to iteratively find parameters for each frequency band. The algorithm also provides multiple time delay estimates while simultaneously estimating the intensity distribution of the frequency bands for each of the corresponding time delays. The distributions are valuable for subsequent tasks such as target classification and identification. The performance of the algorithm is assessed by simulations and field experiments.

A maximum a posteriori estimation based method for estimating pulse time delay

The accuracy of the classical time delay estimation algorithms cannot exceed Cramér-Rao bound (CRB), and it is difficult to obtain a higher precision estimation. In order to break through the limitation of CRB, this paper integrates prior information into estimation algorithm. Through combining priori information with pulsar observation, the pulse time delay estimation algorithm based on maximum a posteriori (MAP) estimation is derived, thereby presenting the lower bound of the proposed estimator. Experimental results based on observational data for the Crab pulsar show that the estimation precision of the proposed estimator is not only 2 orders of magnitude higher than that of the classical algorithms, but also asymptotically efficient, providing more accurate observation for X-ray pulsar navigation.