Delay Estimation Method Research Articles

Group delay of a signal in the receiving path estimation of measuring devices with the use of the step response

The current parameters coordinate-time measuring instruments calibration methods of global navigation satellite systems are considered. For coordinate-time measuring instruments calibration in the process of their development and testing, the global navigation satellite systems signals simulators are used. However, the simulators also need a calibration procedure. Currently, there are various methods for ensuring the metrological characteristics of simulators, including their calibration using oscilloscope. However, this method has not only advantages, but also limitations related to the use of an oscilloscope. VNIIFTRI develops a new reference measuring device – the calibrator of the global navigation satellite systems simulator. Since the work of the calibrator is based on the same principles as the work of the navigation receiver and the calibrator determine the time delay of accepted signal from the calibrated simulator, it is extremely important to accurately evaluate the own group time delay of the calibrator by the reception circuit and develop the methodology of determining the determination this metrological characteristic. The schematic solutions used of creating a calibrator include digital blocks, such as digital-analog or analog-cyphrane converters. The purpose of the study is to evaluate the group time delay in the input circuit of the calibrator containing an analog-digital converter. Traditional group delay estimation methods using S-parameters are not suitable for this purpose because they cannot compare analog and digital signals. This article has developed an indirect method for assessing the grouping time delay in the calibrator input circuit. The method proposed by the authors determines the group time delay time in the reception of the calibrator according to the circuit transition characteristic. The method is verification and calibration of measuring equipment using the input and output signals with an analog-digital converting. Using the proposed method, the group time delay in the calibrator circuit containing an analog-digital converter is estimated. The results of studies are given by the proposed method of this parameter of circuits with various microwave devices (power splitter, circulator). The proposed method allows you to obtain accurate assessments of the frequency characteristics of the measuring devices circuits and normalize their metrological characteristics.

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.

Preliminary result of time delay estimation method based on range vernier technique

Preliminary result of time delay estimation method based on range vernier technique

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.

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.

Delay estimation for cortical-muscular interaction with wavelet coherence time lag

BackgroundCortico-muscular coherence (CMC) between the cerebral cortex and muscle activity is an effective tool for studying neural communication in the motor control system. To accurately evaluate the coherence between electroencephalogram (EEG) and electromyogram (EMG) signals, it is necessary to accurately calculate the time delay between physiological signals to ensure signal synchronization. New methodWe proposed a new delay estimation method, named wavelet coherence time lag (WCTL) and the significant increase areas (SIA) index as a measure of the specific region enhancement effect of the magnitude squared coherence (MSC) image. ResultsThe grip strength level had a small effect on the information transmission time from the cortex to the muscles, while the transmission time from the cortex to different muscle channels was different for the same task. A positive correlation was found between the grip strength level and the SIA index on the β band of C3-B and the α and β bands of C3-FDS.Comparison with Existing Method: The WCTL method was found to accurately calculate the delay time even when the number of repeated segments was low in a simple motor control model, and the results were more accurate than the rate of voxels change (RVC) and CMC with time lag (CMCTL) methods. ConclusionsThe WCTL is an effective method for detecting the transmission time of information between the cortex and muscles, laying the foundation for future rehabilitation treatment for stroke patients.

Data-driven sensor delay estimation in industrial processes using multivariate projection methods

A key step in preparing industrial data for multivariate statistical modelling of (batch-)continuous processes is the estimation of sensor delays along the production line, to use as a correction for understanding relationships between them. Without such a correction, the measurements collected from the sensors do not all relate to the same portion of material travelling through the plant, which is where from a physical point of view the correlations are expected to arise from. Most methods to do these corrections currently reported in literature are limited in that they optimize only correlations bivariately between the different sensors, despite the eventual goal of being understood as a multivariate process model. This work proposes several methods for multivariate sensor delay estimation, based on multivariate projection methods, and critically investigates these using simulated and empirical process data from two industrial facilities. The objective is to provide more clarity on if, how, and why taking into account these multivariate correlations using such projection methods is beneficial. One of the proposed methods, named PLS-SEQ, was shown to outperform bivariate sensor delay estimation, which is regarded as benchmark method in this work, for all datasets. The average reduction in delay estimation error achieved by using PLS-SEQ is between 6% and 64%. The other newly proposed multivariate projection-based methods did not show such unanimous improvement in accuracy, but helped identifying the presence of sensor clusters in industrial data as a novel key challenge for sensor delay estimation. The presented results illustrate that projection-based multivariate methods, in particular the newly proposed method PLS-SEQ, show promising potential for sensor delay estimation, outperforming the bivariate sensor delay estimation methods used as benchmark. Ultimately, using these methods can improve the predictive and descriptive quality of statistical models for key industrial processes.

Using Deep-Learning for 5G End-to-End Delay Estimation Based on Gaussian Mixture Models

Deep learning is used in various applications due to its advantages over traditional Machine Learning (ML) approaches in tasks encompassing complex pattern learning, automatic feature extraction, scalability, adaptability, and performance in general. This paper proposes an end-to-end (E2E) delay estimation method for 5G networks through deep learning (DL) techniques based on Gaussian Mixture Models (GMM). In the first step, the components of a GMM are estimated through the Expectation-Maximization (EM) algorithm and are subsequently used as labeled data in a supervised deep learning stage. A multi-layer neural network model is trained using the labeled data and assuming different numbers of E2E delay observations for each training sample. The accuracy and computation time of the proposed deep learning estimator based on the Gaussian Mixture Model (DLEGMM) are evaluated for different 5G network scenarios. The simulation results show that the DLEGMM outperforms the GMM method based on the EM algorithm, in terms of the accuracy of the E2E delay estimates, although requiring a higher computation time. The estimation method is characterized for different 5G scenarios, and when compared to GMM, DLEGMM reduces the mean squared error (MSE) obtained with GMM between 1.7 to 2.6 times.

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.

Uncalibrated phase delay estimation and ambiguity resolution for BDS-3 six-frequency uncombined PPP with legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals

Multi-frequency integration can accelerate the ambiguity resolution (AR) and shorten the convergence time of precise point positioning (PPP). BDS-3 satellites can broadcast legacy B1I/B3I and new B1C/B2a/B2b/B2a + b signals, which facilitates the multi-frequency PPP. An uncalibrated phase delay (UPD) estimation method and a fast AR method are extended for BDS-3 six-frequency uncombined PPP. The characteristics of UPD estimates are analyzed in terms of stability, ambiguity residuals, and usage rate. The data sets on seven consecutive days from 224 globally distributed stations are selected for UPD estimation, and those from 21 stations are employed for PPP AR. The results indicate that the static convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions (with a threshold of 10 cm) can reach 8.2, 4.0, and 13.4 min in the east, north, and up directions, respectively, and the three-dimensional (3D) convergence time is shortened by 21.1 % and 26.5 % compared with the six-frequency ambiguity-float solutions and the dual-frequency ambiguity-fixed solutions, respectively. The corresponding kinematic convergence time can reach 13.0, 7.0, and 33.2 min in three directions, respectively, and the corresponding improvement rates are 21.0 % and 33.7 %, respectively. In addition, the convergence time of BDS-3 six-frequency PPP ambiguity-fixed solutions can be slightly shortened even compared with the five-frequency case. The static and kinematic positioning accuracy of BDS-3 six-frequency PPP ambiguity-fixed solutions can reach 4, 3, and 9 mm, and 18, 14, and 38 mm in three directions, respectively, which is slightly better than other cases.

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.

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.

FPGA Implementation of Integer Loop Delay Estimation with Low Complexity in Undersampling Digital Predistortion System

In a digital predistortion (DPD) system, accurate loop delay estimation is one of the prerequisites for precise calculation of the DPD coefficient. Multiplications of plural numbers are needed in most of the conventional loop delay estimation algorithms. Based on the Euclidean loop delay estimation (ELDE) method, this paper proposes a simplified Euclidean loop delay estimation (SELDE) method that can avoid the operation of the multiplication of plural numbers. The ELDE and SELDE method are implemented in actual undersampling systems, separately. The results of the experiments prove the feasibility and effectiveness of the methods. Compared with the ELDE method, the hardware resource consumption of SELDE is decreased, mainly reflected in the reduction of registers and look-up tables by 41.26% and 42.84%, respectively.

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.

Low sampling rate digital dechirp for Inverse Synthetic Aperture Ladar imaging processing

The application of digital dechirp technology to Inverse Synthetic Aperture Ladar (ISAL) can greatly reduce the sampling rate burden on analog-to-digital converters. We address the disadvantage of signal sampling and imaging processing in linear frequency-modulated continuous waveform (LFMCW) ISAL systems and suggest a delay estimation method based on a reference channel to reduce the impact of echo delay error. Our method uses the strongest point in the scene as the scene center to estimate the delay and target distance via dechirped pulse compression. The reference channel data are also used to align the dechirped pulse signal and, in turn, reduce clock errors and ensure azimuth signal quality. To our knowledge, our experiment represents the first successful application of digital dechirp to ISAL systems. Experimental results confirm the applicability of our digital dechirp method to ISAL system in order to reduce sampling requirements.

Ionospheric delay estimation of Loran skywave using simple cosine model

ABSTRACT Ionospheric delay is the most significant source of error affecting the Loran skywave timing. To improve timing service, we propose a new ionospheric delay estimation method in this paper. It is a cosine model that combines the ionospheric physical characteristics and skywave delay variation law. This semi-empirical and semi-measured model has characteristics of accuracy and simplicity compared with the traditional method. The experimental results show that estimation error of the model is less than 1 µs for a single day and less than 2 µs for 3 days in the stable time. It is sufficient to correct more than 90% of delay when skywave passes through the ionosphere and is less affected by the season. This paper also gives some suggestions on the propagation of ionospheric coefficients required for the model. It allows broadcasting only by modifying the data channel message structure under the normal operation of Loran system.