Time Delay Estimation Research Articles

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.

Trajectory tracking control for a cable-driven space manipulator using time-delay estimation and nonsingular terminal sliding mode

Trajectory tracking control is critical for cable-driven manipulators to achieve long-distance operation. However, the uncertainties and deformations caused by long-distance transmission cables make the existing trajectory tracking control methods for cable-driven space manipulators unable to meet the demand for high accuracy and strong robustness in practical engineering. In this paper, the trajectory tracking control for a new type of cable-driven large space manipulator is investigated. First, the kinematics and dynamics models of the cable-driven space manipulator are established by using the principle of virtual work. Then, a trajectory tracking control scheme is designed for the cable-driven space manipulator based on the time-delay estimation and the nonsingular terminal sliding mode control approach. The main advantage of the proposed control scheme is to improve the performance of the time-delay estimator by rationally introducing a tuning parameter, which improves the performance of the whole control system. The asymptotic stability of the resulting closed-loop system is proven by the Lyapunov stability theory. The simulation and experiment results show that the proposed control scheme can effectively overcome the influence of disturbance and achieve high-precision trajectory tracking control of the cable-driven space manipulator.

Synchronous PD Control Using a Time Delay Estimator for a Four-Degree-of-Freedom Parallel Robot in Practice

This paper presents a synchronous proportional derivative (PD) control method using a time delay estimator (SPD-TDE) for a four-degree-of-freedom (DOF) parallel robot in practice. The proposed control is a method that is developed from a synchronous PD control method combined with a time delay estimator to guarantee the tracking objectives and synchronous requirements of the robot. Firstly, the synchronous PD control method is designed by defining cross-coupling errors. A cross-coupling error is determined by incorporating the tracking error and deviation of tracking error among two adjacent joints or synchronous errors. Then, the asynchronous problem between the kinematic chains is solved and guarantees that the goal of synchronicity is achieved. Consequently, to improve the tracking performance of the robot, a time delay estimator is used to estimate and eliminate the uncertainty components of the system, such as modeling errors and actuator faults. In addition, the Lyapunov theory is also used to demonstrate the stability and robustness of the proposed control method. Finally, a testbench 4-DOF parallel robot is built, and the controllers are embedded in the control board from MATLAB Simulink using the Waijung block set library to operate the robot preset trajectory tracking. The experimental results of the proposed control method for the 4-DOF parallel robot are compared with those obtained using other controllers to prove its effectiveness.

Model-free adaptive robust control based on TDE for robot with disturbance and input saturation

AbstractA model-free adaptive robust control based on time delay estimation (TDE) is proposed for robot in the presence of disturbance and input saturation. TDE is utilized to estimate the complicated nonlinear terms of the robot including unknown dynamics and disturbance, and a TDE error observer is developed to estimate the inevitable TDE error. When the input torque of the robot exceeds the upper or lower limit of the input saturation, an auxiliary system and a saturation deviation boundary adaptive law are employed to mitigate the negative impact of input saturation on the position tracking. Finally, the robust control law is obtained by backstepping. The stability of the closed-loop system is proved by Lyapunov functions, and the validity of the proposed method is demonstrated by comparative simulations and experiments. Compared with the model-based controllers and other model-free controllers, the proposed method does not necessitate the accurate dynamic model of the complicated system and with lower computation. Moreover, it can guarantee the desired position tracking performance of the robot even subject to disturbance and input saturation simultaneously.

A Greedy Pursuit Hierarchical Iteration Algorithm for Multi-Input Systems with Colored Noise and Unknown Time-Delays

This paper focuses on the joint estimation of parameters and time delays for multi-input systems that contain unknown input delays and colored noise. A greedy pursuit hierarchical iteration algorithm is proposed, which can reduce the estimation cost. Firstly, an over-parameterized approach is employed to construct a sparse system model of multi-input systems even in the absence of prior knowledge of time delays. Secondly, the hierarchical principle is applied to replace the unknown true noise items with their estimation values, and a greedy pursuit search based on compressed sensing is employed to find key parameters using limited sampled data. The greedy pursuit search can effectively reduce the scale of the system model and improve the identification efficiency. Then, the parameters and time delays can be estimated simultaneously while considering the known orders and found locations of key parameters by utilizing iterative methods with limited sampled data. Finally, some simulations are provided to illustrate the effectiveness of the presented algorithm in this paper.

Estimation time delay from field emission to secondary electron emission avalanche in vacuum surface flashover

Vacuum surface flashover is the main factor limiting the development of pulsed power system. In this work, a quantitative dynamical model is built to investigate the vacuum surface flashover from field emission to secondary electron emission avalanche (SEEA). The results show that positive charges accumulating on the dielectric surface caused by field emission electrons play a dominant role when the normal electric field on the dielectric surface Edc is small. The growth of the number of positive surface charges exponentially decreases with the distance from the cathode triple junction (CTJ). With the increase in the density of positive surface charges, the growth of positive surface charges mainly depends on the secondary electrons cascade. As a result, the saturation state of Edc will first occur on the dielectric surface at a distance hundreds of micrometers from the CTJ. In addition, the effect of dielectric permittivity on positive surface charges is considered. The density of positive surface charges equals (1+εr) ε0Edc rather than 2ε0Edc. Particle-in-cell simulations are employed to verify the correctness of the theory model, and the agreement of comparisons is favorable. Furthermore, the space charge effect is discussed. When SEEA reaches saturation, electrons can significantly change the spatial distribution of the electric field.

Trajectory tracking of two-stage anaerobic digestion process: A predictive control with guaranteed performance and saturated input, based on ultra-local model

To address the robust output feedback tracking problem for total outflow rate of two-stage anaerobic digestion (AD) process with input saturation, a novel performance guaranteed ultra-local model (ULM)-based predictive control (PG-ULMPC) is proposed. First, model of the two-stage AD process is considered which presents the characteristics of the production rate of hydrogen and methane. Then, a new control strategy is developed, which relies only on input/output data and does not require any model knowledge of two-stage AD process. Based on ULM, the designed PG-ULMPC strategy consists of time-delay estimation (TDE), prescribed performance function (PPF) as well as predictive control using feedback correction (FC). The ULM is utilized to approximate the complex model of two-stage AD process in a short sliding time window and simplify controller design. The TDE is employed to estimate the lumped disturbance. The PPF guarantees that the tracking error is limited within the performance bounds whose convergence time and precision can be artificially preset. The predictive control using FC stabilizes the closed-loop system and provides saturated control input. To demonstrate the PG-ULMPC performances, numerical simulations of two-stage AD process in presence of unknown parameter disturbances with nonlinear Proportional–Integral (PI) controller, with ULMPC and with PG-ULMPC are realized by using Matlab/Simulink. The obtained results illustrate the better performance of the proposed PG-ULMPC strategy. Moreover, under the measurement noise, by using filtered derivative technique, the proposed method can still achieve satisfactory performance and has little control chattering.

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.

Model-based Estimators of QT Series Time Delay in Following Heart-Rate Changes.

Sudden cardiac death is the leading cause of death among cardiovascular diseases. Markers for patient risk stratification focusing on QT-interval dynamics in response to heart-rate (HR) changes can be characterized in terms of parametric QT to RR dependence and QT/RR hysteresis. The QT/RR hysteresis can be quantified by the time delay the QT interval takes to accommodate for the HR changes. The exercise stress test has been proposed as a proper test, with large HR dynamics, to evaluate the QT/RR hysteresis. The present study aims at evaluating several time-delay estimators based on noise statistic (Gaussian or Laplacian) and HR changes profile at stress test (gradual transition change). The estimator's performance was assessed on a simulated QT transition contaminated by noise and in a clinical study including patients affected by coronary arteries disease (CAD). As expected, the Laplacian and Gaussian estimators yield the best results when noise follows the respective distribution. Further, the Laplacian estimator showed greater discriminative power in classifying different levels of cardiac risk in CAD patients, suggesting that real data fit better the Laplacian distribution than the Gaussian one. The Laplacian estimator appears to be the choice for time-delay estimation of QT/RR hysteresis lag in response to HR changes in stress test.Clinical Relevance-The proposed time-delay estimator of QT/RR hysteresis lag improves its significance as biomarkers for coronary artery diseases risk stratification.

Point-cloud acquisition in CFRP composites using ultrasonic location estimation with the phase-shift reference pulse

Wrinkles in carbon fiber reinforced plastics (CFRP) degrade the mechanical performance. The numerical study on wrinkles requires internal structural point cloud for the meso-structure reconstruction. This paper explores the ultrasonic location estimation with the phase-shift reference pulse for the point-cloud acquisition. The point-cloud acquisition using pulse-echo signals is a time-delay estimation which is a multi-reflection and multi-delay problem. We theoretically simplify the multi-reflection problem as a single-reflection problem and propose a normalized-cross-correlation-peaks (NCCPeaks) method for the multi-delay problem. The proposed method can eliminate some amplitude decrease and balance the smearing and frequency-dependent effects. Simulation shows that the proposed method has the maximum detectable depth without missing inter-ply estimations and a stronger noise resistance than the instantaneous phase method. An experiment is implemented on the 32-ply CFRP sample with an induced wrinkle. The estimation results of the instantaneous phase and NCCPeaks methods are almost the same at the first thirteenth layers. After the thirteenth layer, the NCCPeaks method has a stabler estimation and lower false estimation index than the instantaneous phase method.

Asymptotic properties of Spearman’s footrule and Gini’s gamma in bivariate normal model

This paper aims at rejuvenating the two rank correlation coefficients, Spearman’s footrule (SF) and Gini’s gamma (GG), which were forgotten in the literature for a long time due to lack of knowledge concerning their statistical properties. Under the common bivariate normal model, we establish the asymptotic analytical expressions of the mean and variance of SF and GG, and investigate the performances of SF and GG from the aspects of biased effect, approximate variance and asymptotic relative efficiency (ARE). Moreover, we further study the robustness of SF and GG under contaminated normal models. In order to get a deeper understanding of their performances, we also compare SF and GG with Kendall’s tau (KT) and Spearman’s rho (SR), the most widely used rank correlation coefficients, in terms of bias and mean square error (MSE) under both the normal and contaminated normal models. Finally we show an application of SF and GG in the field of signal processing through the example of time-delay estimation. Simulation results indicate that SF and GG outperform SR and KT in some cases. The new findings discovered in this paper enable SF and GG to play complementary roles to KT and SR in practice.

Adaptive leak signal extraction based on EMD-CC for water pipeline leak location

When using acoustic methods for water pipeline leak localization, noise will significantly affect the accuracy of localization, especially for the case that the noise intensity far exceeds the signal intensity, the traditional noise reduction methods will be ineffective. Therefore, an empirical mode decomposition and cross-correlation (EMD-CC) method for leak localization is proposed, which can adaptively extract effective leak signals from low signal-to-noise ratio (SNR) detection signals, and then can significantly improve the accuracy of localization. In this paper, the principle and steps of the algorithm are elaborated, and the effectiveness is verified in simulations and experiments. In the simulations, the SNR of the reconstructed signal −15 dB is dramatically increased to −6 dB. Compared with conventional noise reduction methods, the time-delay value estimation of EMD-CC is more accurate, more reliable, and more noise resistant. In full-size experiments, the accuracy of localization after processing is significantly improved.

Probing Intrinsic Neural Timescales in EEG with an Information-Theory Inspired Approach: Permutation Entropy Time Delay Estimation (PE-TD).

Time delays are a signature of many physical systems, including the brain, and considerably shape their dynamics; moreover, they play a key role in consciousness, as postulated by the temporo-spatial theory of consciousness (TTC). However, they are often not known a priori and need to be estimated from time series. In this study, we propose the use of permutation entropy (PE) to estimate time delays from neural time series as a more robust alternative to the widely used autocorrelation window (ACW). In the first part, we demonstrate the validity of this approach on synthetic neural data, and we show its resistance to regimes of nonstationarity in time series. Mirroring yet another example of comparable behavior between different nonlinear systems, permutation entropy-time delay estimation (PE-TD) is also able to measure intrinsic neural timescales (INTs) (temporal windows of neural activity at rest) from hd-EEG human data; additionally, this replication extends to the abnormal prolongation of INT values in disorders of consciousness (DoCs). Surprisingly, the correlation between ACW-0 and PE-TD decreases in a state-dependent manner when consciousness is lost, hinting at potential different regimes of nonstationarity and nonlinearity in conscious/unconscious states, consistent with many current theoretical frameworks on consciousness. In summary, we demonstrate the validity of PE-TD as a tool to extract relevant time scales from neural data; furthermore, given the divergence between ACW and PE-TD specific to DoC subjects, we hint at its potential use for the characterization of conscious states.

Efficient Graph-based Signal Motif Discovery with Performance Bounds

In this paper, we investigate the problem of signal motif discovery. In the formulation considered, the goal is to find an unknown pattern (or motif) repeated across multiple data sets. This problem formulation can be applied to various domains, such as DNA sequence alignment and matching, motif discovery in time-series, and object detection and localization in images. We take the approach of minimizing an objective that is the sum over a measure of the difference between a candidate instance in each signal collection (or set) and the unknown pattern. Additionally, a non-negative instance dependent penalty is introduced. The proposed general objective can be used to capture well-known problems (e.g., blind joint time-delay estimation). Due to the non-convex nature of the problem and often the integer programming flavor of the approach, brute-force solution is non-polynomial and computationally prohibitive for large scale problems. We propose an efficient polynomial time (quadratic in the number of instances) bipartite graph based approximation to solve the problem. We provide a theoretical analysis for the proposed solution including bounds on the gap from the optimal solution and conditions for optimality. In particular, we show that the objective value for the proposed solution is no more than twice the objective value of the optimal solution. To illustrate the merit of the proposed approach, we present qualitative and quantitative empirical analysis of the proposed approach on several applications and compare our method to appropriate alternatives.

Model-free sliding mode prescribed performance control of robotic manipulator based on new reaching law

The article proposes a model-free sliding mode prescribed performance control method for robotic manipulator. For accelerating the errors converging rate as well as bringing down the real-time control torque, an error-driven nonsingular fast terminal sliding mode is employed in this control method. Besides, a modified power reaching law is newly designed, which is able to offer better chattering elimination performance than traditional power reaching law. To solve the problem that the controller’s performance highly relies on the accuracy of robotic model, a model-free control idea is introduced where an ultra-local model is established and the estimation of time delay is used to approximate the unknown part of the ultra-local model. Considering the transient performance is a significant element that effects the using security and system stability, the technique of prescribed performance control is introduced to limit the state errors in a prescribed region. The closed-loop stability proof of the whole system is achieved according to Lyapunov’s stability theorem. The proposed controller’s superiority and feasibility compared with other controllers are demonstrated by numerical simulations.

An Experimental Study on Trajectory Tracking Control of Torpedo-like AUVs Using Coupled Error Dynamics

In this paper, we propose a trajectory tracking controller with experimental verification for torpedo-like autonomous underwater vehicles (AUVs) with underactuation characteristics. The proposed controller overcomes the underactuation problem by designing the desired error dynamics in a coupled form using state variables in body-fixed and world coordinates. Unlike the back-stepping control requiring high-order derivatives of state variables, the proposed controller only requires the first derivatives of the states, which can alleviate noise magnification issues due to differentiation. We adopt time delay estimation to estimate the dynamics indirectly using control inputs and vehicle outputs, making the proposed controller relatively easy to apply without requiring the all of the vehicle dynamics. We also address some practical issues that commonly arise in experimental environments: handling measurement noises and actuation limits. To mitigate the effects of noise on the controller, a filtering technique using a moving window average is employed. Additionally, to account for the actuation limits, we design an anti-windup structure that takes into consideration the nonlinearity between the thrusting force and rotating speed of the thruster. We verify the tracking performance of the proposed controller through experimentation using an AUV. The experimental results show that the 3D motion control of the proposed controller exhibits an RMS error of 0.3216 m and demonstrate that the proposed controller achieves accurate tracking performance, making it suitable for survey missions that require tracking errors of less than one meter.

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.

TD-CARMA: Painless, Accurate, and Scalable Estimates of Gravitational Lens Time Delays with Flexible CARMA Processes

Cosmological parameters encoding our understanding of the expansion history of the universe can be constrained by the accurate estimation of time delays arising in gravitationally lensed systems. We propose TD-CARMA, a Bayesian method to estimate cosmological time delays by modeling observed and irregularly sampled light curves as realizations of a continuous auto-regressive moving average (CARMA) process. Our model accounts for heteroskedastic measurement errors and microlensing, an additional source of independent extrinsic long-term variability in the source brightness. The semiseparable structure of the CARMA covariance matrix allows for fast and scalable likelihood computation using Gaussian process modeling. We obtain a sample from the joint posterior distribution of the model parameters using a nested sampling approach. This allows for “painless” Bayesian computation, dealing with the expected multimodality of the posterior distribution in a straightforward manner and not requiring the specification of starting values or an initial guess for the time delay, unlike existing methods. In addition, the proposed sampling procedure automatically evaluates the Bayesian evidence, allowing us to perform principled Bayesian model selection. TD-CARMA is parsimonious, and typically includes no more than a dozen unknown parameters. We apply TD-CARMA to six doubly lensed quasars HS2209+1914, SDSS J1001+5027, SDSS J1206+4332, SDSS J1515+1511, SDSS J1455+1447, and SDSS J1349+1227, estimating their time delays as −21.96 ± 1.448, 120.93 ± 1.015, 111.51 ± 1.452, 210.80 ± 2.18, 45.36 ± 1.93, and 432.05 ± 1.950, respectively. These estimates are consistent with those derived in the relevant literature, but are typically two to four times more precise.

A Gaussian process cross-correlation approach to time-delay estimation in active galactic nuclei

Context. We present a probabilistic cross-correlation approach to estimate time delays in the context of reverberation mapping (RM) of active galactic nuclei (AGN). Aims. We reformulate the traditional interpolated cross-correlation method as a statistically principled model that delivers a posterior distribution for the delay. Methods. The method employs Gaussian processes as a model for observed AGN light curves. We describe the mathematical formalism and demonstrate the new approach using both simulated light curves and available RM observations. Results. The proposed method delivers a posterior distribution for the delay that accounts for observational noise and the non-uniform sampling of the light curves. This feature allows us to fully quantify the uncertainty on the delay and propagate it to subsequent calculations of dependant physical quantities, such as black hole masses. The method delivers out-of-sample predictions, which enables us to subject it to model selection, and can calculate the joint posterior delay for more than two light curves. Conclusions. Because of the numerous advantages of our reformulation and the simplicity of its application, we anticipate that our method will find favour not only in the specialised community of RM, but also in all fields where cross-correlation analysis is performed. We provide the algorithms and examples of their application as part of our Julia GPCC package.

Improved Methods for UHF Localization of Partial Discharge in Air-Insulated Substations

A time-difference-of-arrival-based partial discharge (PD) location system that utilises prior knowledge of substation layout is presented. We propose a new time delay estimator that employs onset detection techniques and demonstrate, through experimental results, that it is at least 2.8 times more accurate than other conventional estimators. Using knowledge of a substation’s layout, we develop a minimum mean-square-error (MMSE)-based location estimator and an algorithm that optimises antenna placement to maximise location accuracy in regions occupied by high-voltage equipment. Simulation results show that a system that uses the proposed techniques is 5.9 times more accurate than a more conventional system in a high-noise environment.