Time Delay Estimation Research Articles

Adaptive Time Delay Estimation Based on Signal Preprocessing and Fourth-Order Cumulant

Adaptive Time Delay Estimation Based on Signal Preprocessing and Fourth-Order Cumulant

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).

Model‐free prescribed performance fast nonsingular terminal sliding mode control with practical finite‐time stability of uncertain robot manipulators

AbstractThis paper addresses the problem of robust and high precision trajectory tracking control of uncertain robot manipulators with prescribed performance. Time delay estimation (TDE) technique is employed to estimate system model, then a new self‐adjusting strategy (SAS) is designed to adjust TDE gain online. Prescribed performance control (PPC) method is used to guarantee transient response speed and steady‐state accuracy. Moreover, the transform function of PPC employed in this paper has unlimited domain, which greatly improves the robustness and stability of system. An improved fixed‐time dynamical system is firstly deduced and analyzed, then a new fast nonsingular terminal sliding mode surface is designed to accelerate convergence rate of tracking errors. Finally, the whole system is strictly proven to be practical finite‐time stable, which means that tracking errors can converge to a small neighborhood of zero within a uniformly bounded convergence time. Main advantages of the proposed approach include model‐free, robust, singularity‐free, faster transient response and higher steady‐state tracking precision. Experimental results carried out on the Rethink Sawyer Robot also verified the effectiveness of the proposed scheme.

An Enhanced Adaptive Time Delay Control-Based Integral Sliding Mode for Trajectory Tracking of Robot Manipulators

This article proposes an enhanced adaptive time delay controller (ATDC) for robot manipulators subjected to external disturbances. This approach is model-free and uses time delay estimation (TDE) to estimate complex and unknown robot dynamics. First, to remove the reaching phase and improve the robustness of the control, an integral sliding surface (ISS) is used. Second, to speed up the convergence and compensate for the TDE errors and external disturbances, the gains of time delay control and the sliding mode have been made adaptive. In this article, we clearly point out using the Lyapunov method that the position and velocity tracking errors are guaranteed to be uniformly ultimately bounded (UUB). The effectiveness and the robustness of the designed controller over existing methods are experimentally verified on a parallel Delta robot. The novel model-free proposed control is robust and highly accurate, which is appropriate and recommended for industrial robotic applications.

A Comprehensive Expectation Identification Framework for Multirate Time-Delayed Systems

The expectation maximization (EM) algorithm has been extensively used to solve system identification problems with hidden variables. It needs to calculate a derivative equation and perform a matrix inversion in the EM-M step. The equations related to the EM algorithm may be unsolvable for some complex nonlinear systems, and the matrix inversion has heavy computational costs for large-scale systems. This paper provides two expectation based algorithms with the aim of constructing a comprehensive expectation framework concerning different kinds of time-delayed systems: (1) for a small-scale linear system, the classical EM algorithm can quickly obtain the parameter and time-delay estimates; (2) for a complex nonlinear system with low order, the proposed expectation gradient descent (EGD) algorithm can avoid derivative function calculation; (3) for a large-scale system, the proposed expectation multi-direction (EMD) algorithm does not require eigenvalue calculation and has less computational costs. These two algorithms are developed based on the gradient descent and multi-direction methods. Under such an expectation framework, different kinds of models are identified on a case-by-case basis. The convergence analysis and simulation examples show effectiveness of the algorithms.

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.

USE OF SIMILARITY METRICS IN ROBUST TIME DELAY ESTIMATION

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

Immersion and invariance sliding mode control with time-delay estimation for rigid spacecraft with uncertainties and actuator faults

This paper investigates the attitude control of rigid spacecraft with uncertainties and actuator faults. An immersion and invariance sliding mode control with time-delay estimation (IISMCTDE) is proposed to cope with uncertainties, disturbances, and actuator faults. First, time-delay estimation is utilized to reconstruct the total disturbances including uncertainties, disturbances, and actuator faults. Then, based on the time-delay estimation, an immersion and invariance sliding mode control (IISMC) scheme is developed to achieve accurate attitude tracking from the reconstructed knowledge. The proposed IISMCTDE can not only achieve finite-time convergence but also be simple and easy to operate. Simulations are provided to demonstrate the effectiveness of the proposed approach.

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.

Approximate maximum likelihood time-delay estimation for two closely spaced sources

The study of ground reflections of Global Navigation Satellite System (GNSS) signals, as in GNSS Reflectometry (GNSS-R) can lead to the receiver height estimation. The latter is estimated by comparing the time of arrival difference between the direct and reflected signals, also called path separation. In ground-based scenarios, this path separation can be very small, inducing important interference between paths, which makes it difficult to correctly obtain altimetry products. The path separation estimation can be obtained by a brute force dual source maximum likelihood estimator (2S-MLE), but this solution has a large computational cost. On the other hand, the path separation is so small that a number of approximations can be done. In this study, a third order Taylor approximation of the dual source likelihood criterion is proposed to reduce its complexity. The proposed algorithm performance is compared to the non approximated 2S-MLE for the estimation of the path separation, and to a standard single source processing for the estimation of the direct signal time-delay. These results, along with the corresponding lower bounds, prove that the proposed approach may be of interest for two applications: ground-based GNSS-R altimetry (or radar with low elevation targets) and GNSS multipath mitigation.

Asymmetric time‐varying BLF‐based model‐free hybrid force/position control for SEA‐based 2‐DOF manipulator

SummaryIn this work, an asymmetric time‐varying barrier Lyapunov function‐based model‐free hybrid force/position controller (ABLF‐MFC) is proposed for the series elastic actuator‐based 2‐DOF manipulator. Inspired by large surface machining, many scenarios require hybrid force/position control, and the simple position control can no longer meet the above requirements. Therefore, ABLF‐MFC with a dual‐loop structure is established, which are force sub‐control loop and position sub‐control loop. Based on the idea of admittance control, the force sub‐control loop generates a reference trajectory according to the desired interaction force and trajectory. Then, for the position sub‐control loop, to simplify the controller design process, an ultra‐local model (ULM) is introduced, which can approximate the original system. Since the ULM has an unknown term, time‐delay estimation (TDE) is applied to estimate it, which can also reduce the dependence on accurate model parameters. The position sub‐control loop is designed by an asymmetric time‐varying barrier Lyapunov function, an integral‐type Lyapunov function and an adaptive compensation term, so the tracking error can be kept within the preset boundary while ensuring the convergence, and the TDE estimation error can be compensated. Rigorous mathematical proofs and simulation results verify the effectiveness of ABLF‐MFC.

Model-free adaptive control based on prescribed performance and time delay estimation for robotic manipulators subject to backlash hysteresis

Aim to solve the problem of over-dependence on dynamics model and low tracking accuracy of robotic manipulators under uncertainties and backlash hysteresis, an adaptive continuous nonsingular fast terminal sliding mode controller combining time delay estimation (TDE) and prescribed performance control (PPC) is formulated. Firstly, TDE is applied to estimate the model information and external disturbances, so that the dynamics model of robotic manipulators is simplified into a local model. Then, an adaptive terminal sliding mode controller is established based on the local model and PPC, which solves the singularity problem of traditional terminal sliding mode and improves the transient and steady-state performance of robotic manipulators. Next, by combining the reaching law with the adaptive term, robotic manipulators achieve favorable tracking performance, fast convergence time, and chattering suppression under complex disturbances. And the Lyapunov theory is applied to prove that the robotic manipulators can reach the steady state in finite time. Meanwhile, a saturation compensator is formulated to settle actuator saturation and the compensator can converge within a finite time. Finally, the simulation is applied to verify the formulated control strategy can effectively improve the tracking performance and enhance the robustness against disturbances.

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.

Time-delay metric for TDE of SISO delay systems

The time-delay intrinsic in the time series sampled from dynamic systems results in the chaotic correspondence between the elements of the time series. Therefore, accurate estimation of the time-delay is essential in time series-based tasks. In this paper, we propose two time-delay metrics for time-delay estimation (TDE) of single-input single-output (SISO) delay systems with unknown structures. The two proposed metrics are based on the ellipse shape ratio (ESR) and called the linear ellipse shape ratio (LESR), and the nonlinear ellipse shape ratio (NESR). In the devised TDE process employing the proposed metrics, an iteratively updated ellipse is used to filter out the outliers from the system input and output samples. Simulation experiments confirm the efficiency of the proposed time-delay metrics.

Data science methodology for time-delay estimation and data preprocessing of the time-delay challenge

ABSTRACT The vast amount of astronomical information that has become available over this decade has far exceeded that of the last century. The heterogeneity of the data and its overwhelming magnitude have made it impossible to perform manual analysis. As a consequence, new techniques have been developed and different strategies have been amalgamated, such as data science and data mining, in order to carry out more in-depth and exhaustive analyses in search of the extraction of the knowledge contained in data. This paper introduces a data science methodology that consists of successive stages, with the core of this proposal being the step of data preprocessing, with the aim of reducing the complexity of the analysis and enabling hidden knowledge in the data to be uncovered. The proposed methodology was tested on a set of data consisting of artificial light curves that try to mimic the behaviour of the strong gravitational lens phenomenon, as supplied by the Time Delay Challenge 1 (TDC1). Under the data science methodology, diverse statistical methods were implemented for data analysis, and cross-correlation and dispersion methods were applied for the time-delay estimation of strong lensing systems. With this methodology, we obtained time-delay estimations from the TDC1 data set and compared them with earlier results reported by the COSmological MOnitoring of GRAvItational Lenses project (COSMOGRAIL). The empirical evidence leads us to conclude that, with the proposed methodology, we achieve a greater accuracy in estimating time delays compared with estimations made with raw data.

Disrupted multi-scale topological organization of directed functional brain networks in patients with disorders of consciousness.

Disorders of consciousness are impaired states of consciousness caused by severe brain injuries. Previous resting-state functional magnetic resonance imaging studies have reported abnormal brain network properties at different topological scales in patients with disorders of consciousness by using graph theoretical analysis. However, it is still unclear how inter-regional directed propagation activities affect the topological organization of functional brain networks in patients with disorders of consciousness. To reveal the altered topological organization in patients with disorders of consciousness, we constructed whole-brain directed functional networks by combining functional connectivity analysis and time delay estimation. Then we performed graph theoretical analysis based on the directed functional brain networks at three topological scales, from the nodal scale, the resting-state network scale to the global scale. Finally, the canonical correlation analysis was used to determine the correlations between altered topological properties and clinical scores in patients with disorders of consciousness. At the nodal scale, we observed decreased in-degree and increased out-degree in the precuneus in patients with disorders of consciousness. At the resting-state network scale, the patients with disorders of consciousness showed reorganized motif patterns within the default mode network and between the default mode network and other resting-state networks. At the global scale, we found a lower global clustering coefficient in the patients with disorders of consciousness than in the controls. The results of the canonical correlation analysis showed that the abnormal degree and the disrupted motif were significantly correlated with the clinical scores of the patients with disorders of consciousness. Our findings showed that consciousness impairment can be revealed by abnormal directed connection patterns at multiple topological scales in the whole brain, and the disrupted directed connection patterns may serve as clinical biomarkers to assess the dysfunction of patients with disorders of consciousness.

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).

Fast Finite-Time Path-Following Control for Autonomous Vehicle via Complete Model-Free Approach

Without any knowledge of the vehicle model and its parameters, a novel complete model-free path-following control strategy is developed for autonomous vehicles based on the time-delay estimation (TDE) technique. Different from the existing time-delay control (TDC) approaches, an adaptive nonsingular terminal sliding mode (ANTSM) control law is designed to stabilize the path-following errors without any information of the suitable control gain, which is significant in the conventional TDC scheme, and the boundary of the TDE error, which is necessary for the sliding-mode-based control scheme. The proposed model-free control structure can dynamically update the gain of the designed controller and the boundaries of the TDE error, and the practical finite-time convergence of the preview error can be achieved. In the HIL tests, the comparative results demonstrate that the proposed ANTSM model-free control strategy can provide superior comprehensive tracking performance over both the model-based sliding mode controller and the conventional TDC controller, while the autonomous vehicle follows desired paths.

Model and data-driven homework problems for learning signal processing concepts

The Electrical and Computer Engineering Department at Portland State University offers a course in Sensor Array Processing. The content is designed to be introductory and approachable for undergraduate, first year graduate and students from other disciplines such as Mechanical Engineering or Physics. The signal processing techniques explored use two or more sensors and can be applied to acoustics or electromagnetic waves. I have two favorite homework problems: one is based on simulated data and the other based on measured data and both help solidify important concepts. For the simulations, a model is developed based on the method of images and can be applied to signals from a sonar in the ocean or to voices in a room. These multipath environments are used to illustrate how a signal (such as an audio clip the student creates) would change in different environments or source/receiver geometry. The channel impulse response is modeled and together with convolution allows different waveform responses to be easily computed. My favorite problem using measured data is based on recordings of a broadband source on two sensors. Cross-correlation is used to determine the source direction. This problem explores the concepts of pulse compression and pre-whitening for time-delay and direction estimation.

A two-state Markov chain model for slug flow in horizontal ducts

Intermittent flows are common flow patterns in gas–liquid horizontal flow and attract attention and great research effort due to its importance for industrial and engineering applications. The slug flow is typically modelled based on a unit cell varying from an elongated air bubble with a liquid film in segregated flow pattern and an aerated liquid plug, the slug region, with remarkable stochastic characteristics of its alternating regions. In this paper, a two-state Markov chain model is proposed to represent the stochastic dynamics of developed slug flow in horizontal pipes. Each state represents either the liquid slug or the elongated bubble regions and the transition probabilities dictate the change of the given discrete time measurement to stay at a given state or change. This simple but insightful description of the phenomenon allows an analytical treatment of the statistics of Markov chain stochastic process. Measurement stations with two double wire resistive sensors are used to obtain the void fraction time series and a corresponding two-state representation. Each state is classified by a threshold defined by an unsupervised and non-parametric pattern recognition approach. The state transition matrix is then estimated for each corresponding experimental point. Thus random samples can be synthetically regenerated with the same statistical features of the corresponding measurements. It is shown that the Markov chain model can successfully represent second-order statistics of the measurement, such as the autocorrelation and power spectral density, given an appropriate choice of the chain order. Moreover, a cross correlation-based time delay estimation is proposed for the two-sensor measurement station and additional information is obtained from the slug flow. Subsequently, statistics of some slug flow features are estimated using the proposed approach and their interpretation as random variables derived from the void fraction stochastic process is discussed.