Problem Of Time Delay Estimation Research Articles

A D-norm cross-correlation method for particle velocity measurement through electrostatic sensing

The cross-correlation (CC) method is conventionally used for measuring the velocity of gas–solid flows using electrostatic sensors, wherein velocity measurement is transformed into a time-delay estimation problem. However, owing to the intricacies of signals in gas–solid flows, the cross-correlation function may exhibit multiple peaks, resulting in peak misjudgment and time-delay estimation bias. To address these issues, this paper proposes a D-norm cross-correlation (DCC) velocity measurement method and applies it to flow velocity measurements in pneumatic conveying. Such a technique leverages the sensitivity of D-norm to pulses, highlighting the pulse characteristics of measurement signals. This approach increases the accuracy of time-delay estimation for upstream and downstream signals, mitigating the issues caused by multi-peaks and fake peaks in the cross-correlation function. Compared to conventional CC, the DCC can eliminate the problem of multiple and fake peaks in cross-correlation functions more effectively, thereby increasing the reliability of velocity measurements.

Sparsity-Based Time Delay Estimation Through the Matched Filter Outputs

In this letter, we deal with the problem of high-resolution time delay estimation (TDE) in multipath environments exploiting the matched filter (MF) outputs data. To this end, we develop a systematic post-processing framework, consisting of two sparsity-based algorithms and a refining procedure aimed at reducing the computational load. The TDE problem is formulated as a sparse signal recovery problem and efficiently solved resorting to a majorization-minimization paradigm and a cyclic procedure. At the design stage, we assume a complex-valued Gaussian distribution model for the MF samples and incorporate a module-product prior that promotes the sparsity more significantly than the conventional complex Laplacian distribution. The preliminary performance assessment, conducted on simulated data, shows that, at least for the considered parameter values, the proposed delay estimators approach the Cramér-Rao bound for different signal-to-noise ratios and bandwidths.

Combining First- and Second-Order Continuity Constraints in Ultrasound Elastography.

Ultrasound elastography is a prominent noninvasive medical imaging technique that estimates tissue elastic properties to detect abnormalities in an organ. A common approximation to tissue elastic modulus is tissue strain induced after mechanical stimulation. To compute tissue strain, ultrasound radio frequency (RF) data can be processed using energy-based algorithms. These algorithms suffer from ill-posedness to tackle. A continuity constraint along with the data amplitude similarity is imposed to obtain a unique solution to the time-delay estimation (TDE) problem. Existing energy-based methods exploit the first-order spatial derivative of the displacement field to construct a regularizer. This first-order regularization scheme alone is not fully consistent with the mechanics of tissue deformation while perturbed with an external force. As a consequence, state-of-the-art techniques suffer from two crucial drawbacks. First, the strain map is not sufficiently smooth in uniform tissue regions. Second, the edges of the hard or soft inclusions are not well-defined in the image. Herein, we address these issues by formulating a novel regularizer taking both first- and second-order derivatives of the displacement field into account. The second-order constraint, which is the principal novelty of this work, contributes both to background continuity and edge sharpness by suppressing spurious noisy edges and enhancing strong boundaries. We name the proposed technique: Second-Order Ultrasound eLastography (SOUL). Comparative assessment of qualitative and quantitative results shows that SOUL substantially outperforms three recently developed TDE algorithms called Hybrid, GLUE, and MPWC-Net++. SOUL yields 27.72%, 62.56%, and 81.37% improvements of the signal-to-noise ratio (SNR) and 72.35%, 54.03%, and 65.17% improvements of the contrast-to-noise ratio (CNR) over GLUE with data pertaining to simulation, phantom, and in vivo tissue, respectively. The SOUL code can be downloaded from code.sonography.ai.

Временные корреляционные методы оценки задержки комплексных сигналов, некратной периоду дискретизации, на основе полиномиальной интерполяции.

This paper deals with the problem of subsample time delay estimation of complex signal based on polynomial interpolation. Time delay estimation is performed by cross-correlation time approach. Three polynomial interpolation techniques applied to the discrete complex cross-correlation function in the neighborhood of its maximum are proposed. These methods show high processing speed and allow obtaining accurate real-valued time delay estimation when digital complex signals are processed. The comparative analysis between these methods is performed. A rigorous analytical solution for the correction of time delay estimation for one of the proposed methods is obtained for the case of the third-order polynomial interpolation. This solution is applied for an equidistant grid of discrete cross-correlation function samples. One can improve the accuracy of time delay estimates by using aforementioned correction. A numerical simulation is performed to quantify the accuracy of the time delay estimates when using the proposed methods for the case where a stationary random process described by the first-order autoregressive mode is chosen as a model of original signal. The main results were presented and discussed at XIV All-Russian conference “Radar and telecommunication”.

System modeling oriented time-delay estimation

Training models to approximate target systems is the dominant method applied to unknown-structure delay system modeling. Due to limited learning ability of the models, the time-delay estimation (TDE) process should be executed prior to the training. The TDE for unknown-structure multi-input multi-output (MIMO) delay systems remains a challenge due to the physical interaction within the system the correlations among the system inputs and outputs. This paper addresses the TDE problem of unknown-structure MIMO delay systems. A dependence measure employed from copula theory, which is named C-dependence, is introduced to measure the dependence among the system inputs and outputs. The relationship between the C-dependence and the time-delays is studied, and the time-delays are estimated by maximizing the C-dependence. The highlight of the proposed method is that no prior decoupling process and system structure are required during the TDE process. Simulation and real data experiments are provided to demonstrate the effectiveness of the proposed method.

On TDE techniques for the radar signal

The time-delay estimation (TDE) arises in many applications, especially in radar signal processing. In this study, different TDE techniques are considered based on well-known approaches such as classical matched filter, multiple signal classification, standard least squares (LS), regularisation LS, and compressive sensing for the radar signal. In order to understand the particular behaviour of each technique, comparisons by theoretical analysis and numerical simulations are made. Then some brief conclusions can be obtained from simulation results. Finally, associated with primary factors, future research is prospected on the TDE problem.

Compressed Sensing OFDM Time Delay Estimation Based on Atomic Evolution and Elimination

Aiming at the problem of time delay estimation for orthogonal frequency division multiplexing (OFDM) signals with small samples, a new compressed sensing time delay estimation method based on atomic evolution and elimination is proposed. This method introduces the idea of evolution and elimination from Darwin's evolutionism, abandons the fixed and invariable way of grid points in the traditional algorithm, takes grid points as adjustable parameters, and updates grid points in each iteration process to promote the evolution of atoms. In order to deal with the off-grid effect, the exponential function is directly modified instead of linear approximation, which effectively eliminates the modeling error caused by the original off-grid algorithm. In the process of calculation, the atomic elimination mechanism is adopted, which reduces the amount of calculation and improves the speed of it. The simulation results show that the proposed algorithm can significantly improve the performance of time delay estimation, especially when using coarse grids. Based on the universal software radio peripheral (USRP), the validity of the proposed algorithm is verified by the actual signal.

Time-delay estimation for SISO systems using SWσ

This paper addresses the time-delay estimation problem of SISO systems using uniformly sampled input-output data. A dependence measure known as Schweizer and Wolff's σ (SWσ) from the copula theory is employed to measure the dependence of the input-output data. The quantitative relation between the time-delay and SWσ is studied, and the time-delay is estimated given that the SWσ of the input-output data reaches its maximum value when the time-delay is removed. The major advantage of our work is that no other parameters of the system must be estimated before or during the time-delay estimation process. Experiments and comparisons are used to verify the feasibility and effectiveness of the proposed method.

Eigenvalue-based time delay estimation of repetitive biomedical signals

The time delay estimation problem associated with an ensemble of misaligned, repetitive signals is revisited. Each observed signal is assumed to be composed of an unknown, deterministic signal corrupted by Gaussian, white noise. This paper shows that maximum likelihood (ML) time delay estimation can be viewed as the maximization of an eigenvalue ratio, where the eigenvalues are obtained from the ensemble correlation matrix. A suboptimal, one-step time delay estimate is proposed for initialization of the ML estimator, based on one of the eigenvectors of the inter-signal correlation matrix. With this approach, the ML estimates can be determined without the need for an intermediate estimate of the underlying, unknown signal. Based on respiratory flow signals, simulations show that the variance of the time delay estimation error for the eigenvalue-based method is almost the same as that of the ML estimator. Initializing the maximization with the one-step estimates, rather than using the ML estimator alone, the computation time is reduced by a factor of 5M when using brute force maximization (M denoting the number of signals in the ensemble), and a factor of about 1.5 when using particle swarm maximization. It is concluded that eigenanalysis of the ensemble correlation matrix not only provides valuable insight on how signal energy, jitter, and noise influence the estimation process, but it also leads to a one-step estimator which can make the way for a substantial reduction in computation time.

Parameter identification of nonlinear multirate time-delay system with uncertain output delays

The joint parameter and time-delay estimation problems for a class of nonlinear multirate time-delay system with uncertain output delays are addressed in this paper. The practical process typically has time-delay properties and the process data are often multirate, sampled with output data inevitably corrupted by uncertain delays. The linear parameter varying (LPV) finite impulse response (FIR) multirate time-delay model is initially built to describe the considered system. The problems of over-parameterization and the existence of both continuous model parameters and discrete time-delays have made the conventional maximum likelihood difficult to solve the considered problems. In order to handle these problems, the joint parameter and time-delay estimation for the LPV FIR multirate time-delay model are formulated in the expectation-maximization scheme, and the algorithm to estimate the model parameters and time-delays is derived, simultaneously based on multirate process data. The efficacy of the proposed method is verified through a numerical simulation and a practical chemical plant.

Maximum Likelihood Time Delay Estimation From Single- and Multi-Carrier DSSS Multipath MIMO Transmissions for Future 5G Networks

In this paper, we address the problem of time delay estimation (TDE) from single-carrier (SC) or multi-carrier (MC) direct-sequence spread spectrum (DSSS) multipath transmissions in the presence of multiple transmit and/or receive antennas that will characterize future 5G radio interface technologies (RITs), such as coded-domain nonorthogonal multiple access. We derive for the first time a closed-form expression for the Cramer-Rao lower bound (CRLB) and develop two maximum likelihood (ML) multipath TDEs for SC DSSS single-input multiple-output (SIMO) in the non-data-aided (NDA) case. The first TDE, based on iterative expectation maximization (EM), provides accurate estimates whenever a good initial guess of the parameters is available at the receiver. The second TDE implements the ML criterion in a non-iterative way and finds the global maximum of the compressed likelihood function using the importance sampling (IS) technique without requiring any initialization. We also extend both the SC DSSS SIMO CRLB and the two new SC DSSS SIMO ML NDA TDEs to MC DSSS RITs and to multiple-input multiple-output structures with any diversity versus multiplexing pre-coding type before generalizing them all to the data-aided (DA) case. Simulations suggest that the EM TDE is suitable for large observation in space, time, and/or frequency, whereas the IS TDE is preferred in the opposite case of very short data records. Moreover, we show in the NDA case, both analytically and by simulations, that spatial (transmit and receive), temporal, and frequency samples interchangeably have the same impact on estimation accuracy and performance bound regardless of the channel correlation type and amount present in each dimension. Furthermore, we are able to properly cope with such channel correlations that do indeed arise in practice and, hence, become very challenging both in estimation and CRLB derivation in the DA case, but that have been so far overlooked in previous works.

An Adaptive Time Delay Estimator Based on ETDE Algorithm with Noisy Measurements

We address the problem of adaptive time delay estimation with noisy measurements. We develop a computationally efficient adaptive time delay estimator based on Explicit time delay estimation (ETDE) algorithm, by applying the unbiased impulse response estimation approach. In this algorithm, a weighted error function is derived, and the time delay is explicitly parameterized in the filter coefficients and iteratively updated directly by utilizing the modified error function. Simulations validate the performance of the proposed algorithm for colored input and low signal-to-noise ratio scenarios.

An Innovative Approach for Optimal Time Delay Estimation in System Identification

In this study, a novel strategy for time delay estimation (TDE) is proposed. The method, OTDE-Gen, uses a genetic algorithm to find the best time delay, so that the identified model presents the best performance. OTDE-Gen also allows to evaluate different model structures and distinct orders for processes of any dimension. A brief review of classical TDE techniques is presented, and the TDE problem is further analyzed from a System Identification perspective, through examples that illustrate and quantify how the time delay affects the model performance, and also how the identification setup (signal-to-noise ratio, model structure and order) affects the choice of the best time delay. The OTDE-Gen and the classical TDE methods are tested in a benchmark and performance comparisons are carried out.

Classical robots perturbed by L\xe9vy processes: analysis and L\xe9vy disturbance rejection methods

The stability and convergence of state, disturbance and parametric estimates of a robot have been analyzed using the Lyapunov method in the existing literature. In this paper, we analyze the problem of stochastic stability and also prove some results regarding behavior of statistically averaged Lyapunov energy function in the presence of jerk noise modeled as the sum of independent random variables hitting the robot at Poisson times. This type of noise is also called jerk noise in contrast to white Gaussian noise. Jerk noise is a Lévy process, i.e., a process with stationary independent increments, and is the natural non-Gaussian generalization of white Gaussian noise. Jerk noise can successfully be used to model hand tremor occurring at sporadic time intervals. We also study here the problem of time delay estimation in Lévy noise.

디콘볼루션을 이용한 시간지연추정

This paper deals with the problem of time delay estimation using de-convolution. Two approaches, conjugate gradient method and the total lease square method have been presented to solve the de-convolution problem. Numerical simulation demonstrates the superior performance of the proposed methods over the conventional GCC based algorithms and FIR filter method.

Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation

We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in two aspects: (i) we extend the formulation from real non-negative amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch between the manifold described by the parameters and its polar approximation. To quantify the improvements afforded by the proposed extensions, we evaluate six algorithms for estimation of parameters in sparse translation-invariant signals, exemplified with the time delay estimation problem. The evaluation is based on three performance metrics: estimator precision, sampling rate and computational complexity. We use compressive sensing with all the algorithms to lower the necessary sampling rate and show that it is still possible to attain good estimation precision and keep the computational complexity low. Our numerical experiments show that the proposed algorithms outperform existing approaches that either leverage polynomial interpolation or are based on a conversion to a frequency-estimation problem followed by a super-resolution algorithm. The algorithms studied here provide various tradeoffs between computational complexity, estimation precision, and necessary sampling rate. The work shows that compressive sensing for the class of sparse translation-invariant signals allows for a decrease in sampling rate and that the use of polar interpolation increases the estimation precision.

A Geometric Approach to Sound Source Localization from Time-Delay Estimates

This paper addresses the problem of sound-source localization from time-delay estimates using arbitrarily-shaped non-coplanar microphone arrays. A novel geometric formulation is proposed, together with a thorough algebraic analysis and a global optimization solver. The proposed model is thoroughly described and evaluated. The geometric analysis, stemming from the direct acoustic propagation model, leads to necessary and sufficient conditions for a set of time delays to correspond to a unique position in the source space. Such sets of time delays are referred to as feasible sets. We formally prove that every feasible set corresponds to exactly one position in the source space, whose value can be recovered using a closed-form localization mapping. Therefore we seek for the optimal feasible set of time delays given, as input, the received microphone signals. This time delay estimation problem is naturally cast into a programming task, constrained by the feasibility conditions derived from the geometric analysis. A global branch-and-bound optimization technique is proposed to solve the problem at hand, hence estimating the best set of feasible time delays and, subsequently, localizing the sound source. Extensive experiments with both simulated and real data are reported; we compare our methodology to four state-of-the-art techniques. This comparison clearly shows that the proposed method combined with the branch-and-bound algorithm outperforms existing methods. These in-depth geometric understanding, practical algorithms, and encouraging results, open several opportunities for future work.

Further Results on the Joint Time Delay and Frequency Estimation Without Eigendecomposition

Joint Time Delay and Frequency Estimation (JTDFE) problem of complex sinusoidal signals received at two separated sensors is an attractive problem that has been considered for several engineering applications. In this paper, a high resolution null (noise) subspace method without eigenvalue decomposition is proposed. The direct data Matrix is replaced by an upper triangular matrix obtained from Rank-Revealing LU (RRLU) factorization. The RRLU provides accurate information about the rank and the numerical null space which make it a valuable tool in numerical linear algebra. The proposed novel method decreases the computational complexity of JTDFE approximately to the half compared with RRQR methods. The proposed method generates estimates of the unknown parameters which are based on the observation and/or covariance matrices. This leads to a significant improvement in the computational load. Computer simulations are included in this paper to demonstrate the proposed method.

Time Delay Tracking for Multiuser Synchronization in CDMA Networks

Multipath propagation, multiple access interference and non-line of sight propagation, etc. have impeded the accuracy in mobile data measurements. Multiuser receivers in asynchronous Code Division Multiple Access (CDMA) systems require the knowledge of several parameters such as timing delay between users. In this paper, the problem of time delay estimation for CDMA systems is examined by proposing an approach based on blind nonlinear least mean squares (LMS) based early-late delay tracker. A system model is developed and a delay tracking algorithm is presented. The simulation results of the proposed delay tracker are compared with the classical delay-locked loop (DLL) approach in a multipath scenario and these show that the proposed delay tracker provides very good performance in challenging cases of closely spaced multipath delays.

Dynamical lag correlation exponent based method for gas–solid flow velocity measurement using twin-plane electrical capacitance tomography

In a twin-plane electrical capacitance tomography (ECT) system, velocity measurement of two-phase flow is transformed into the time delay estimation problem, while the nongaussianity and nonstationarity of two-phase flow signals have put the validity of the conventional cross-correlation algorithm in jeopardy. To improve the robustness and reliability of flow velocity measurement, an alternative method is proposed based on the dynamical lag correlation exponent and applied to coal ash measurement in a pneumatic pipeline. Different from the cross-correlation method which picks the peak point of the cross-correlation function as the delayed frames between the upstream and downstream signals, the proposed method determines the delayed frames by finding the minimum point of the dynamical lag correlation exponent. The preliminary results of flow velocity measurement indicate that the proposed method is capable of detecting various velocities (8–25 m s−1), which is useful for monitoring and predicting flow instability.