FPGA implementation of adaptive time delay estimation for real‐time near‐field electromagnetic ranging

Time delay estimation is a very important operation in ultrasound time-domain flow mapping and correction of phase aberration of an array transducer. As the interest increases in the application of one and a half-dimensional (1.5-D) and two-dimensional (2-D) array transducers to improving image quality and three-dimensional (3-D) imaging, the need of simple, fast, and sufficiently accurate algorithms for real-time time delay estimation becomes exceedingly crucial. In this paper, we present an adaptive time-delay estimation algorithm which minimizes the problem of noise sensitivity associated with the one bit correlation while retaining simplicity in implementation. This algorithm converts each sample datum into a two bit representation including the sign of the sample and an adaptively selected threshold. A bit pattern correlation operation is applied to find the time delay between two engaged signals. By using the criterion of misregistration as an indicator, we are able to show that the proposed algorithm is better than one bit correlation in susceptibility to noise level. Analytical results show that the improvement in reducing misregistration of the two bit correlation over its counterpart is consistent over a wide range of noise level. This is achieved by an adaptive adjustment of the threshold to accommodate signal corruption due to noise. The analytical results are corroborated by results from simulating the blood as a random distribution of red blood cells. Finally, we also present a memory-based architecture to implement the two bit correlation algorithm whose computation time does not depend upon the time delay of the signals to be correlated.

The time (shift) delay parameter between two signals is modeled as a finite-impulse response filter whose coefficients are samples of a sinc function. The time-domain LMS (least-mean-squares) adaptive algorithm is used, but only the weight with the largest magnitude is updated, which involves less computation. The result is a faster adaptation and the elimination of interpolation needed in previous approaches to obtain nonintegral (multiples of sampling period) time-delay estimates. >

Accurate localization in harsh indoor environments has long been a challenging problem due to the presence of multipath. Since joint direction-of-arrival (DOA) and time delay (TD) estimation has the capability to separate the line-of-sight signal from multipath signals in the TD space, it has recently become a key technique for accurate indoor localization in next-generation WiFi and 5G networks. This paper addresses the problem of joint azimuth, elevation, and TD estimation of multiple reflections of a known signal. First, we propose an efficient approximate maximum likelihood algorithm for this problem, which updates the DOA and TD parameters alternatingly. This algorithm applies to arbitrarily distributed (planar or 3-D) arrays. Then, we present the closed-form Cramer–Rao bound for joint DOA and TD estimation, based on which we provide further analysis to show the benefit of joint DOA and TD estimation over DOA-only estimation. Although the benefit of joint estimation has been empirically shown long ago, our analysis is the first theoretical proof of it. Finally, simulation results have been provided to demonstrate the theoretical finding and the effectiveness of the new algorithm. Matlab code for the new algorithm is available at https://github.com/FWen/JADE.git .

In most of biomedical signal processing applications the presence of interference signals is inevitable. Processing of lung sounds is not an exemption. In this case the heart sounds are unavoidable and sometimes a severe disturbing noise source. Previous studies indicated that the performance of any interference cancellation scheme relies strongly on an adequate time delay estimation between the reference and the primary signals. Here, a new procedure for time delay estimation using the multi-resolution framework is presented. The proposed methodology possesses such key benefits as the multiple looks information of a signal at different bands, robustness in presence of noise and a validation procedure for the delay estimates. The procedure is applicable to a broad range of problems where time delay estimation is required. Results obtained with lung sounds show the promise of the scheme for the time delay estimation and subsequent interference cancellation.

The use of active vibration control may induce a delay leading to detrimental degradation of the performance of active vibration control. This is particularly true in the case of mechanical systems subjected to friction-induced vibration and noise for which such time-delays can lead to the appearance of undesirable instability. Furthermore, conducting a stability analysis of time-delay systems and estimation of the critical time delay are challenging, due to the infinite nature of the characteristic (quasi) polynomial of the associated closed-loop system, having an infinite number of roots.The objective of this paper is to discuss a strategy for the estimation of the critical time delay for the problem of Friction-Induced Vibration and noisE (FIVE). To achieve such an objective, the prediction of the stability analysis of time delay systems and the estimation of the associated critical time delay are first performed by applying the frequency sweep test and the eigenvalue problem approximation using the Taylor series expansion of the delayed term. In a second time, a mixed approach is proposed to predict effectively the real critical time delay of autonomous controlled systems subjected to friction-induced vibration. The efficiency of the proposed approach is illustrated by numerical examples for the prediction of self-sustaining vibrations of a phenomenological model with two degrees of freedom for which it is possible to provide a clear understanding and illustration of the phenomena involved and observed.

In this paper, we present a new computationally efficient and accurate so-called explicit modulated Lagrange adaptive frequency estimation (EMLAFE) algorithm that is based on a variable delay element of Etter and Hush and the modulated Lagrange adaptive frequency estimator (MLAFE) of Dooley and Nandi. Adopting a similar idea as in So et al., on explicit time delay estimation, we introduce explicit frequency estimation in our EMLAFE algorithm in order to speed up the frequency estimation. Our development of the EMLAFE algorithm is based on the fact that the cost function of the modulated Lagrange interpolation delay filter (MLIDF), which is used as a FIR delay system in the frequency estimator, is sinusoidal in form with respect to the product of signal frequency and time delay under a high signal to noise ratio (SNR) condition. This leads to a simple formula relating the estimated delay to the unknown frequency, and thus to an efficient frequency estimator. The superior performance of the new algorithm is demonstrated in the context of tracking and estimating a chirp or constant frequency signal in noise. We also derive the Cramer-Rao bound and the steady state variance, for the frequency estimate.

Neuro-fuzzy based time-delay estimation using DCT coefficients

Time delay estimation is the basis of target location of multi-sensor network, while the basic analysis of the signal is of key importance to the time delay estimation. In this paper, a time delay analysis system is designed by virtual instrument development tools. The analysis system contains: virtual oscilloscope, virtual spectrum analyzer, virtual filter and virtual time delay analyzer. Using this analysis system on a set of field collected acoustic target signal, spectrum analysis and filtering is made. Then the time delay estimation has been carried out for several sampling data segments selected by certain rules, and curve of the time delay vs. time is given. Analysis shows the main frequency of the target signal: 85Hz, 13Hz, 170Hz and 125Hz. The regular pattern of the time delay curve is consistent with the target motion. Application reveals that the system is helpful in the research of time delay estimation.

The three-hydrophone array is often used for underwater passive ranging. It uses the time delay estimation (TDE) between hydrophone pairs to calculate the target range. Traditionally, the generalized cross correlation (GCC) algorithm is used for TDE. However, when the available bandwidth is limited, the accuracy of GCC decreases severely and thus, fails to meet the performance requirement. To solve this problem, we propose a new TDE algorithm based on time-dimensional Capon beamforming. The proposed method uses Capon beamforming to process sampled signals at hydrophones to obtain the time-domain output and accordingly calculates the time delays between hydrophone pairs. Specifically, we extract several subband components from GCC outputs in the frequency domian. To suppress the amplitudes fluctuation between different subbands, the subband amplitude modification and the diagonal loading (DL) algorithm are used to improve the robustness of time-dimensional Capon beamforming. Finally, we estimate the range of target using the TDE result obtained by the proposed method. What's more, to analyze the TDE accuracy of the time-dimensional Capon beamforming, we compare the TDE variance of both GCC and the proposed method with Cramér-Rao lower bound (CRLB) under different simulation conditions. The results demonstrate that the proposed algorithm could significantly improve the performance of passive ranging in three-hydrophone array, in the case of relatively short bandwidth associated with subband amplitude fluctuations.

The localization of acoustic reflectors is a fundamental component in various applications, including room acoustics analysis, sound source localization, and acoustic scene analysis. Time delay estimation (TDE) is essential for determining the position of reflectors relative to a sensor array. Traditional TDE algorithms generally yield time delays that are integer multiples of the operating sampling period, potentially lacking sufficient time resolution. To achieve subsample TDE accuracy, various interpolation methods, including parabolic, Gaussian, frequency, and sinc interpolation, have been proposed. This paper presents a comprehensive study on time delay interpolation to achieve subsample accuracy for acoustic reflector localization in reverberant conditions. We derive the Whittaker-Shannon interpolation formula from the previously proposed sinc interpolation in the context of short-time windowed TDE for acoustic reflector localization. Simulations show that sinc and Whittaker-Shannon interpolation outperform existing methods in terms of time delay error and positional error for critically sampled and band limited reflections. Performance is evaluated on real-world measurements from the MYRiAD dataset, showing that sinc and Whittaker-Shannon interpolation consistently provide reliable performance across different sensor-source pairs and loudspeaker positions. These results can enhance the precision of acoustic reflector localization systems, vital for applications, such as room acoustics analysis, sound source localization, and acoustic scene analysis.

Time delay estimation is very important in many applications such as radar, sonar, communication, geological exploration, biomedical engineering, etc. We propose a SINC filtering algorithm (SFA), i.e., one based on the sinc function. The algorithm can get an accurate time delay estimate with little or no prior knowledge about the statistical characteristics of the received signals. SFA is based on the theory that time delay estimation can be transformed to the parameter estimation of a SINC filter, and the time delay estimate can be obtained when the maximum of the filter coefficients is known. When the time delay of two received signals is formulated, the LMS algorithm can be used to get the estimate of the SINC filter coefficients, then the time delay estimate can be obtained. Compared with the traditional parabolic fitting method, the SFA can get more accurate results without increasing the computation burden. Computer simulations and water tank experiments both indicate that the SFA can obtain accurate time delay estimation.

High-frequency (HF) communication is critical for applications such as over-the-horizon positioning and ionospheric detection. However, precise time-delay estimation in complex HF channels faces significant challenges from multipath fading, Doppler shifts, and noise. This paper proposes a Modulation Signal-based Adaptive Time-Delay Estimation (MATE) algorithm, which effectively decouples carrier and modulation signals and integrates phase-locked loop (PLL) and delay-locked loop (DLL) techniques. By leveraging the autocorrelation properties of 8PSK (Eight-Phase Shift Keying) signals, MATE compensates for carrier frequency deviations and mitigates multipath interference. Simulation results based on the Watterson channel model demonstrate that MATE achieves an average time-delay estimation error of approximately 0.01 ms with a standard deviation of approximately 0.01 ms, representing a 94.12% reduction in mean error and a 96.43% reduction in standard deviation compared to the traditional Generalized Cross-Correlation (GCC) method. Validation with actual measurement data further confirms the robustness of MATE against channel variations. MATE offers a high-precision, low-complexity solution for HF time-delay estimation, significantly benefiting applications in HF communication systems. This advancement is particularly valuable for enhancing the accuracy and reliability of time-of-arrival (TOA) detection in HF-based sensor networks and remote sensing systems.

Time-delay estimation (TDE) sensors can be used to effectively locate a transmitting source. Our aim is to use distributed TDE sensors that are relatively inexpensive. The latter is the result of two constraints: a single analog to digital converter is used for sampling the sum of two sensor output signals, and the sampling interval is substantially larger than the practically required time delay resolution. This approach leads to the requirement for sub-sample interval delay estimation from overlapping different echoes of a received signal. No specific a priori assumptions are made regarding the nature of the received signal. We adapt the time-frequency ratio of mixtures (TFRM) approach for blind source separation for our TDE sensor. Our experimental set-up consists of two microphones placed at non-equal distances from an acoustic source. The TDEs are then used for source localization.

A time delay estimation-based PD-sliding mode control method is proposed to implement high performance trajectory tracking control for a hybrid robot used for automobile electro-coating conveying. First, to exempt the difficulty of real-time dynamic control from calculations of hybrid robot dynamics equations due to its complex mechanism, the time delay estimation-based dynamic model is established by linearizing the dynamic model with time delay estimation technology. Then, a sliding mode control method for the hybrid robot based on time delay estimation-based linearized dynamic model is presented for solving the problem of time delay estimation errors and overcoming the external interferences dramatically. Moreover, the calculation on system dynamics of sliding mode control for the hybrid robot is avoided by substituting the PD control item for the equivalent item of sliding mode control. Lyapunov stability theorem is used to prove the stability of the proposed control law. Finally, the PD control and the proposed control method for the hybrid robot are simulated by MATLAB, and the experiment is carried out on the prototype. The results demonstrate that the proposed control method is independent of complex dynamic model which could avoid the calculation on system dynamics of sliding mode control for the hybrid robot, and it could realize high-accuracy trajectory tracking control compared to PD control under external disturbances.KeywordsHybrid robotPD controlSliding mode controlTime delay estimation

Magnitude squared coherence (MSC) and time delay are two important quantities needed for passive detection and localization of a radiating source using several sensors. This paper presents a novel approach to estimating the MSC and time delay from the outputs of two sensors. It first models the MSC as the product of the transfer functions of two auto-regressive moving-average (ARMA) filters. The ARMA coefficients are then determined by a least squares, matrix pseudoinverse solution to the estimation equation. Time delay estimation follows as a by-product since both phase and MSC estimates are now available. Simulation results obtained from this modeling approach are compared against those estimated from the traditional periodograms. In the majority of cases studied, the ARMA approach appears to be superior, giving smaller bias and variances in both MSC and time delay estimations.