Explicit Time Delay Estimator Research Articles

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

SummaryThe near‐field electromagnetic ranging systems exploit the near‐field phase behavior of low frequency signals for indoor real‐time ranging. Conventionally, phase detector is used to determine the phase of electric and magnetic fields. Subsequently, the phase difference is used to estimate a distance value. In adaptive time delay estimation approach, the time delay between electric and magnetic signals is used instead of phase difference for an estimation. This method does not require a priori knowledge of the transmitting signals and can obtain better performance in low signal‐to‐noise ratio environment. In this paper, we propose a digital near‐field electromagnetic ranging system design and implement it on field‐programmable gate array. This system is composed of time delay estimator, frequency estimator, and received signal strength indicator. A maximum correntropy criterion–based explicit time delay estimation algorithm with a delay in the coefficient update is implemented to estimate the time delay in real time. The fast Fourier transform and received signal strength indicator modules determine the signal frequency and the signal strength received, respectively. Our experimental results indicate that the delayed maximum correntropy criterion–based explicit time delay estimation algorithm has fast convergence rate and good steady‐state performance in an impulsive noise environment.

Adaptive Noise Cancellation Based on Time Delay Estimation for Low Frequency Communication

Low frequency communication, taking advantage of the features of low frequency electromagnetic signals in near field, is widely used in through-the-earth (TTE) wireless applications. However, the low frequency non-Gaussian noise severely limits the communication performance. In this paper, an adaptive noise cancellation algorithm based on time delay estimation (ANC-TDE) and maximum correntropy criterion (MCC) is proposed. The explicit time delay estimation algorithm based on MCC (MCC-ETDE) is used to estimate the time-varying delay and the noise correlationship between the primary input and reference inputs. With a reference noise selected and time delay compensated, the non-Gaussian noise is canceled by adaptive filter based on MCC. The proposed algorithm is implemented on field programmable gate array (FPGA) and the performance is evaluated by simulation and experiment. As shown in the results, the ANC-TDE algorithm can reduce the complexity of ANC filter and adaptively compensate the varied time delay between the primary input and reference input. With the time delay compensated, the ANC-TDE algorithm has better performance in non-Gaussian noise environment and is more suitable for real-time systems.

An Iteration-Based Variable Step-Size Algorithm for Joint Explicit Adaptation of Time Delay

By using an adaptive technique similar to the joint explicit time delay estimator, a novel variable step-size algorithm is derived. This algorithm employs the iteration time to control the step-size update and its respective performance analysis is also given. It is also proved that the proposed algorithm efficiently improves the convergence speed and the delay variance with only increasing a little computational cost compared to the conventional adaptive time delay estimation algorithm.

A New Adaptive Subsample ETDE for Large‐Range Time‐Varying Delay Estimation Using Low‐Order Interpolators

We present a new adaptive subsample Explicit time delay estimator (ETDE) that is well suitable for determining and tracking the large-range time-varying delay between two noisy bandlimited signals only using low-order interpolators. Unlike conventional ETDE where a Fractional delay filter (FDF) is used, the new ETDE is based on a novel on-line interpolator which has the ability to optimally synthesize any continuously variable nonintegral sample delay. The theoretical derivations for our proposed on-line interpolator and the new ETDE algorithm are provided. Simulations are presented to evaluate the performance of the new estimator and to compare the performance with other estimators. Simulation results show that the new ETDE significantly outperforms FDF-based ETDE when the delay is large or varies in a large range, and the same filter orders are used.

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 enhanced mixed modulated Lagrange explicit time delay estimator with noisy input

The mixed modulated Lagrange explicit time delay estimation (MMLETDE) algorithm provides an efficient time delay estimation between narrowband or sinusoidal signals. However, it does not explicitly consider the additive measurement noise at the input, which actually exists in practice. Aiming at this issue, an enhanced MMLETDE algorithm is proposed for noisy inputs based on the unbiased impulse response estimation technique, assuming that the noise power ratio is known a priori. Simulation results show that for narrowband signals or sinusoids over a wide frequency range, the proposed algorithm with a small filter order performs well in moderate and high noise scenarios.

Fractional time delay estimation algorithm based on the maximum correntropy criterion and the Lagrange FDF

In this paper, a novel algorithm for fractional time delay estimation is proposed. It is based on the maximum correntropy criterion and the Lagrange fractional delay filter (FDF). The instantaneous correntropy is introduced to measure the similarity between received signals and estimated ones in the proposed algorithm. It leads to an effective performance under both Gaussian and impulsive noises. The performances, including the convergence of the algorithm and the variance of the time delay estimation, are theoretically analyzed. Simulations demonstrate that the time delay estimation precision of the proposed algorithm is higher than that utilizing the mixed modulated Lagrange explicit time delay estimation (MMLETDE) especially under low generalized signal-to-noise ratio (GSNR).

EXPLICIT FREQUENCY ESTIMATION AND TRACKING USING MODULATED LAGRANGE DELAY FILTER

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.

A new time delay estimator based on ETDE

In this paper, we address the problem of online subsample time delay estimation of narrowband signals of known center frequency. We propose a new so-called mixed modulated Lagrange explicit time delay estimation (MMLETDE) algorithm and study its performance through computer simulations. The MMLETDE is a modulated Lagrange ETDE, but the delay estimate adaptation process is based on the truncated sinc fractional delay filter algorithm. We provide theoretical derivations for our proposed estimator, a proof of its convergence performance, learning characteristics of its error performance surface, and an expression for its delay variance. Using simulations, we show that MMLETDE requires only a small filter order and has no noticeable estimation bias over a wide frequency range.

Adaptive subsample time delay estimation using Lagrange interpolators

This letter addresses the problem of on-line sub-sample time delay estimation of narrowband signals of known center frequency. A new form of the Lagrange interpolator filter is presented in this letter, which is incorporated into the explicit time delay estimator (ETDE) method. Simulations show that ETDE with the filter modulated to the signal center frequency significantly outperforms conventional ETDE.

On explicit time delay estimation using the Farrow structure

This letter addresses the problem of adaptive, computationally inexpensive fractional sample delay estimation using the well-known explicit time delay estimator technique. The Farrow structure approximation for fast filter realisations is suggested which is then used to derive closed form update equations for arbitrary filter designs, with much reduced computational complexity.

The virtual engineer™

In this paper, a novel algorithm for fractional time delay estimation is proposed. It is based on the maximum correntropy criterion and the Lagrange fractional delay filter (FDF). The instantaneous correntropy is introduced to measure the similarity between received signals and estimated ones in the proposed algorithm. It leads to an effective performance under both Gaussian and impulsive noises. The performances, including the convergence of the algorithm and the variance of the time delay estimation, are theoretically analyzed. Simulations demonstrate that the time delay estimation precision of the proposed algorithm is higher than that utilizing the mixed modulated Lagrange explicit time delay estimation (MMLETDE) especially under low generalized signal-to-noise ratio (GSNR).

Fast algorithm for nonstationary delay estimation

A computationally efficient algorithm for estimating time delay between signals received at two spatially separated sensors is proposed. The delay estimate is adapted directly to maximise the mean product of the first sensor output and the filtered output of the second received signal. The convergence behaviour and variance of the delay estimate are derived. It is shown that the proposed algorithm outperforms the explicit time delay estimator at a low signal-to-noise ratio.

Adaptive TDOA estimation in presence of impulsive noise

A fractional lower-order, moment-based adaptive algorithm for estimating the time difference of arrival between signals received at two spatially separated sensors in the presence of impulsive noise modelled as a stable process is proposed. The method is computationally efficient and is a generalisation of the simplified explicit time delay estimator. Convergence of the algorithm is analysed and simulation results are included to evaluate its estimation performance for both static and nonstationary delays.

A new algorithm for explicit adaptation of time delay

By using an adaptive technique similar to the one developed by Etter and Stearns (1981), a novel constrained algorithm for explicit time delay estimation (TDE) is derived. The adaptive process provides an unbiased delay estimate and its respective performance surface, learning characteristics and delay variance will be given. The mean-square error surface, though a function of the estimated delay only, is multimodal and proper initialization is required to guarantee global convergence. Simulation results are included to validate the convergence behavior of the TDE system. >

Adaptive predictive control of systems with time‐varying time delay

AbstractThis paper discusses three different methodologies for performing adaptive predictive control in the presence of unknown or time‐varying time delays. The first methodology is the well‐known extended B‐polynomial. The second methodology consists of describing the process dynamics by a network of Laguerre functions. The third methodology, named the variable regressor estimator (VRE), consists of an explicit time delay estimator running in parallel with a standard recursive estimator. Theoretical as well as practical aspects of these methodologies will be discussed. Finally, our industrial experience with these is discussed.