Neural-Network-Based Time-Delay Estimation
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Neural-Network-Based Time-Delay Estimation Samir Shaltaf Department of Electronic Engineering, Princess Sumaya University for Technology, P.O. Box 1438, Al-Jubaiha 11941, Amman, Jordan Email: [email protected] Received 4 May 2003; Revised 13 August 2003; Recommended for Publication by John Sorensen A novel approach for estimating constant time delay through the use of neural networks (NN) is introduced. A desired reference signal and a delayed, damped, and noisy replica of it are both filtered by a fourth-order digital infinite impulse response (IIR) filter. The filtered signals are normalized with respect to the highest values they achieve and then applied as input for an NN system. The output of the NN is the estimated time delay. The network is first trained with one thousand training data set in which each data set corresponds to a randomly chosen constant time delay. The estimated time delay obtained by the NN is an accurate estimate of the exact time-delay values. Even in the case of noisy data, the estimation error obtained was a fraction of the sampling time interval. The delay estimates obtained by the NN are comparable to the estimated delay values obtained by the cross-correlation technique. The main advantage of using this technique is that accurate estimation of time delay results from performing one pass of the filtered and normalized data through the NN. This estimation process is fast when compared to the classical techniques utilized for time-delay estimation. Classical techniques rely on generating the computationally demanding cross-correlation function of the two signals. Then a peak detector algorithm is utilized to find the time at which the peak occurs. Keywords and phrases: Neural networks, time-delay estimation.
1.
INTRODUCTION
Time-delay estimation problem has received considerable attention because of its diverse applications. Some of its applications exist in the areas of radar, sonar, seismology, communication systems, and biomedicine [1]. In active source location applications, a continuous reference signal s(t) is transmitted and a noisy, damped, and delayed replica of it is received. The following model represents the received waveform: r(t) = αs(t − d) + w(t),
(1)
where r(t) is the received signal that consists of the reference signal s(t) after being damped by an unknown attenuation factor α, and delayed by an unknown constant value d, and distorted by additive white Gaussian noise w(t). A generalized cross-correlation method has been used for the estimation of fixed time delay in which the delay estimate is obtained by the location of the peak of the crosscorrelation between the two filtered input signals [2, 3]. Estimation of time delay is considered in [4, 5], where the least mean square (LMS) adaptive filter is used to correlate the two input data. The resulting delay estimate is the location at which the filter obtains its peak value. To obtain the noninteger value of the delay, peak estimation that involves inter-
polation is used. Etter and Stearns have used gradient s
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