Neural-Network-Based Time-Delay Estimation

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.