Inter-sensor Time Delay Estimation using Cepstrum of Sum and Difference Signals in Underwater Multipath Environment

Inter-sensor Time Delay Estimation (TDE) can be obtained using Generalized Cross-correlator (GCC), Phase Transform (PHAT) and Hilbert Transform of the cross-correlator. The accuracy of the estimate is affected by signal reflections generated due to the multipath structure of the channel. In this paper, a novel cepstrum based algorithm is proposed for estimating the Time Difference of Arrival (TDOA) across a pair of sensors in multipath environment. The proposed algorithm uses the concept of echo arrival time estimation. It computes the sum of the received signal at two omnidirectional hydrophones and then calculates its power cepstrum. The power cepstrum of the addition of two signals, is termed as the "additive cepstrum". By addition of the two hydrophone signals in time domain, a virtual echo is generated and the additive cepstrum shows peaks at intervals corresponding to the magnitude of time delay between the two signals and its integer multiples. The algorithm then computes the power cepstrum of the difference of the signals received at the two hydrophones. It is called as the "difference cepstrum". The difference cepstrum is subtracted from the additive cepstrum and the result is called as the "residual cepstrum". The residual cepstrum shows peaks at the inter-sensor time delay value and its odd multiples plus the multiplicative noise. The inter-sensor time delay is estimated using a peak detection algorithm. The algorithm gives the absolute time difference of arrival for the sensor pair. Hence, the sign of the time delay is obtained using a further step involving the cross-correlation function in a preceding stage. The time delay estimation algorithm has been implemented for bandlimited white Gaussian noise as source signal and background noise, for various levels of Signal to Noise Ratio (SNR). The performance has been compared with the GCC and PHAT algorithms using standard performance measures and found to be more accurate in terms of reduced percentage of anomalies and reduced MSE of the non-anomalous estimates.