On wavelet denoising and its applications to time delay estimation

In this correspondence, the application of dyadic wavelet decomposition in the context of time delay estimation is investigated. We consider a model i n which the source signal is deterministic and the received sensor outputs are corrupted by additive noises. Wavelet denoising is exploited to provide an effective solution for the problem. Denoising is first applied to prepr ocess the received signals from two spatially separated sensors with an att empt to remove the contamination, and the peak of their cross correlation f unction is then located from which the time delay between the two signals c an be derived. A novel wavelet shrinkage/thresholding technique for denoisi ng is introduced, and the performance of the algorithm is analyzed rigorous ly. It is proved that the proposed method achieves global convergence with a high probability. Simulation results also corroborate that the technique is efficient and performs significantly better than both the generalized cr oss correlator (GCC) and the direct cross correlator (CC).