Application of the robust discrete wavelet transform to signal detection in underwater sound
Shun‐Hsyung Chang, Fu-Tai Wang · International Journal of Electronics · 2003
This paper applies the notion of robust discrete wavelet transform (robust DWT) to recursive density estimation as a solution to detecting multipath signals underwater. Though there are no obvious distribution assumptions that can be made to model underwater noise, a recursive density estimator of the initial background noise reconstructed by the discrete wavelet transform (DWT) can be established as an empirical model. Observations that are identified as an outlier are then flagged as potential signals. In a multipath environment, where many signal components arrive with arbitrary delays, the DWT's lack of translation invariance is a problem for processing multipath signals. We adopt a robust DWT as a solution. Using an iterative algorithm in the Zak domain, a scaling function can be turned to a robust one. By designing a robust scaling function we can obtain a robust DWT. The performance of the robust DWT, exhibiting much better shift invariance than the conventional DWT, is illustrated. Utilizing the robust DWT reconstruction to establish the recursive density estimator of the underwater background noise, the ability to detect a multipath signal in an underwater environment is improved compared to that of the conventional DWT.