Power Spectral Density Estimation via Universal Truncated Order Statistics Filtering

Abstract

Loud transient signals in underwater acoustic data increase the bias and variance of background noise power spectral density (PSD) estimates based on sample mean. Recently, two PSD estimators mitigated the loud transient impact on PSD estimates by applying order statistics filtering (OSF). The first, the Schwock and Abadi Welch Percentile, scales a single rank order statistic (OS) of consecutive periodograms. The second, the truncated linear order statistics filter, is a weighted sum of OS up to a chosen rank. In order to minimize variance, both OSFs must carefully choose the highest rank that still eliminates the loud transients. However, in real-time applications in dynamic environments, loud transients occur at unpredictable rates, requiring dynamic adjustment of the OSF ranks to keep low bias and variance. To circumvent the challenges of real-time rank selection, this paper proposes a convex sum of OSFs across ranks with blending weights that are sequentially adjusted to favor the lowest variance OSFs over a recent time window. The performance of the blended sum provably approaches the performance of the best fixed rank OSF. Simulations and real data confirm the blended OSFs effectively filter loud transients out of spectrograms without explicitly choosing a threshold rank.