Robust power spectral density estimation via a performance-weighted blend of order statistics

Abstract

Loud transients introduce bias to background spectrum estimates based on the sample mean, like the Welch Overlapped Segment Averaging (WOSA) [1967]. The Schwock and Abadi [2021] Welch Percentile (SAWP) estimator avoids the loud transient bias by replacing the averaging of the WOSA with a scaled order statistic (OS) of the sample power spectrum. While the scaling ensures the SAWP is unbiased regardless of which OS is chosen, the 80th percentile minimizes the variance of the SAWP estimator in a scenario without loud transients. However, the 80th percentile SAWP is still vulnerable to bias and increased variance from more frequent loud transients. Also, the rate of occurrence of loud transients may change with time, requiring the SAWP to adapt which percentile is used. To approach this challenge, this talk proposes a Universal SAWP estimator which is a weighted sum across different fixed percentile SAWP estimators. At each iteration, the Universal SAWP updates the blend weights to promote the percentile with the lowest sample variance over recent observations. In computer simulations, the Universal SAWP quickly assigns higher weights to the lowest variance estimators as the occurrence of loud transients increases. Overall, the Universal SAWP achieves equal or lower variance as the best fixed percentile SAWP estimator. [Work supported by ONR Code 321US.]