Robust Power Spectral Density Estimation With a Truncated Linear Order Statistics Filter

The background power spectral density (PSD) of underwater acoustic signals carries important information about the environment. However, loud transients from human or natural sources are outliers that undermine the precision and accuracy of PSD estimators, such as Welch's overlapped segment averaging (WOSA). Estimators based on order statistics (OSs), such as Schwock and Abadi's Welch Percentile (SAWP), avoid the loud transient bias by employing a normalized chosen OS of the periodograms as an estimator of the background PSD. This article proposes the truncated linear order statistics filter (TLOSF), a hybrid approach between WOSA and SAWP that estimates the background PSD with a weighted average of the OS below a chosen percentile. The TLOSF weights minimize the estimator variance subject to a constraint that the estimator remain unbiased. Including all of the OS below a threshold rank in the weighted average allows TLOSF to achieve a lower variance than the SAWP estimator, but still retain the same robustness against loud outliers. Experiments with synthetic data and underwater recordings demonstrate the improved performance of the TLOSF estimator over the SAWP and Welch estimators in the presence of outliers.