Modifying the Welch method to estimate power spectral percentiles
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Abstract:
Welch overlap segment averaging method is a popular approach for estimating power spectra of stochastic signals due to its computational efficiency, its ability to scale estimation variance, and its potential to reduce spectral leakage. However, in its original form, the Welch method is prone to spectral outliers caused by transient signals. A computationally efficient solution is to replace the common mean averaging for each frequency bin by a percentile estimation, which has proven to be a robust alternative to the original method. The statistical properties of this approach, such as estimation variance and limiting distribution, have not yet been analyzed in greater detail. In this talk, we present respective expressions for the Welch percentile estimator by using concepts from order statistics and spectral estimation theory. The Welch percentile estimator is applied to the ocean ambient noise data which are compromised by transient signals from an Acoustic Doppler Current Profiler (ADCP) co-located with the hydrophone. Based on the statistical properties of the percentile estimation, confidence intervals for the ocean noise levels have been computed to provide a measure for the estimation quality.