This paper addresses the problem of optimal signal detection in the context of high-sensitivity (HS) global navigation satellite system (GNSS) receivers. Contrary to the traditional belief that second-order statistics are optimal for signal detection/estimation under the Gaussian assumption, this paper shows that optimal signal detection turns out to be based on the absolute moments of the input signal. This result opens the door for the introduction of fractional lower-order statistics (FLOS), a wider family of statistics with links to algebraic-tailed processes such as the ones affected by abnornals or outliers. In that sense, the proposed detection strategy and its extension to FLOS seems to be the best candidate for application onto harsh working scenarios such as the ones involved in HS-GNSS receivers.
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