Methods and systems to diminish false-alarm rates in multi-hypothesis signal detection through combinatoric navigation

Methods and systems to detect navigation signals, including to identify up to multiple range-Doppler hypotheses from each of j range-Doppler correlation grids based on a relatively low first threshold, generate navigation solutions from combinatorial sets of k of the identified hypotheses, evaluate the navigation solutions to identify plausible solutions, iteratively and combinatorially augment the plausible solutions with additional hypotheses from grids that are not represented in the corresponding k-hypotheses based navigation solutions, replace plausible solutions with corresponding augmented plausible solutions when appropriate, and select one of a plurality of plausible solutions as a best plausible solution, j and k being positive integers. Where a grid energy peak exceeds a second threshold, a corresponding hypothesis may be identified as a sole hypothesis for the corresponding navigation signal. The relatively low first threshold permits detection of weaker signals. Subsequent evaluations effectively transform a per-navigation-signal false alarm rate to per-navigation-solution false alarm rate.