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You could use cross correlation for this purpose. For an uncorrelated signal $x(t)$, $\textrm{corr}(x(t), x(t + \Delta t)) = c \delta(\Delta t)$, i.e. an delayed impulse. This can be expanded to comprise multiple echoed copies $$ \textrm{corr}\left( \sum_{i=0}^{N} a_i x(t + \Delta t_i), \sum_{j=0}^{N} b_j x(t + \Delta t_j) \right) = c \sum_{i=0}^{N} \sum_{...

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