A method and apparatus are provided for estimating the water speed of a first acoustic node D belonging to a network of acoustic nodes, at least some of the acoustic nodes being arranged along towed acoustic linear antennas (S). The method includes steps of: a) defining a N-dimensional base, the center of which is the first acoustic node and comprising a single axis, when N=1, or N non-collinear axes, when N=2 or N=3, each axis being associated with a base vector extending from the first acoustic node to another acoustic node; and b) estimating an amplitude of the water speed, as a function of: for each given other acoustic node defining the base vector: an acoustic propagation duration of an acoustic signal transmitted from the first acoustic node to the given other acoustic node, and an acoustic propagation duration of an acoustic signal transmitted from the given other acoustic nodes to the first acoustic node; and a value c of the underwater acoustic sound velocity.