A method for maintaining a planned arrangement of autonomous underwater vehicles, AUVs, deployed in water, comprising: detecting , by an autonomous underwater vehicle, AUV, among the AUVs, one or more signals emitted at a predetermined moment by one or more among the AUVs, respectively; automatically estimating a current position of the AUV relative to the one or more AUVs, based on the detected one or more signals; and performing a corrective motion to adjust the current position to better match a planned position of the AUV in the planned arrangement, wherein any of the one or more AUVs emitting has potentially drifted to be away from a respective planned position in the planned arrangement, at the predetermined moment, wherein the one or more signals have individual signatures enabling the AUV to determine identity of each of the one or more AUVs emitting one of the one or more signals, a time of arrival corresponding to each of the one or more signals and an angle relative to a reference direction from which each of the one or more signals has arrived and characterized in that the estimating of the current position includes: calculating each of one or more distances between the AUV and the one or more AUVs emitting the one or more signals, based on the time of arrival, respectively; determining positions of each of the one or more AUVs relative to the AUV, using corresponding one of the distances and the angle, respectively; calculating possible corrective motions based on the positions, respectively; generating a box in a thrust versus heading space, the box covering representations of the possible corrective motions; and selecting the corrective motion inside the box according to a predetermined rule. detecting , by an autonomous underwater vehicle, AUV, among the AUVs, one or more signals emitted at a predetermined moment by one or more among the AUVs, respectively; automatically estimating a current position of the AUV relative to the one or more AUVs, based on the detected one or more signals; and performing a corrective motion to adjust the current position to better match a planned position of the AUV in the planned arrangement, wherein any of the one or more AUVs emitting has potentially drifted to be away from a respective planned position in the planned arrangement, at the predetermined moment, wherein the one or more signals have individual signatures enabling the AUV to determine identity of each of the one or more AUVs emitting one of the one or more signals, a time of arrival corresponding to each of the one or more signals and an angle relative to a reference direction from which each of the one or more signals has arrived and characterized in that the estimating of the current position includes: calculating each of one or more distances between the AUV and the one or more AUVs emitting the one or more signals, based on the time of arrival, respectively; determining positions of each of the one or more AUVs relative to the AUV, using corresponding one of the distances and the angle, respectively; calculating possible corrective motions based on the positions, respectively; generating a box in a thrust versus heading space, the box covering representations of the possible corrective motions; and selecting the corrective motion inside the box according to a predetermined rule. calculating each of one or more distances between the AUV and the one or more AUVs emitting the one or more signals, based on the time of arrival, respectively; determining positions of each of the one or more AUVs relative to the AUV, using corresponding one of the distances and the angle, respectively; calculating possible corrective motions based on the positions, respectively; generating a box in a thrust versus heading space, the box covering representations of the possible corrective motions; and selecting the corrective motion inside the box according to a predetermined rule. <EOS>