Passive underwater acoustic localization by time difference of arrival(TDOA) has been successfully applied in determining the entering target position in shallow sea, but when it comes to deep sea, the large test sea area, curved ray paths and limited measuring conditions increase the uncertainty on localization performance. According to this problem, a TDOA localization model using multiple base stations was presented based on the assumption that the medium in deep sea was stratified, by which differences between the constant velocity medium and stratified medium in solving the target position was compared, and effects of the key variable, equivalent sound velocity (ESV), on time difference intersection were discussed by theoretical and numerical method. The variability of TDOA intersection under inhomogeneous ESV conditions in deep sea was revealed. The TDOA contour tended to be standard hyperbolic curves when the ESVs from two different stations were close, and it showed an irregular distribution when the ESVs from two base stations had an obvious bias, which tended to be close on the one side and parallel to the another one. A worse localization performance appeared as all TDOA contours were on the same side with close curves. The method was examined by the simulation case in a summer environment of Northwest Pacific, in which the test sea area was set to 8 km ×8 km in coverage and 5500 m in depth. A 4-receivers array in the squared configuration was used, and the target located at x =1 km, z =3 km. According to the simulated results, the localization performance related to receiver depth: (1) When the receiver depth was 1000 m, the favorable intersection situation was formed by the mixed acoustic ray paths composed of the direct wave and the seabed first-reflected wave, such that the relative high accuracy was achieved, the root mean square error (RMSE) was 30.4 m with typical errors randomly added; (2) when the receiver depth was 100 m, the terrible intersection situation was formed by nearly tangent and close quadratic curves which was formed by a single kind of seabed first-reflected ray paths, and the RMSE was nearly double compared with the one under 1000 m receiver depth condition; (3) when the receiver depth was 5450 m, a better intersection situation was achieved due to full coverage of direct wave, and the relative accuracy without random errors was superior to that under 1000 m receiver depth condition. This work indicates that intersecting localization by TDOA is evidently limited by sound channel in the stratified deep sea, and multipaths make the ESV different as arriving at each base station, such that intersection characteristics of the TDOA contour are changed. So the intersection condition of TDOA should be carefully considered in designing the measurement system and the array configuration and deployed receiver depth should be reasonably arranged to adapt the specific oceanographic environment.
Read full abstract