Sensor position estimation and source ranging in a shallow water environment

Underwater acoustic transient signals are generated mechanically at known positions along a wharf. These signals are received by a wide aperture planar array of four underwater acoustic sensors, whose positions relative to the wharf are unknown. A method is described that enables the positions of the sensors to be estimated from accurate differential time-of-arrival measurements (with 0.1 μs precision) as the signal wavefronts traverse the array. A comparison of the estimated positions with the nominal positions of the first three sensors, which form a 20-m-wide aperture horizontal line array, reveals a 2-cm displacement of the middle sensor from the line array axis. This slight bowing of the line array results in overranging (bias error of 3%) when the wavefront curvature method is used with the nominal collinear sensor positions to locate a static source of active sonar transmissions at a range of 59.2 m. The use of the spherical intersection method coupled with the estimated sensor positions of the line array provides an order of magnitude improvement in the range estimate (within 0.3% of the actual value). However, systematic ranging errors are observed when the sound propagation medium becomes nonstationary. Next, the differences in the arrival times of the direct path and boundary-reflected path signals at the middle sensor of the wide aperture line array are estimated using the differential phase residue of the analytic signal at the sensor output. These multipath delays are used to estimate the range and depth of the source. Although the average value of the multipath range estimates is within 0.5% of the actual value, the variance of the range estimates is 50 times larger when compared with the results of the spherical intersection and wavefront curvature methods. The multipath delay data are also processed to provide a reliable estimate of the temporal variation in the water depth enabling the tidal variation to be observed.