Source depth estimation by matching broadband coherent and incoherent energy ratios of normal modes in shallow water

Passive source depth estimation is always one of the difficult problems in underwater acoustic field.Aiming at the estimation of low-frequency broadband pulse source depth in the shallow water waveguide,a model-based approach employing the ratio of energy between coherent terms and incoherent terms of normal modes in the signal autocorrelation function by a single hydrophone is proposed.It eliminates the influence of the source radiating spectrum and reduces greatly the computation amount of the source depth estimation as an independent variable with the prior estimated source range.Moreover,it also enhances the stability of parameter estimation because of employing same normal modes for the coherent energy feature match between the measured data and the replica field.At first,the relationship of the uniqueness for source depth estimation with normal mode orders is discussed through the mathematical theory on vector’s linear correlation.When at least three-order normal modes are employed,it is proved that there exists unique solution for source depth estimation in the ideal waveguide environment.Furthermore,the simulations show that the mean error of source depth estimation is less than 5 meters when the signal-to-noise ratio is greater than 0 dB.The robustness of the approach is analyzed when the hydrological parameters,the acoustic parameters of sediments and source range are mismatched.Finally,the approach is verified by using the low-frequency broadband pulse data received by the vertical array in shallow water and the probability of source depth estimation within the error of 5 meters is greater than 79.1%.The approach could be generalized to estimate the low-frequency broadband source depth by a horizontal or vertical array.