Tensor decomposition based normal mode parameter estimation

A tensor-decomposition-based method is proposed for modal depth function and modal horizontal wavenumber (i.e., modal parameter) estimation, which avoids the dependence of the traditional subspace-based methods on modal orthogonality. The method exploits the shift-invariance of the range-compensated pressure field to transform the mode parameter estimation problem into the canonical polyadic decomposition (CPD) problem of a third-order tensor. Decomposed factor matrices are used to simultaneously yield the modal depth function and the modal horizontal wavenumber estimates. The uniqueness condition of tensor decomposition for the modal parameter estimation problem is also given, which shows that modal parameter estimation can be achieved by using a small number of depth-dimension samplings and range-dimension samplings under the condition that the sampling vectors of modal depth function are linearly independent. Simulation results also demonstrate the method has a good performance when the range aperture is short. The method is applied to SwellEx-96 experiment data and the obtained modal parameter estimates are consistent with the environment at the experiment sea. Both simulation and experimental data verify the effectiveness of the method.