Matched-Mode Source Localization Under Fluctuating Ocean Environments

Matched-mode processing(MMP), developed from matched-field processing, has long been used for passive source localization in an acoustic waveguide. Environmental flunctuations are common in oceans, leading to erroneous or incomplete information of environmental parameters. Considering the fixed model uesd in matched-field processing often fails, we study the method of matched-mode processing. MMP works in the mode space:a modal decomposition is first applied to the measurements on a vertical array to obtain individual mode amplitudes; then the measured mode amplitudes are used to match with the replica mode amplitudes, which is computed for a grid of possible source locations. The output of MMP is expected to achieve the maximum around the true range and depth of source due to the freedom in controlling sensitivity to environmental flucations.On the basis of single coherent modal group model, we start with the investigation of modal decomposition based on sampled-mode shapes and least-squares, then consider the problem as a convex optimization problem under the fact that many elements in modal space have close-to-zero amplitudes, which can be solved by the 11-norm cosntraint. For two conditions:well-sampled case and limited vertical apretrue size, we introduce three modal decomposition methods including sampled-mode shapes、least-squares(combined with two kinds of singular-value decomposition) and convex optimization. Matched-mode processing based on sampled-mode shapes provides a fast and efficient solution as long as the sampled modes matrix preserves mode orthogonality. Matched-mode processing based on least-squares is determined by minimizing the data misfit to yield an unbiased estimate of the true solution provided the inverse matrix is non-singular. In the presence of ill-conditioned matrix, the inversion can be unstable. Singular-value decomposition is a common approach for solving unstable inversions based on least-squares, where small singular values characterizing an ill-conditioned matrix can be omitted, however the resolution is degraded. The convex optimization in matched-mode processing is implemented by 11-norm regularization, where we introduce a regularization parameter to balance the relative tolerance, which often leads to high resolution and good robustness.For single coherent modal group model, performance analysis of the three methods mentioned above is conducted under perfectly known environment and uncertain environment. For well-sampled case, we investigate the Cramer-Rao bound(CRB) of matched-mode processing, which yields the same result as that of matched-field processing. For uncertain environment, simulations of the three methods for limited vertical aperture size are conducted. As singular-value decomposition neglects small singular values, the CRB slightly ascends. For sound-speed mismatch, the results demonstrate the effectiveness of convex optimization and some advantages over other methods, including high resolution and flexibility in algorithm tuning.Furthermore, for mutli-coherent modal group model(MCMG), accounting for the decorrelation in modal space, the conventional normal-mode function is decomposed as a sum of coherent modal groups. The autoregressive processes is applied to MCMG and the decomposition of a mixtrue of two coherent modal groups, as well as MFP and MMP localization results under this model, is simulated. The CRB of matched-mode processing under MCMG is studied, and comparisons made with that of matched-field processing.