A variety of localization methods with normal mode theory have been established for localizing low frequency (below a few hundred Hz), broadband signals in a shallow water environment. Gauss-Markov inverse theory is employed in this paper to derive an adaptive normal mode back-propagation approach. Joining with the maximum a posteriori mode filter, this approach is capable of separating signals from noisy data so that the back-propagation will not have significant influence from the noise. Numerical simulations are presented to demonstrate the robustness and accuracy of the approach, along with comparisons to other methods. Applications to real data collected at the edge of the continental shelf off New Jersey, USA are presented, and the effects of water column fluctuations caused by nonlinear internal waves and shelfbreak front variability are discussed.