A unified framework for mode filtering and the maximum a posteriori mode filter

A unified framework is presented for examining the performance of linear mode filtering algorithms. Two common mode filters, samples of the mode shapes and the pseudo-inverse of the mode shapes, are presented in this framework as a tradeoff between sensitivity to other modes and sensitivity to white noise. The maximum a posteriori mode filter is presented as an alternative which gracefully transitions between these extremes, and attains the minimum mean squared error when the modes to be estimated are well modeled as samples of a Gaussian random process. Numerical simulations in both shallow and deep water environments confirm the analytically derived properties of these mode filters.