Performance of Mode Space Detector in Uncertain Shallow Water and Its Robust Realization

The statistics of the mode space detector (MSD) whose modes are characterized by some degree of mismatch to truth [that is, the mismatched mode space detector (MMSD)] are derived. As a measure of the “containing relation” between the mode spaces derived from different environmental realizations we propose the relative projection error metric, through which the performance of the MMSD can be further investigated and compared to the MSD using accurate environmental knowledge. From this performance analysis, we suggest that by simply using the greatest dimensional physically supported mode space, we can obtain a robust MSD. It can achieve the same performance robustness as the energy detector-the performance is only determined by the array signal energy and is insensitive to the specific source position and environmental conditions. It can also avoid the potentially-significant performance degradation of the Bayesian detector when applied to certain deterministic scenarios at a cost of small average performance degradation. Numerical simulations in a typical uncertain shallow-water environment support our assertions.