Robust Mode Space Detection in Uncertain Shallow Water With Incomplete Mode Sampling

We consider detection of a source by a vertical line array (VLA) in shallow water: the source position is unknown and the environmental parameters (such as water depth) are known only in that they are within certain limits. The performances of familiar correlation detectors, e.g., generalized likelihood ratio, Bayesian, robust matched field processing detectors, can deteriorate markedly in some environment/source-position pairs. Previous work proposed a robust mode space detector, robust in the sense that the performance only depends on the signal-to-noise ratio and is insensitive to the unknown environmental and source-position specifics, with the mode space being spanned by VLA sampled modes (modal depth functions). However, only complete mode sampling was considered. Given that modes are generally incompletely sampled due to insufficient array aperture, robustness absent complete mode sampling is here investigated. We propose to use the physically supported greatest dimensional effective mode space to implement a robust subspace detector, as opposed to the original greatest dimensional one as before: the former is exactly the latter, but with nuisance modes rejected, thus leading to a better robust performance. The resulting greatest dimensional effective mode space detector (GE-MSD) suffers only light performance decreases relative to the correlation detectors' performance peaks, and is much more computationally efficient. The effect of surface-generated noise on the GE-MSD's robustness is numerically investigated. The results suggest that surface noise indeed degrades the GE-MSD's robustness, but that incomplete mode sampling, which causes an approximate collinearity among sampled modes, can mitigate this.