Detectors based on stochastic resonance, Part 2: Convergence analysis and perturbative corrections

This paper considers convergence properties and perturbative corrections for stochastic resonant (SR) detectors operating in a realistic marine environment. The description of such a detector is reviewed in the weak signal limit. A deterministic algorithm is developed to globally optimize the performance of the SR detector. It is established that this algorithm converges with logarithmic complexity. Scaling arguments demonstrate an improvement over standard, deterministic algorithms in two important limiting cases: (i) increasing accuracy of the optimization procedure and (ii) increasingly heavy-tailed marine noise probability density functions (PDFs), corresponding to increasingly turbulent ocean conditions. Perturbative corrections due to small nonzero input SNRs, temporal drift in the marine noise PDF and the effect of uncertainty in signal frequency are derived. The correction due to frequency error is found to be of second order, and hence subdominant to the former two which are of first order. For a class of marine noise PDFs, these corrections are expressed in terms of standard mathematical functions which are easy to compute in real-time. Numerical simulations indicate that the SR detector is stable under the perturbative corrections considered and that finite input SNRs constitute the dominant perturbative effect for standard ocean acoustic scenarios. It is stressed that these results imply efficient and inexpensive upgrades to existing sonar hardware.