Variability in modelled sonar and target depth distributions

Abstract

When attempting to detect a reflecting target using active sonar, the relationship between the sensor and target depths is of key importance. This is due to the non-uniform vertical sound speed profile in the water column, which is itself subject to spatio-temporal variations, and will therefore also vary along the propagation path. The availability of high-resolution and accurate ocean models provides new opportunities to take this variability into account when modelling active sonar performance. The full exploitation of the increased amount of available data motivates an automated and general approach derived from first principles. This study delves into the intricate dynamics of active sonar detection by applying game theory, specifically Nash equilibria, to determine the optimal depths for both the target and the active sonar transmitter and receiver, where the target depth is selected to avoid active detection and the sonar depth is selected to enable active detection. The selected target depth must also provide passive counter-detection ability from this depth to the surface. Acknowledging the inherent variability in the underwater environment, our approach integrates an acoustic ray trace model incorporating ocean model data and variable topography. Assuming knowledge of the active sonar’s position and time, we extract range-dependent sound speed profiles from the ocean model and bottom profiles from the topographic model. The uncertainty in the oceanographic conditions is captured by introducing temporal variation in the selection of sound speed profiles. The Nash equilibrium is determined for each of these environmental realizations, effectively providing a distribution of Nash equilibria for sonar and target depths rather than a single equilibrium. The resulting equilibrium distributions may be used as input to automated algorithms and Monte Carlo simulations where sonar and target depths are required to evaluate expected performance.