Linear optimization models with integer solutions for ping control problems in multistatic active acoustic networks

The typical ping control objective for a multistatic network is to optimize a sonar performance metric within a search area over the mission scenario time horizon subject to available ping energy at sources. Assuming sonar performance models and near real-time multistatic target trackers are available, sonar performance metric predictions for near-future time window can be obtained. However, for Anti-Submarine Warfare applications, it is not realistic to accurately predict performance metrics involving an unknown number of evasive targets over a long scenario time horizon. Therefore, effective and efficient ping control methods must consider effective strategies to obtain desired performance over the spectrum of operational objectives and time frames. In this paper, we develop four integer-linear goal programming models to provide intelligent ping control decisions for various operational modes that depend on remaining ping energy and remaining scenario time. We incorporate the multiple objectives of: maximizing the sonar performance metric, judicious use of energy-limited sources and maintaining a certain level of ping activity. We show that the constraint matrix of each relaxed linear model possesses the total unimodularity property, guaranteeing optimal integer ping control solutions. Therefore, computationally efficient linear programming methods can be used in the implementation of these models. We simulate multiple operational scenarios and demonstrate the properties of the resulting ping strategies in terms of the performance metric and individual source and network lifetime. Results are compared to the baseline ping strategy, which considers the sonar performance metric alone.