Nonlinear trajectory generation for unmanned air vehicles with multiple radars

The problem of finding a real time optimal trajectory to minimize the probability of detection of unmanned air vehicles by opponent radar detection systems is investigated. This paper extends our preliminary results on low observable trajectory generation in three ways. First, trajectory planning in the presence of detection by multiple radar systems, rather than a single radar system, is considered. Second, an overall probability of detection function is used for the multiple radar case. In previous work, both probability of detection by a single radar and signature were used in the theory section, but the examples used only signature constraints. In this work, the overall probability of detection function is used, both because it aids in the extension to multiple radar systems and because it is a more direct measure of the desirable optimization criteria. The third extension is the use of updated signature and probability of detection models. The new models have a greater number of sharp gradients than the previous models, with low detectability regions for a cone shaped areas centered around the nose as in the previous paper, as well as a cone-shaped area centered around rear of the air vehicle. The nonlinear trajectory generation method (NTG) is used and motivated by the ability to provide real time solutions for constrained nonlinear optimization problems. Numerical simulations of multiple radar scenarios illustrate UAV trajectories optimized for both detectability and time.