Framework for Low-Observable Trajectory Generation in Presence of Multiple Radars

Abstract

This paper explores the problem of finding a real-time optimal trajectory for unmanned aerial vehicles to minimize their probability of detection by opponent multiple radar detection systems. The problem is handled using the nonlinear trajectory generation method developed by Milam et al. (Milam, M., Mushambi, K., and Murray, R., "New The paper presents a formulation of the trajectory generation task as an optimal control problem, where temporal constraints allow periods of high observability interspersed with periods of low observability. This feature can be used strategically to aid in avoiding detection by an opponent radar. The guidance is provided in the form of sampled tabular data. It is then shown that the success of nonlinear trajectory generation on the proposed low-observable trajectory generation problem depends upon an accurate parameterization of the guidance data. In particular, such an approximator is desired to have a compact architecture, a minimum number of design parameters, and a smooth continuously differentiable input-output mapping. Artificial neural networks as universal approximators are known to possess these features, and thus are considered here as appropriate candidates for this task. Comparison of artificial neural networks against B-spline approximators is provided, as well. Numerical simulations on multiple radar scenarios illustrate unmanned air vehicle trajectories optimized for both detectability and time. NomenclatureB j;k i t = B-spline basis function for the output z i C i j = coefficients of the B-splines e ac = aircraft positions along the east axis k i = degree of spline polynomial l i = number of knot intervals m i = number of smoothness conditions at knot points n ac = aircraft positions along the north axis p i = number of coefficients of each output r = slant range s"; = signature function u ac = aircraft positions along the up axis ut = control input xt = state of the system z = differentially flat output = azimuth angle " = elevation angle = heading angle

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