This paper considers an evasion maneuver for low-altitude aircraft (A/C) in the presence of the threat of a guided missile. The missile has boost and sustain phases and its trajectory is estimated by a 7-D motion parameter vector. The maximum likelihood estimator is used to estimate the missile motion parameters based on angle measurements from an A/C-borne passive sensor. Based on the estimated closest point of approach distance between the missile and the aircraft, a warning alert is then given to execute an evasion maneuver. The aircraft can bank away from the missile by a turning maneuver in the horizontal plane. Simulation shows that the aircraft can evade the missile by using the turning maneuver. The survivability probability of the aircraft is evaluated and it can be enhanced by an early maneuver start time and a large acceleration during the maneuver.
The 3D trajectory estimation and observability problems of a target have been solved by using angle-only measurements. In previous works, the measurements were obtained in the thrusting/ballistic phase from a single fixed passive sensor. The present work solves the motion parameter estimation of a ballistic target in the reentry phase from a moving passive sensor on a fast aircraft. This is done with a 7-dimension motion parameter vector (velocity azimuth angle, velocity elevation angle, drag coefficient, target speed and 3D position). The maximum likelihood (ML) estimator is used for the motion parameter estimation at the end of the observation interval. Then we can predict the future position at an arbitrary time and the impact point of the target. The observability of the system is verified numerically via the invertibility of the Fisher information matrix. The Cramer–Rao lower bound for the estimated parameter vector is evaluated, and it shows that the estimates are statistically efficient. Simulation results show complete observability from the scenario considered, which illustrates that a single fast moving sensor platform for a target can estimate the motion parameter in the reentry phase.
This paper considers the problem of estimating the launch point (LP) of a thrusting object from a single fixed sensor’s 2-D angle-only measurements (azimuth and elevation). It is assumed that the target follows a mass ejection model and the measurements obtained are available starting a few seconds after the launch time due to limited visibility. Previous works on this problem estimate the target’s state, which, for a passive sensor, requires a long batch of measurements, is sensitive to noise and ill-conditioned. In this paper, a polynomial fitting with the least squares approach is presented to estimate the LP without motion state estimation. We provide a statistical analysis to choose the optimal polynomial order, including overfitting and underfitting evaluation. Next, we present Monte Carlo simulations to show the performance of the proposed approach and compare it to the much more complicated state of the art technique that relies on state estimation. It is shown that the proposed method provides a much simpler and effective way than the state estimation methods to implement in a real-time system.
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