Optimal Trajectory Regulation for Radar Imaging Guidance

Abstract

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This paper investigates optimal trajectory tracking for air-to-surface missiles using bank-to-turn steering and equipped with Doppler-beam-sharpening seekers. The seeker generates a radar image of the terrain that is continually updated in flight. The guidance problem for this type of sensor is complex, because constraints must be imposed on the flight path of the missile to ensure that the seeker can obtain adequate crossrange resolution for target recognition and aim-point selection. Terminal position, incidence, and angle constraints are also imposed in the guidance problem. An offline optimal trajectory can be obtained through trajectory optimization techniques that have been presented in previous papers. The focus of this work is on following the precomputed optimal trajectories. The method presented uses a linear quadratic regulator to calculate closed-loop in-flight controls. We also investigate the effectiveness of a preview term based on the prediction of the future trajectory from the current state. Preview control is an optimal tracking method that uses future trajectory samples within a preview window to improve the tracking accuracy. A set of preview gains is computed and is used in addition to the regulator gains. Over the last 2 km of flight, an impact-angle guidance law that minimizes the miss distance and impact-angle error is used to achieve the terminal constraints. The guidance scheme is evaluated for tracking offline Doppler-beam-sharpening trajectories in the presence of modeling errors, sensor noise, and disturbances.