
doi: 10.2514/1.61792
IMPACT angle control shapes the trajectories of antiship and antitank missiles to increase warhead effectiveness and survivability against missile defense systems. The guidance law design with specific impact direction has been a hot topic in the past four decades. Kim and Grider [1] were pioneers in this field. Since then, many algorithms have emerged to achieve a common objective. Optimal control is the most popular tool used to solve this problem [1–4]. Unfortunately, the range between missile and target is necessary for all these methods. Therefore, these optimal guidance laws cannot be directly applied to the missiles with passive seekers, such as infrared or optical ones. Although the Kalman-type filter can estimate the range [5], it is time consuming to tune suitable parameters and hard to implement in reality. Adding extra compensation terms to the traditional proportional navigation or the biased proportional navigation provides another possibility of controlling the impact angle [6]. The result of Kim andGrider [1] also falls within this category. Nevertheless, both of [1] and [6] rely on the range information. Lu et al. [7] proposed an adaptive proportional navigation to achieve the specific impact angle without the range information. Ratnoo and Ghose [8,9] developed this idea further to capture all possible impact angles in a surface-to-surface planar engagement. The recent Note of [10] presented a two-phase biased proportional navigation to achieve impact angle control in the absence of the range information, too. However, the methods in [7–10] are all based on the line-of-sight rate; they may encounter a critical difficulty when employed in low-cost air-to-ground or antiship missiles equipped with a strap-down seeker for measuring the needed information. This is because the line-of-sight rate must be calculated from noisy data since it is not available directly. In addition, the signal-to-noise ratio of the line-of-sight rate for the airto-ground or antiship missiles is rather low on account of the weak maneuverability of the target. The poor quality of line-of-sight rate degrades the feasibility of these approaches because the homing loop with high proportional gainwill be quite sensitive to themeasurement noises and even may be destabilized by the most serious unwanted feedback paths between the angular rates of the missile and the lineof-sight rate. Therefore, to lower the effect of the line-of-sight rate, an alternative way beyond the framework of proportional navigation should be investigated toward a true passive guidance law with impact angle constraints. In this Note, a passive guidance law against surface targets only with the line-of-sight information is proposed first, and the theoretical analysis proves that it can achieve the specified impact angle with the appropriate handover from the midcourse phase to the terminal guidance phase. Its relationship with the adaptive proportional navigation is then revealed. To raise the impact accuracy of the guidance law, the line-of-sight rate is incorporated by introducing the autopilot dynamics based on the traditional threeloop acceleration control structure. The recursive least-squares method is employed to estimate the time constant of autopilot online to check aerodynamic uncertainties. The adjoint analysis is employed to investigate the essence behind the precision improvement. The proposed method demonstrates its effectiveness in the comparative simulations.
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