Abstract: Abstract： An airtoair missile trajectory optimization problem is discussed in the case of overthe shoulder. The scheme takes the angle of attack constraints into consideration. A virtualtargetbased guidance law is designed for large offboresight launching of airtoair missile. After studying the results of the optimal trajectory, which is solved by gauss pseudospectral method（GPM）, a threesegment guidance command is proposed. The differences in command due to flight height, flight velocity and the position of virtual target are studied. Meanwhile, the robustness of the guidance law is improved via correcting it online. Simulation results indicate that the proposed command can make the missile turn rapidly with body axis pointing toward virtual target after turning.

Key words: Keywords： airtoair missile, virtual target, trajectory optimal, gauss pseudospectral method