A biased proportional navigation guidance law with large impact angle constraint and the time-to-go estimation

For large impact angle control problem (here, the “large impact angle” means the impact angle in the closed interval from −180° to 180°), estimating the time-to-go accurately is the key of impact time and impact angle control guidance (ITIACG). The objectives of this paper are to construct a new impact angle control guidance (IACG) law suitable for large impact angle control and present a time-to-go estimation procedure for the new IACG law suitable for designing ITIACG law. The constructed IACG law is a biased proportional navigation guidance law with large impact angle constraint, the rule of the cosine of the lead angle in the biased term is to guarantee that the lead angle remains in the open interval from −90° to 90°, which is required in the development of time-to-go estimation procedure. To estimate the time-to-go, by introducing a self-convergent angle named as alfa, the closed equations of motion are transformed to a different form, which can be solved conveniently under the assumption of small lead angle. For the case of large lead angle, the time interval of time-to-go is partitioned into n segments, the maximum increment of lead angle is supposed to be a small angle in each segment, the transformed closed equations of motion can be expressed as function of alfa angle and solved analytically. A geometric approach is proposed to determine conservatively a suitable alfa angle to guarantee that the maximum increment of lead angle is a small angle in each segment. The time-to-go estimation procedure for the new IACG law are illustrated. Simulations are performed to verify the effectiveness of the proposed IACG law and the accuracy of the time-to-go estimation procedure.