Optimal Guidance with Active Observability Enhancement for Scale Factor Error Estimation of Strapdown Seeker

This article investigates the problem of scale factor error estimation for missiles with a strapdown seeker. We first theoretically prove that the seeker scale factor error will introduce a parasitic loop in the guidance loop and, hence, result in instability of the guidance loop. This fact reveals that it is necessary to extract the required guidance information and estimate the scale factor error simultaneously in real time. To this end, the observability of scale factor error estimation is analyzed, and the theoretical results show that this information is weakly or poorly observable under conventional proportional navigation guidance. To address this problem, a new optimal guidance law that can be utilized to improve the estimation performance is proposed by optimizing terminal miss distance, control energy, and observability in an integrated manner. The characteristics of the proposed optimal guidance law are also theoretically analyzed to provide better insights of the proposed approach. Extensive numerical simulations are conducted to support the proposed algorithm.