An unified approach to missile guidance laws: a 3D extension

Since the proportional navigation guidance law was first introduced, many of the researchers had proposed different methodologies to investigate the corresponding performances of all the existing guidance laws. In 1997, Yang and Yang introduced an unified approach, in that paper the authors found that under the proposed framework, all the existing guidance laws, namely TPN, IPN and PPN, are indeed special cases of the mentioned general guidance law. But their results were restricted to two dimensional space. In this paper, the author not only extends the results to three dimensional space, but also to GTPN, GIPN and PPN. Unlike conventional researchers, a modified polar coordinate (MPC) is adopted. It is shown that with the property of this modified polar coordinate, the number of differential equations required to describe the relative dynamics can be reduced from six to three, and all the terms of differential equations involve only products and additions of variables. For all the mentioned guidance laws in this paper, to describe the capture area we need only two transformed variables, while the third variable is required to provide the condition of finite turn rate.