### 高阶线性比例制导系统脱靶量幂级数解

1. 北京航空航天大学 宇航学院, 北京 100083
• 收稿日期:2018-04-24 修回日期:2018-05-28 出版日期:2018-11-15 发布日期:2018-08-16
• 通讯作者: 周浩 E-mail:zhouhao@buaa.edu.cn
• 基金资助:
航空科学基金（20150151002）

### Power series solution for miss distance of higher-order linear proportional navigation guidance systems

HE Tailong, CHEN Wanchun, ZHOU Hao

1. School of Astronautics, Beihang University, Beijing 100083, China
• Received:2018-04-24 Revised:2018-05-28 Online:2018-11-15 Published:2018-08-16
• Supported by:
Aeronautical Science Fundation of China (20150151002)

Abstract: Miss distance is a most important performance index for the design and evaluation of a missile guidance system. For a first-order linear propprtional guidance system, closed-form solutions miss distance can be obtained. However, such solutions do not exist for a generic higher-order guidance system matching reality better, in which case miss distance is usually achieved by direct simulation or adjoint technique. In this paper, power series solutions for miss distance of high-order linear proportional navigation are explored to provide a new method for calculation of miss distance. First, the adjoint system of a generic higher-order linear proportional navigation guidance system is constructed and normalized, and the solutions in form of the product of a power series and an exponential decay are assumed. Then a recursion relation for coefficients is derived by using the power series method. Moreover, it is proved that these power series solutions converge everywhere. For single-lag and higher-order binomial guidance systems, the recursion relation is simplified significantly by selecting the appropriate exponential decay constant. In practice, partial sums of power series are used to numerically calculate miss distance, and how many terms of partial sums are adequate is related to the exponential decay constant. Therefore, the influence of the exponential decay constant on the convergence rate of power series solutions is analyzed, and selection methods for the constant are proposed, laying the foundation for practical applications of power series solutions.