重返大氣層之彈道飛彈追蹤與彈道係數估計

Abstract

眾所皆知，重返大氣層之彈道飛彈追蹤是一個非常複雜的問題。現有的方法通常是使用擴展式卡爾曼濾波器或者unscented卡爾曼濾波器來處理此問題。在這些方法中，目標之彈道係數都被假設為常數，且已經事先得知。不過，在實際上彈道係數是跟目標之物理特性有關而且是速度的一個函數，通常我們是無法事先得知。在本篇論文裡，我們提出一種方法來解決這個問題，我們假設目標的彈道係數是目標速度的一個線性函數，而將其未知參數納入目標狀態方程式，因此擴展式卡爾曼濾波器或者unscented卡爾曼濾波器能同時估計彈道係數和目標狀態。模擬結果顯示我們所提出的演算法能適當地估計彈道係數，並且達到令人滿意的追蹤性能。

It is known that the re-entry ballistic missile tracking is a highly complex problem. Existing approaches often use extended Kalman filter (EKF) or the unscented Kalman filter (UKF) to tackle the problem. In these methods, the ballistic coefficient of the tracked target is assumed to be a constant and its value is known. However, in reality the ballistic coefficient is related to target’s physical properties and is a function of the target speed. In general, it cannot be known in advance. In this thesis, we propose a method to overcome the problem. We assume that the ballistic coefficient of the target is a linear function of the target speed, and include the unknown parameters into the state equation. Then, the EKF or the UKF can simultaneously estimate the ballistic coefficient and the target states. Simulations show that the proposed algorithm can properly estimate the ballistic coefficient and achieve satisfactory tracking performance.