Estimating the ballistic coefficient of a re-entry vehicle

Abstract

Theoretical bounds for estimating the ballistic coefficient of a ballistic object during the re-entry phase have been addressed. One essential characteristic of the vehicle trajectory is its deceleration when it reaches dense atmospheric layers. The intensity of the phenomenon is proportional to a scalar, called the ballistic coefficient. This leads to an highly nonlinear time-varying dynamic. To understand the dimensioning parameters for estimating the ballistic coefficient, accurate approximations of the Fisher information matrix are developed. The main result is a closed-form expression of a lower bound for the variance of the ballistic coefficient estimate.Notations † Let S be the object cross-section, C X its drag coefficient and M its mass, † the ballistic coefficient b is the product C x S/m and is expressed in m 2 kg 21 , † go ¼ 29.8 ms 22 is the gravitational acceleration (at ground level), † alt is the altitude; alt W y in the coordinate system of the

Evidence-Theoretic Reentry Target Classification Using Radar: A Fuzzy Logic Approach

“…Compared to warheads, which are designed to have low atmospheric deceleration, intercepted debris have lighter weights and irregular shapes. Thus, it is possible to distinguish between warheads and debris based on the lower speed of the latter, caused by drag [1], [35]. We, therefore, use the BF to distinguish between the movements of warheads, debris, and other objects.…”

“…The typical BF of a warhead ranges from 1 × 10 −4 to 5 × 10 −4 m 2 /kg, whereas that of debris is 0.01-0.1 m 2 /kg [35]. The equation of theoretical atmospheric density ρ(H) is expressed as follows [51]:…”

“…Table 4 presents the calculation results for Example 1. For all propositions, the degree of support is calculated through (35) and (36). Using Algorithm 1, the conflicts between propositions are resolved.…”

Sensor Fusion of Gaussian Mixtures for Ballistic Target Tracking in the Re-Entry Phase

“…Practical applications are in the fields of surveillance for safety against the re-entry of space debris produced by old satellites or spacecraft at the end of their lifetime [ 1 , 2 , 3 ]. Tracking a ballistic target has been identified as a stressful filtering problem due to the strong nonlinearity exhibited by the forces acting on the target [ 2 , 4 , 5 ]. Besides, the nonlinearity also results from the bearing and range measurements which are given with nonlinear measurement functions in relation to the target [ 6 ].…”

Ballistic Coefficient Estimation for Classification of Projectiles

“…참고문헌 [3]은 2D 환경에 서 여러 종류의 칼만 필터를 사용하여 발사체의 탄도계 수를 추정하고, 그 성능을 비교분석하였다. 참고문헌 [4] 와 참고문헌 [5] 발사체의 운동방정식은 다음 뉴튼의 운동방정식으로 부터 얻을 수 있다 [6] . 발사체는 하나의 질점이라고 가정 되었다.…”