本文關(guān)鍵詞： 碰撞預(yù)警 軌道預(yù)報(bào)誤差 相對(duì)運(yùn)動(dòng) 泊松級(jí)數(shù) 碰撞概率 顯式表達(dá)式 漏警率 虛警率　出處：《國(guó)防科學(xué)技術(shù)大學(xué)》2013年博士論文　論文類型：學(xué)位論文

【摘要】：隨著人類航天活動(dòng)的日益頻繁，在軌空間目標(biāo)數(shù)量快速增長(zhǎng)，已對(duì)空間環(huán)境和航天事業(yè)的可持續(xù)發(fā)展產(chǎn)生了重大影響，必須加強(qiáng)對(duì)空間目標(biāo)碰撞預(yù)警問(wèn)題的研究。本文以空間目標(biāo)碰撞預(yù)警過(guò)程為研究對(duì)象，，針對(duì)碰撞預(yù)警中涉及的軌道預(yù)報(bào)誤差和碰撞概率問(wèn)題進(jìn)行研究。主要成果如下： 基于相對(duì)運(yùn)動(dòng)理論研究了空間目標(biāo)初始誤差傳播特性和位置速度誤差的負(fù)相關(guān)特性�？紤]到軌道預(yù)報(bào)誤差與目標(biāo)矢徑相比是小量，將目標(biāo)的真實(shí)狀態(tài)和預(yù)報(bào)狀態(tài)分別對(duì)應(yīng)于一“實(shí)”一“虛”兩個(gè)近距離空間目標(biāo)，將軌道預(yù)報(bào)誤差看作它們之間的相對(duì)運(yùn)動(dòng)�；诖鷶�(shù)法模型的C-W方程和T-H方程分別進(jìn)行了圓軌道和橢圓軌道的初始誤差傳播分析�；趲缀畏Ｐ驮诮鼒A軌道假設(shè)下對(duì)位置速度誤差的負(fù)相關(guān)特性進(jìn)行了分析，討論了該特性在初始誤差協(xié)方差選取中的應(yīng)用。利用歷史軌道數(shù)據(jù)對(duì)負(fù)相關(guān)特性進(jìn)行了驗(yàn)證。 提出了基于歷史軌道數(shù)據(jù)的軌道預(yù)報(bào)誤差周期特性分析方法和泊松級(jí)數(shù)擬合方法。選取軌道數(shù)據(jù)歷元時(shí)刻前后半個(gè)周期內(nèi)的狀態(tài)預(yù)報(bào)值為參考值，在全軌道周期內(nèi)求差以反映周期特性。利用最小二乘方法擬合得到了泊松系數(shù)矩陣，分別討論了多項(xiàng)式項(xiàng)、三角函數(shù)項(xiàng)、混合項(xiàng)的作用。作為誤差擬合函數(shù)，泊松級(jí)數(shù)可以描述誤差隨預(yù)報(bào)時(shí)間的長(zhǎng)期變化和隨在軌位置的周期變化，而且泊松系數(shù)矩陣可以在進(jìn)行碰撞預(yù)警分析之前就得到。 在接近幾何分析的基礎(chǔ)上推導(dǎo)了圓軌道和一般軌道情形下碰撞概率的顯式表達(dá)式。在圓軌道情形下推導(dǎo)了接近距離的RSW分量表示和接近幾何關(guān)系（過(guò)軌道面交線高度差和時(shí)間差、軌道夾角等）表示的碰撞概率顯式表達(dá)式。在一般軌道情形下推導(dǎo)了接近幾何關(guān)系（過(guò)速度公垂線高度差、時(shí)間差、速度夾角、速度大小比）表示的和接近距離的NTW分量表示的碰撞概率顯式表達(dá)式。分析了圓軌道情形下顯式表達(dá)式適用的偏心率范圍，對(duì)于大多數(shù)LEO目標(biāo)，圓軌道情形下顯式表達(dá)式的精度對(duì)于碰撞風(fēng)險(xiǎn)評(píng)估和預(yù)警決策而言是足夠的。 基于碰撞概率的顯式表達(dá)式分析了碰撞概率靈敏度和最大碰撞概率的計(jì)算方法，給出了計(jì)算最大碰撞概率的完整步驟。根據(jù)碰撞概率的顯式表達(dá)式，分析了碰撞概率對(duì)接近距離的RSW分量、軌道誤差標(biāo)準(zhǔn)差、接近角度和目標(biāo)大小的兩類靈敏度。在誤差橢球形狀固定和不定兩種情況下推導(dǎo)得到了以接近幾何關(guān)系或接近距離的分量表示的最大碰撞概率的解析表達(dá)式。討論了當(dāng)接近距離的一個(gè)分量為零時(shí)的特殊情況，給出了計(jì)算最大碰撞概率的完整步驟。 基于碰撞概率的顯式表達(dá)式對(duì)碰撞預(yù)警的漏警率和虛警率進(jìn)行了分析，介紹并實(shí)現(xiàn)了考慮多因素的碰撞風(fēng)險(xiǎn)綜合評(píng)估方法。碰撞預(yù)警實(shí)質(zhì)上是一個(gè)判別分析問(wèn)題。根據(jù)碰撞概率的顯式表達(dá)式定義了碰撞預(yù)警的安全區(qū)域和危險(xiǎn)區(qū)域，給出了漏警率和虛警率的定義、計(jì)算公式和基本規(guī)律。介紹并實(shí)現(xiàn)了綜合考慮風(fēng)險(xiǎn)參數(shù)和軌道品質(zhì)參數(shù)的碰撞風(fēng)險(xiǎn)綜合評(píng)估方法。 介紹了空間目標(biāo)碰撞預(yù)警軟件系統(tǒng)，利用編目目標(biāo)的兩行軌道根數(shù)（TLE）數(shù)據(jù)給出了系統(tǒng)應(yīng)用實(shí)例。介紹了空間目標(biāo)碰撞預(yù)警軟件系統(tǒng)的模塊組成和并行計(jì)算環(huán)境，本文提出的軌道預(yù)報(bào)誤差分析方法和碰撞概率分析方法在軟件系統(tǒng)中得到了應(yīng)用。利用編目目標(biāo)的TLE數(shù)據(jù)給出碰撞預(yù)警軟件系統(tǒng)的應(yīng)用實(shí)例。 論文以我國(guó)空間目標(biāo)碰撞預(yù)警工程需求為牽引，研究了碰撞預(yù)警涉及的軌道預(yù)報(bào)誤差和碰撞概率問(wèn)題，解決了制約工程實(shí)踐的關(guān)鍵問(wèn)題，發(fā)展了碰撞預(yù)警分析方法，可為空間目標(biāo)碰撞預(yù)警工程系統(tǒng)的建立和完善提供技術(shù)支持。
[Abstract]:With the increasing number of human space activities , the rapid growth of target quantity in orbit has exerted great influence on the sustainable development of space environment and space industry . Based on the theory of relative motion , the negative correlation between the initial error propagation characteristics and the position velocity error of the space target is studied . Considering that the orbit prediction error is small compared with the target vector diameter , the real state and the prediction state of the target are respectively corresponding to the two short distance space targets of " real " and " virtual " , and the orbit prediction error is regarded as the relative motion between them . Based on the algebraic method model , the negative correlation property of the circular orbit and the elliptical orbit is analyzed . The application of the characteristic in the selection of initial error covariance is discussed . The negative correlation characteristic is verified by historical orbit data . In this paper , a method for analyzing the periodic characteristics of orbit forecast errors based on historical orbit data and the fitting method of Poisson ' s series are presented . The value of the state prediction in the half cycle before and after the epoch of the track data is selected as the reference value , and the function of the polynomial term , trigonometric function term and mixing term is obtained by fitting the least square method . As the error fitting function , the Poisson ' s series can describe the long - term variation of the error with the prediction time and the periodic variation with the orbit position , and the Poisson coefficient matrix can be obtained before the collision early warning analysis is carried out . The explicit expression of collision probability in the case of circular orbit and general orbit is derived on the basis of near geometric analysis . The explicit expression of collision probability represented by the approximate distance RSW component representation and the approximate distance is deduced in the case of circular orbit . In the case of the general orbit , the explicit expression of the collision probability represented by the NTW component close to the geometric relation ( the height difference , the time difference , the velocity included angle and the velocity - size ratio ) of the approximate distance is derived . The eccentricity range suitable for explicit expression in the case of circular orbit is analyzed . For most LEO targets , the accuracy of explicit expression in the case of circular orbit is sufficient for the collision risk assessment and early warning decision . Based on the explicit expression of collision probability , the calculation method of collision probability sensitivity and maximum collision probability is analyzed , and a complete step of calculating the maximum collision probability is given . According to the explicit expression of the collision probability , the analytic expression of the maximum collision probability of the collision probability on the close distance RSW component , the orbit error standard deviation , the approach angle and the target size is analyzed . Based on the explicit expression of collision probability , the leakage alarm rate and false alarm rate of collision early warning are analyzed , and the comprehensive evaluation method of collision risk considering many factors is introduced and realized . The collision early warning is a discriminant analysis problem . According to the explicit expression of collision probability , the definition , calculation formula and basic law of collision warning are given . The comprehensive evaluation method of collision risk considering risk parameters and track quality parameters is introduced and realized . This paper introduces the system of space target collision early warning , and gives an example of system application by using two rows of orbit root number ( TLE ) data of cataloged target . The module composition and parallel computing environment of space target collision early warning software system are introduced . The application of the method of orbit prediction error analysis and collision probability analysis in software system is presented in this paper . The application example of collision warning software system is given by using TLE data of the target . Based on the demand of space target collision early - warning project in China , the problems of track forecast error and collision probability related to collision early warning are studied , the key problem of restricting engineering practice is solved , and collision early warning analysis method is developed , which can provide technical support for the establishment and improvement of space target collision early warning engineering system .

【學(xué)位授予單位】：國(guó)防科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2013
【分類號(hào)】：V528

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