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本書系統地介紹了純距離目標運動分析的理論及應用等相關知識。全書共分10章，系統討論了純距離目標運動分析涉及的可觀測性分析、目標定位與跟蹤算法、單站機動航路優化、靜止多站站址佈局優化等基礎問題，並對純距離系統在水下聲學傳感器中的應用進行了論述。
作者簡介
璐，女，博士，主要研究方向為目標運動分析、系統建模與仿真，發表純距離目標運動分析領域研究論文10餘篇，參與完成科研項目6項，編寫教材3部。
序
通過獲取運動目標的距離信息，並利用這些隨時間變化的距離序列來實時估計目標運動參數的技術，稱為純距離目標運動分析（Range-only TargetMotion Analysis，RTMA）。隨著無線傳感器網絡的不斷發展，純距離目標運動分析在艦艇雷達組網定位、聲呐浮標搜潛、艦炮射擊協同式檢靶等領域中得到越來越廣泛的應用。由於純距離系統本質上的強非線性以及受到應用領域中觀測條件的限制，因此，關於純距離系統的可觀測條件、目標定位與跟蹤算法、單站機動航路優化、靜止多站站址佈局優化的理論研究成果很少，尚未形成完整的體系。本書內容正是基於此背景展開的，將純距離目標運動分析劃分為單觀測站和多觀測站問題，開展系統可觀測性、目標定位與跟蹤算法、單站機動航路優化、靜止多站站址佈局優化的研究，豐富了這一領域的理論研究成果，同時圍繞純距離系統在水下聲學傳感器中的應用進行了論述。
本書由10 章組成，主要內容如下：
第1 章為緒論。介紹了純距離目標運動分析的概念、研究現狀、研究熱
點及本書的組織結構。
第2 章研究了單站純距離系統的可觀測性問題。建立單站純距離系統的數學模型，給出了可觀測性定義，分析觀測站與目標在不同運動規律下的可觀測性條件。
第3 章研究了單站純距離系統目標定位與跟蹤算法問題。從適用性的角度出發，分別給出了基於最小二乘原理、極大似然估計原理、無跡卡爾曼濾波的改進算法。
第4 章研究了單站機動航路優化問題。採用可觀測度及幾何定位散佈精純距離目標運動分析及應用度GDOP 作為衡量目標定位跟蹤精度的指標，從全域尋優與單步局部尋優角度分析了觀測站在一次轉向航路和勻速轉彎航路時的優化航路。
第5 章研究了多站純距離系統的可觀測性問題。建立了多站純距離系統的數學模型，分析了影響多站純距離系統可觀測性的因素，並與多站純方位系統、多站距離差系統可觀測性條件進行了比較。
第6 章研究了多站純距離系統目標定位與跟蹤算法問題。從適用性的角度出發，給出了“蛙跳”算法、集中融合式定位算法、基於最小二乘原理的線性迭代法與全域收斂迭代算法，以及基於簡化入侵式野草優化理論的改進粒
子濾波算法。
第7 章研究了靜止多站站址佈局的優化問題。通過合理佈局多觀測站的幾何位置，在觀測站數量受限的情況下，建立了站址佈局優化模型，提高了對目標的定位跟蹤精度。
第8 章研究了純距離在水下聲學傳感器網絡節點定位中的應用問題。
第9 章研究了純距離在水下聲學傳感器網絡目標跟蹤中的應用問題。
第10 章設計了基於水下聲學傳感器網絡的目標跟蹤原型系統。
本書在編寫過程中，得到了各級領導和機關業務部門的關心和支持。此外，電子工業出版社的支持及指導，為本書出版創造了許多便利條件，在此一併表示衷心的感謝。
在本書的編寫過程中，參閱了許多著作和其他參考文獻，在此謹向這些材料的原著作者表示誠摯的謝意。由於作者水平有限，書中難免存在一些疏漏和不足，敬請批評、指正。
編著者
2018 年9 月
本書由10 章組成，主要內容如下：
第1 章為緒論。介紹了純距離目標運動分析的概念、研究現狀、研究熱
點及本書的組織結構。
第2 章研究了單站純距離系統的可觀測性問題。建立單站純距離系統的數學模型，給出了可觀測性定義，分析觀測站與目標在不同運動規律下的可觀測性條件。
第3 章研究了單站純距離系統目標定位與跟蹤算法問題。從適用性的角度出發，分別給出了基於最小二乘原理、極大似然估計原理、無跡卡爾曼濾波的改進算法。
第4 章研究了單站機動航路優化問題。採用可觀測度及幾何定位散佈精純距離目標運動分析及應用度GDOP 作為衡量目標定位跟蹤精度的指標，從全域尋優與單步局部尋優角度分析了觀測站在一次轉向航路和勻速轉彎航路時的優化航路。
第5 章研究了多站純距離系統的可觀測性問題。建立了多站純距離系統的數學模型，分析了影響多站純距離系統可觀測性的因素，並與多站純方位系統、多站距離差系統可觀測性條件進行了比較。
第6 章研究了多站純距離系統目標定位與跟蹤算法問題。從適用性的角度出發，給出了“蛙跳”算法、集中融合式定位算法、基於最小二乘原理的線性迭代法與全域收斂迭代算法，以及基於簡化入侵式野草優化理論的改進粒
子濾波算法。
第7 章研究了靜止多站站址佈局的優化問題。通過合理佈局多觀測站的幾何位置，在觀測站數量受限的情況下，建立了站址佈局優化模型，提高了對目標的定位跟蹤精度。
第8 章研究了純距離在水下聲學傳感器網絡節點定位中的應用問題。
第9 章研究了純距離在水下聲學傳感器網絡目標跟蹤中的應用問題。
第10 章設計了基於水下聲學傳感器網絡的目標跟蹤原型系統。
本書在編寫過程中，得到了各級領導和機關業務部門的關心和支持。此外，電子工業出版社的支持及指導，為本書出版創造了許多便利條件，在此一併表示衷心的感謝。
在本書的編寫過程中，參閱了許多著作和其他參考文獻，在此謹向這些材料的原著作者表示誠摯的謝意。由於作者水平有限，書中難免存在一些疏漏和不足，敬請批評、指正。
編著者
2018 年9 月
目次
第1 章 緒論 ················································································ 1
1.1 純距離目標運動分析基本概念 ·············································· 1
1.2 純距離目標運動分析的研究現狀 ··········································· 4
1.2.1 可觀測性分析的研究現狀 ············································ 4
1.2.2 目標定位與跟蹤算法的研究現狀 ··································· 6
1.2.3 單觀測站機動航路優化的研究現狀 ································ 7
1.2.4 靜止多觀測站站址佈局優化的研究現狀 ·························· 7
1.2.5 基於純距離的水下聲學傳感器網絡節點自定位算法的研究現狀 ························································ 8
1.2.6 基於純距離的水下聲學傳感器網絡目標跟蹤算法的研究現狀 ·································································
1.3 純距離目標運動分析的研究熱點 ··········································· 9
1.4 本書的組織結構 ······························································· 10
第2 章 單站純距離系統可觀測性分析 ·············································· 12
2.1 引言 ·············································································· 12
2.2 系統數學描述 ·································································· 13
2.2.1 直角坐標系下的系統數學描述 ····································· 13
2.2.2 極坐標系下的系統數學描述 ········································ 14
2.2.3 修正極坐標系下的系統數學描述 ·································· 15
2.3 系統可觀測性定義 ···························································· 16
2.4 系統可觀測分析 ······························································· 17
2.4.1 觀測站靜止、目標靜止時的系統可觀測性分析 ················ 18
2.4.2 觀測站靜止、目標勻速直線運動時的系統可觀測性分析 ···· 18
2.4.3 觀測站靜止、目標勻加速直線運動時的系統可觀測性分析 ··· 21
2.4.4 觀測站勻速直線運動、目標靜止時的系統可觀測性分析 ···· 21
2.4.5 觀測站勻速直線運動、目標勻速直線運動時的系統可觀測性分析 ·························································· 24
2.4.6 觀測站勻速直線運動、目標勻加速直線運動時的系統可觀測性分析 ·························································· 25
2.4.7 觀測站勻加速直線運動、目標靜止時的可觀測性分析 ······· 25
2.4.8 觀測站勻加速運動、目標勻速直線運動時的可觀測分析 ···· 26
2.4.9 勻加速運動觀測站、勻加速直線運動目標的可觀測分析 ···· 27
2.4.10 其他結論 ······························································ 31
2.5 單站純距離系統與單站純方位系統可觀測性比較 ······················· 32
第3 章 單站純距離系統目標定位與跟蹤算法研究 ······························· 33
3.1 引言 ·············································································· 33
3.2 系統數學模型 ·································································· 34
3.3 基於最小二乘原理的目標參數估計算法 ·································· 36
3.3.1 遞推格式的目標參數估計算法 ····································· 36
3.3.2 基於全域收斂策略的目標參數估計算法 ························· 40
3.4 基於極大似然原理的目標參數估計算法 ·································· 48
3.4.1 單站純距離系統的極大似然估計 ·································· 48
3.4.2 基於全域收斂策略的改進算法 ····································· 51
3.4.3 仿真試驗及分析 ······················································· 52
3.5 UKF 算法的基本原理 ························································· 57
3.5.1 UT 變換 ································································· 57
3.5.2 標準UKF 算法 ························································ 58
3.5.3 迭代UKF 算法 ························································ 59
3.5.4 仿真試驗及分析 ······················································· 60
3.6 自適應迭代UKF 算法 ························································ 63
3.6.1 自適應迭代UKF 算法步驟 ········································· 63
3.6.2 仿真試驗及分析 ······················································· 64
第4 章 單站機動航路優化研究 ······················································· 70
4.1 引言 ·············································································· 70
4.2 觀測站勻速直線一次轉向機動時的可觀測度分析 ······················ 71
4.2.1 可觀測度的定義 ······················································· 71
4.2.2 仿真試驗及分析 ······················································· 72
4.3 單站純距離測量模型的CRLB ·············································· 74
4.3.1 定位與跟蹤誤差下限 ················································· 74
4.3.2 單站純距離測量模型CRLB 計算 ·································· 76
4.4 觀測站機動航路優化研究 ··················································· 78
4.4.1 航路優化問題的提出 ················································· 78
4.4.2 勻速直線一次轉向機動優化航路 ·································· 79
4.4.3 勻速轉彎機動優化航路 ·············································· 82
4.5 航路優化的方法 ·························
1.1 純距離目標運動分析基本概念 ·············································· 1
1.2 純距離目標運動分析的研究現狀 ··········································· 4
1.2.1 可觀測性分析的研究現狀 ············································ 4
1.2.2 目標定位與跟蹤算法的研究現狀 ··································· 6
1.2.3 單觀測站機動航路優化的研究現狀 ································ 7
1.2.4 靜止多觀測站站址佈局優化的研究現狀 ·························· 7
1.2.5 基於純距離的水下聲學傳感器網絡節點自定位算法的研究現狀 ························································ 8
1.2.6 基於純距離的水下聲學傳感器網絡目標跟蹤算法的研究現狀 ·································································
1.3 純距離目標運動分析的研究熱點 ··········································· 9
1.4 本書的組織結構 ······························································· 10
第2 章 單站純距離系統可觀測性分析 ·············································· 12
2.1 引言 ·············································································· 12
2.2 系統數學描述 ·································································· 13
2.2.1 直角坐標系下的系統數學描述 ····································· 13
2.2.2 極坐標系下的系統數學描述 ········································ 14
2.2.3 修正極坐標系下的系統數學描述 ·································· 15
2.3 系統可觀測性定義 ···························································· 16
2.4 系統可觀測分析 ······························································· 17
2.4.1 觀測站靜止、目標靜止時的系統可觀測性分析 ················ 18
2.4.2 觀測站靜止、目標勻速直線運動時的系統可觀測性分析 ···· 18
2.4.3 觀測站靜止、目標勻加速直線運動時的系統可觀測性分析 ··· 21
2.4.4 觀測站勻速直線運動、目標靜止時的系統可觀測性分析 ···· 21
2.4.5 觀測站勻速直線運動、目標勻速直線運動時的系統可觀測性分析 ·························································· 24
2.4.6 觀測站勻速直線運動、目標勻加速直線運動時的系統可觀測性分析 ·························································· 25
2.4.7 觀測站勻加速直線運動、目標靜止時的可觀測性分析 ······· 25
2.4.8 觀測站勻加速運動、目標勻速直線運動時的可觀測分析 ···· 26
2.4.9 勻加速運動觀測站、勻加速直線運動目標的可觀測分析 ···· 27
2.4.10 其他結論 ······························································ 31
2.5 單站純距離系統與單站純方位系統可觀測性比較 ······················· 32
第3 章 單站純距離系統目標定位與跟蹤算法研究 ······························· 33
3.1 引言 ·············································································· 33
3.2 系統數學模型 ·································································· 34
3.3 基於最小二乘原理的目標參數估計算法 ·································· 36
3.3.1 遞推格式的目標參數估計算法 ····································· 36
3.3.2 基於全域收斂策略的目標參數估計算法 ························· 40
3.4 基於極大似然原理的目標參數估計算法 ·································· 48
3.4.1 單站純距離系統的極大似然估計 ·································· 48
3.4.2 基於全域收斂策略的改進算法 ····································· 51
3.4.3 仿真試驗及分析 ······················································· 52
3.5 UKF 算法的基本原理 ························································· 57
3.5.1 UT 變換 ································································· 57
3.5.2 標準UKF 算法 ························································ 58
3.5.3 迭代UKF 算法 ························································ 59
3.5.4 仿真試驗及分析 ······················································· 60
3.6 自適應迭代UKF 算法 ························································ 63
3.6.1 自適應迭代UKF 算法步驟 ········································· 63
3.6.2 仿真試驗及分析 ······················································· 64
第4 章 單站機動航路優化研究 ······················································· 70
4.1 引言 ·············································································· 70
4.2 觀測站勻速直線一次轉向機動時的可觀測度分析 ······················ 71
4.2.1 可觀測度的定義 ······················································· 71
4.2.2 仿真試驗及分析 ······················································· 72
4.3 單站純距離測量模型的CRLB ·············································· 74
4.3.1 定位與跟蹤誤差下限 ················································· 74
4.3.2 單站純距離測量模型CRLB 計算 ·································· 76
4.4 觀測站機動航路優化研究 ··················································· 78
4.4.1 航路優化問題的提出 ················································· 78
4.4.2 勻速直線一次轉向機動優化航路 ·································· 79
4.4.3 勻速轉彎機動優化航路 ·············································· 82
4.5 航路優化的方法 ·························
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