為了達到節省應答器佈放與定位作業成本、提高作業效率的目的，本論文以單一應答器所提供之斜距資訊來取代長基線定位系統。本研究分別透過擴展式卡曼濾波(EKF)與自適性卡曼濾波(AKF)整合單一應答器、深度計、都卜勒流速計與姿態感測儀之量測資訊，且考慮各個感測儀器之更新頻率，建立無人水下載具之單一斜距定位演算法，完成擴展式單一斜距定位系統(EKF-SR)與自適性單一斜距定位系統(AKF-SR)演算開發，並進一步於不同的起始條件下於數值模擬與實海域定位實驗進行定位估算性能測試。研究結果顯示EKF-SR與AKF-SR在載具起點水平位置已知且誤差共變異矩陣設置理想的情況下進行定位估算，兩單一斜距定位估算法皆具有穩健估算與精準定位之性能，但EKF-SR受到誤差共變異矩陣設置形式影響較大，AKF-SR則是起點水平位置誤差的收斂速度較慢，另一方面，本論文也證實載具軌跡會直接影響兩運算法之收斂起點水平位置誤差性能。雖然EKF-SR與AKF-SR估算性能受到起始條件與載具軌跡路徑之限制，但兩運算法依然能達到校正估測誤差、量測誤差以及穩健估算載具的三維座標之目的。

This study is to develop a range-only positioning approach that integrates the real-time measurements of a pressure sensor, the velocity evaluation from the Doppler velocity log (DVL) and the range information between a single seabed transponder and an underwater vehicle. This technique was used to effectively reduce the cost of deployments of the seafloor transponders, to precisely navigate the underwater vehicles, and to practically improve the variation of the update sampling rate from all rigs. The Extended Kalman filter and the Adaptive Kalman filter were employed to integrate the slant-range measurements from a single transponder, the velocity data from a DVL, the depth data from the pressure sensor, and the attitude angle from a gyrocompass. As a result, both of the filters are called the Extended Kalman filter Slant-range positioning system (EKF-SR) and the Adaptive Kalman filter Slant-range positioning system (AKF-SR), respectively. Numerical simulations and field experiments were conducted to test the performance of the proposed algorithm of this single-transponder underwater navigating method. However, the limitations of the initial condition will be the indicator to decide which filter should be better and the vehicle trajectory will affect algorithm convergence performance. The simulated and experimental results demonstrate that the proposed algorithm is robust to rectify the measurement errors and to provide accurate position for an underwater vehicle.

論文審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
致謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
第一章緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 動機與目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 論文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
第二章研究方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 應答器定位估算. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 都卜勒流速計定位估算. . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 卡曼濾波. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.1 離散式卡曼濾波. . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2 擴展式卡曼濾波. . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.3 自適性卡曼濾波. . . . . . . . . . . . . . . . . . . . . . . . . 18
第三章單一斜距定位系統建模. . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1 單一斜距系統模型. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.1 擴展式單一斜距定位系統. . . . . . . . . . . . . . . . . . . . 24
3.1.2 自適性單一斜距定位系統. . . . . . . . . . . . . . . . . . . . 28
3.2 觀測值非同步更新之定位估算. . . . . . . . . . . . . . . . . . . . . . 29
第四章數值模擬與性能評估. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1 感測儀器誤差來源. . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2 數值模擬設計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.3 直線軌跡定位估算. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.1 數值模擬I . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.2 數值模擬II . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3.3 數值模擬III . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3.4 數值模擬IV . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 圓形軌跡定位估算. . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.4.1 數值模擬I . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.4.2 數值模擬II . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4.3 數值模擬III . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4.4 數值模擬IV . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.5 平行線軌跡定位估算. . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5.1 數值模擬I . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5.2 數值模擬II . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.5.3 數值模擬III . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.5.4 數值模擬IV . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.6 檢視單一斜距定位系統之定位估算性能. . . . . . . . . . . . . . . . . 62
第五章實海域定位實驗與分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.1 實驗規劃. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2 實海域軌跡定位估算. . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2.1 數值模擬I . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2.2 數值模擬II . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2.3 數值模擬III . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2.4 數值模擬IV . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
第六章結論與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.2 討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
附錄A 狀態過度矩陣與Bar-Shalom 程序誤差共變異矩陣推導過程. . . . . . . 85
附錄B 逆威沙特分布與參數選用. . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
附錄C 四種數值模擬之起始參數設置. . . . . . . . . . . . . . . . . . . . . . . . . 93
C.1 數值模擬I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
C.2 數值模擬II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
C.3 數值模擬III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
C.4 數值模擬IV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

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