水下滑翔機系統相對單聲標之觀測度研究

Abstract

本論文為使用單聲標的水下滑翔機，提出了一套事後導航與可觀測性分析的框架。研究提出了一種基於擴展卡爾曼濾波器的平滑方法論，該方法首先利用終點GPS數據來校正流場，而後將修正後的航位推算路徑與GPS和聲學量測進行融合。我們透過李導數建構了一個非線性可觀測性矩陣，以提供一個量化的可觀測性指標。數值模擬確定了在與相對位置向量垂直的運動中，可觀測性會達到最大化。現場試驗驗證了此特性，揭示了成功的軌跡重建，發生在經分析預測具有最高可觀測性程度的聲標配置中。此發現表明，幾何位置關係是達成穩定且準確估計的關鍵因素。本研究所提出的感測器融合策略與可觀測性分析，為未來滑翔機的軌跡規劃與自主導航提供了穩健且考慮幾何因素的理論基礎。

This thesis introduces a framework for the post-navigation and observability analysis of an underwater glider using a single acoustic beacon. An EKF-based smoothing methodology is proposed, which first corrects for ocean currents using end-point GPS data, then fuses the corrected path with acoustic measurements in a Kalman-based framework. A nonlinear observability matrix is constructed via Lie derivatives to provide a quantitative observability metric. Numerical simulations establish that observability is maximized during motion orthogonal to the relative position vector. Field trials validate this framework, revealing that the successful trajectory reconstruction occurred with the beacon configuration that exhibited the highest degree of observability, as predicted by the analysis. This finding suggests that a favorable geometric configuration is a critical factor for achieving a stable and accurate estimation. The proposed sensor-fusion strategy and observability analysis provide a robust, geometry-aware foundation for future glider trajectory planning and autonomous navigation.