非線性卡曼濾波器於飛行姿態計算之研究

Nonlinear Kalman Filter Design for Attitude Determination.

王奕強(I-Chiang Wang)

指導教授 ： 蕭照焜

淡江大學/工學院/航空太空工程學系碩士班/碩士(2011年)

https://doi.org/10.6846/TKU.2011.00305

摘要

在飛行中如何獲得精確的姿態資訊對於飛機的導航與控制是非常重要的，本論文中研究以實驗室自行設計的微機電飛行資訊量測系統為基礎的姿態計算方法，本研究提出了三種基於四元數的非線性濾波器來整合導航四元數與重力場分量這兩種飛行姿態計算方法，包括擴展式卡曼濾波器、無跡卡曼濾波器以及粒子濾波器。
該演算法利用導航四元數計算姿態的演算法中四個元素的更新矩陣作為濾波器的動態模型，以四個元素作為濾波器的狀態。將由重力場分量以及由電子羅盤得到的姿態角視為濾波器的量測，另外，將導航四元數法中四個元素的約束條件視為完美的量測，並加入到濾波器的設計中。並且詳細的推導建立了量測訊號的隨時間變化的雜訊變異數之近似值。該演算法成功地通過一組由本實驗室自行設計的姿態量測系統所收集的飛行測試數據的驗證。

關鍵字

姿態測量 ； 飛行資訊量測系統 ； 擴展式卡曼濾波器 ； 無跡卡曼濾波器 ； 粒子濾波器

並列摘要

Obtaining precise attitude information is essential for aircraft navigation and control. This thesis presents the results of the attitude determination using an in-house designed low-cost MEMS-based flight information measurement unit. This study proposes three quaterni-on-based nonlinear filters to integrate the traditional quaternion and gravitational force de-composition methods for attitude determination algorithm, include extended Kalman filter, unscented Kalman filter, and particle filter. The proposed nonlinear filter utilizes the evolu-tion of the four elements in the quaternion method for attitude determination as the dynamic model, with the four elements as the states of the filter. The attitude angles obtained from the gravity computations and from the electronic magnetic sensors are regarded as the measurement of the filter. The immeasurable gravity accelerations are deduced from the outputs of the three axes accelerometers, the relative accelerations, and the accelerations due to body rotation. The constraint of the four elements of the quaternion method is treated as a perfect measurement and is integrated into the filter computation. Approximations of the time-varying noise variances of the measured signals are discussed and presented with de-tails through Taylor series expansions. The algorithm is intuitive, easy to implement, and reliable for long-term high dynamic maneuvers. Moreover, a set of flight test data is utilized to verify the success and practicality of the proposed algorithm and the filter design.

並列關鍵字

attitude determination ； flight information measurement unit ； extended Kalman filter ； unscented Kalman filter ； particle filter

參考文獻

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