適應性動態補償容積式非線性濾波器的設計及其於GPS導航系統之應用

Abstract

本論文目的為設計一自適應動態補償機制，分別運用Huber M-估測方法與模糊邏輯自適應系統來克服非高斯測量誤差與系統不確定性的問題。衛星定位過程中，其假設導航濾波器於動態系統的估測均可藉由高斯狀態空間模型來近似系統動態和量測過程所涉及的雜訊干擾。然而，隨環境複雜度改變，量測訊號易受汙染而導致量測雜訊呈現非高斯分佈或異常值干擾，使得系統與觀測模型之雜訊統計特性與實際假設不符合，而造成載體狀態之估算精確度大幅降低。因此，針對非高斯雜訊分佈或異常值訊號，本論文提出一結合Huber M-估測方法和容積卡爾曼濾波器的架構機制，稱為Huber-based容積卡爾曼濾波器，透過Huber M-估測方法重新建構容積卡爾曼濾波器的量測資訊，得以提供有效抑制非高斯雜訊分佈的量測誤差。 另一方面，導航系統不確定性因素的容限度，包括雜訊參數和載體動態的不確定性將導致系統建模產生誤差，使得定位效能衰減。由於，車輛或飛行載具運動過程皆是非線性之動態行為。若欲進行系統控制與定位估算，這些不確定性因素將造成模型誤差而導致效能衰減。為了有效解決傳統透過個人經驗或是數值模擬來選擇系統雜訊共變異數的缺點，本論文提出一模糊自適應容積卡爾曼濾波器的演算機制，運用模糊邏輯自適應系統導入至CKF的濾波架構，並鑑別發散程度之參數訊息以作為即時調整系統雜訊共變異數的動態機制。因此，所提出之模糊自適應容積卡爾曼濾波器，方可強健導航精確度並具有良好的追蹤能力。最後，本論文提供模擬與實際實驗結果作為驗證所提出的機制及演算效能。

The objective of this dissertation is to design an adaptive motion-compensated scheme to manage non-Gaussian measurement errors and modeling errors using the Huber M-estimation methodology and a fuzzy logic adaptive system (FLAS), respectively. In practical navigation problems, it is assumed that navigation filters are concerned with the estimation of a dynamical system from noisy measurements, and that dynamic and measurement processes can be approximated by Gaussian state-space models. However, the filter-based estimation of vehicle states can be severely degraded due to contaminated measurements caused by outliers or deviation from a Gaussian distribution assumption. For signals contaminated with non-Gaussian noise or outliers, a robust scheme combining the Huber M-estimation methodology and a cubature Kalman filter (CKF) framework is beneficial where the Huber M-estimation methodology is used to reformulate the measurement information of the CKF. A Global Positioning System (GPS) navigation processing method was developed that uses the proposed Huber-based cubature Kalman filter (HCKF) algorithm; this method provides robustness against deviations from Gaussian behavior. In processing navigation integration, the tolerance of uncertainty factors (including noise uncertainty and system modeling inaccuracy) is not a paramount concern; thus a robust demand is required for navigation filtering schemes. These uncertainty factors will involve performance degradation due to dynamics uncertainties of the vehicle caused by modeling errors. Selecting the process noise covariance through personal experience or numerical simulation would produce inadequate results. In order to produce satisfactory results, a scheme called the fuzzy adaptive cubature Kalman filter (FACKF) is presented. In FACKF, a FLAS is incorporated into a CKF framework for the timely tuning of a process noise covariance matrix on the basis of a degree of divergence (DOD) parameter. The proposed FACKF algorithm shows noteworthy improvements in both navigational accuracy and tracking capability. Results from simulations and practical experiments are provided as validation of the performance of these proposed approaches.