適應約束濾波法之分析及 其在GPS 病態定位之應用

Abstract

本論文設計適應約束濾波法 (Adaptive Constraint-filtering method; ACF )以處理約束濾波法(Constraint-filtering method; CF)無法掌握狀態及量測雜訊變化的缺失。約束濾波法可將限制條件併入非線性動態系統中，在非線性的模式下，使用牛頓-拉普森疊代法 (Newton-Raphson iteration)逼近求解。對於陸上運動之載具，若假設速率為穩定變化，則約束濾波法可應用解決載具上全球衛星定位系統 (Global Positioning System; GPS)在接收機無法觀測到足夠衛星的問題，達成在都市環境中定位的工作。傳統的適應估測法 (Adaptive Estimation)，採用經驗法則決定窗口寬度(Window Size)，本論文提出了模糊新訊息適應估測法 (Fuzzy Innovation Adaptive Estimation; FIAE)，加入模糊系統概念，更適應地掌握窗口寬度以估測未知的雜訊過程。 使用GPS系統定位接收機至少需觀測到四顆衛星，但在都市環境中，卻不易達成此條件。本論文討論的另一主題為如何利用有限的衛星數目及先前成功定位的資訊，達成精確的定位結果。當接收機觀測到三顆衛星時，本論文使用了限制高度變化的方式來進行定位。由於在道路上行駛時，使用者的高度通常呈現緩慢變化的情形。利用地球為橢球的模型，配合先前正常定位所獲得資訊，限制使用者的高度為最近十秒內的平均高度值，便可以在接收機僅觀測到三顆衛星時進行定位。當接收機觀測到二顆衛星時，配合限制高度的作法，以及預估接收機時鐘偏差的方式，配合檢查精度因子 (Dilution of Precision; DOP)的方式以期提供有效的定位解。本論文另外應用了虛擬距離預估器，利用衛星的虛擬距離呈現線性變化的假設，可由現在所解出來的使用者位置及其速度配合衛星的位置和速度，估算出下一秒時刻衛星的虛擬距離值。當某顆衛星被遮蔽時，便可利用所估算出的虛擬距離值來進行定位。利用虛擬距離預估器配合不同衛星數目的定位演算法，更可大幅的改善以往GPS系統僅能在接收機觀測四顆衛星以上定位的限制。 為檢測所發展適應約束濾波器的功能，我們採用蒙地卡羅法 (Monte Carlo method)進行模擬，以評估並比較其與卡爾曼濾波器 (Kalman filter; KF), 適應卡爾曼濾波器 (Adaptive Kalman filter; AKF) 和約束濾波法之性能優異。經由模擬分析，証實適應約束濾波法極具可行性。適應約束濾波法將實際量測，狀態預測和限制條件皆視為可用之量測資訊，由靜態及動態實驗結果顯示，適應約束濾波法可有效降低系統誤差，提高定位解算精度。

To deal with the estimation problem for systems subject to constraints while the corresponding noise processes are not completely known, the adaptive constraint-filtering method is proposed in this study. As having been shown in [1], the constraint-filtering method can accommodate the soft constraint in the filtering process for a nonlinear dynamic system. The method is based on the knowledge of the modeling noise and the sensor noise, which may not be practical. In this study, the fuzzy innovation adaptive estimation (FIAE) approach is proposed to deal with the unknown noise processes. Furthermore, for land vehicles, it may be assumed that the speed of the vehicle is not varying significantly, so that the constraint-filtering method with soft constraint is then applied to solve the ill-conditioned GPS positioning problem. For GPS positioning, it is normally required that there be at least four GPS satellites in view. However, due to the frequent blockage of signals in urban environment, it is difficult to meet that requirement so that the operation of GPS receiver may be interrupted. How to deal with this problem so that the service can be continuous is also the main theme of this study. The pseudorange predictor utilizes the current user and satellite’s positions and velocities to estimate the next time satellite’s pseudorange. In addition, when the receiver observes only two satellites, the receiver clock bias predictor may be used to estimate the clock bias. If there are three satellites in view, the altitude-hold algorithm is developed to provide additional information under the assumption that the altitude of the vehicle is approximately a constant, which is deemed appropriate for urban applications. The integration of these methods yields a successful algorithm to manage the ill-conditioned positioning problem if the number of visible satellites is insufficient. The basic Monte Carlo method is applied to simulation, in order to assess and compare the performance of the various filters, such as the Kalman filter (KF), the adaptive Kalman filter (AKF), the constraint-filtering (CF), and the adaptive constraint-filtering (ACF). The simulation results show that the adaptive constraint-filtering method is evidently better than the other filters. From both static and dynamic experimental results, it is shown that the proposed methodology indeed gives rise to an effective scheme which can sustain the service for a few minutes even if there is no satellite in view at all. The adaptive constraint-filtering method can enhance the accuracy and outperform the Kalman filtering method significantly.