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標題: | 濾波式故障偵測與排除於多頻GNSS接收機之應用 Filter-Type Fault Detection and Exclusion on Multi-Frequency GNSS Receiver |
作者: | Yi-Hsueh Tsai 蔡宜學 |
指導教授: | 張帆人 |
關鍵字: | 多頻,GNSS,自我迴歸移動平均,故障偵測與排除,機率積分轉換,卡爾曼濾波器,距離差量,馬可夫鏈,多模型, GNSS,Kalman filter,Markov chain,multi-frequency,autoregressive moving average,fault detection and exclusion,delta range,multiple model,probability integral transformation, |
出版年 : | 2004 |
學位: | 博士 |
摘要: | 本論文之議題為探討衛星故障之偵測與排除 (fault detection and exclusion; FDE),其目地是為了偵測因衛星故障所引發之嚴重定位誤差,並且進一步將產生誤差的來源消除,以使導航能夠延續;在此提出分別以多頻 (multi-frequency) 技術、自我迴歸移動平均 (autoregressive moving average; ARMA) 濾波器、卡爾曼濾波器 (Kalman filter) 為基礎之三種演算法,以改進現有之故障偵測與排除演算法。
本文首先提出使用多頻量測量於GNSS (GPS + Galileo) 定位以及故障與排除之演算法;傳統演算法只採用 L1單頻,然而民用L2與L5訊號的GPS 衛星將在2005年發射升空,且Galileo 系統預計於2008年完全運轉;因Galileo將與GPS相容運轉,接收機可以設計同時接收Galileo與GPS系統之訊號;所以對於GNSS系統之可視衛星數目將會因此而大幅提升。因電離層效應與載波頻率息息相關,採用多頻量測量將可以消除該效應;此外新載波可作為備用之量測量,藉此可提升導航之安全性,所以採用多頻演算法將可以提升定位精確度、縮短故障偵測時間以及減低故障排除錯誤率 (incorrect exclusion rate; IER)。由模擬結果得知,多頻演算法比起傳統的L1單頻演算法不僅有較精確之定位結果,更能在偵測與排除故障方面有良好成果。 本文接著提出以自我迴歸移動平均 (ARMA) 之演算法來達成衛星系統故障之偵測與排除,該方法在品管領域已被廣泛採用為故障診斷的工具;因故障在被偵測到之前可能已經存於量測量之中,該演算法不僅使用到現在的資料,更用到了先前的資料;其中所提出的演算法包含故障偵測與故障排除兩部分。在故障偵測上,我們提出以自我迴歸移動平均濾波器為基礎之演算法,其藉由對現在與先前之虛擬距離殘差平方和 (sums of the squares of the range residual errors) 之資料來加權平均,以縮短故障偵測時間;而提早偵測到故障可提供駕駛員更多反應時間,以避免載具嚴重偏離預定路徑。然而在決定某一特定假警報率 (false alarm rate; FAR) 下之偵測臨界值 (detection threshold) 時,我們乃先將自我迴歸移動平均模型轉換至狀態空間 (state-space) 模型,再藉由離散有限狀態馬可夫鏈 (Markov chain) 近似法求得臨界值。再者空中可視衛星數目會隨著時間而改變,做資料匯集時,不能直接運算,本文採用機率積分轉換 (probability integral transformation; PIT) 的技巧來解決。至於在故障排除上,我們採用多變量自我迴歸移動平均 (multivariate ARMA) 濾波器,藉由對現在與先前之同位向量 (parity vector) 之資料加權平均,來減低故障排除錯誤率。由模擬結果得知,相較於原來的方法,自我迴歸移動平均濾波器對於偵測小故障量有較佳的性能,而對於偵測大故障量而言其效果差異不大;最後由模擬結果,我們驗證所提出之故障排除演算法能夠減低故障排除錯誤率。 本文最後提出並列式卡爾曼濾波器 (Kalman filter) 來達成衛星定位以及故障之偵測與排除。傳統上,卡爾曼濾波器採用常見的位置-速度-加速度 (position-velocity-acceleration; PVA) 模型為載具之動態模型。然而,在缺乏額外感知器 (如慣性導航感知器) 的情況下,傳統位置-速度-加速度模型將無法正確描述載具劇烈加減速度亦或高速轉彎之移動狀態。因此載具之定位結果將變得較不精確。再者,標準化資訊創新平方 (normalized innovation squared; NIS) 將不再是卡方分布 (chi-square distribution),因而無法作為故障偵測與排除之檢定統計量 (test statistic);而為了解決該問題,我們採用距離差量 (delta range; DR) 方程式來描述速變載具 (maneuvering vehicle) 之動態模型;由模擬結果得知,在載具速變時,若採用距離差量方程式取代位置-速度-加速度模型,將對於定位以及處理故障偵測與排除上可得到較佳的結果。此外,當衛星故障發生且故障尚未被排除之前,載具之定位結果將變的不合理甚至因此而無法使用。在此,我們乃採用多模型 (multiple model; MM) 演算法的技巧來解決。從模擬結果顯示,相較於原來的方法,多模型演算法在衛星故障發生時,亦能正常的執行定位功能。 This thesis is concerned with topics on the problems of satellite fault detection and exclusion (FDE). The purpose of FDE is to detect the presence of unacceptably large positioning error and, further, to exclude the source causing the error, thereby allowing the satellite navigation to continue. To enhance the capability of the existing fault detection and exclusion methods, we propose three type FDE algorithms based on the multi-frequency technique, the autoregressive moving average (ARMA) filter technique and the Kalman filter technique, respectively. At the first part of this thesis, algorithms using multi-frequency measurements are proposed for GNSS (GPS + Galileo) positioning and FDE. Conventional algorithms adopt only the single frequency L1. However, GPS satellites carrying the L2 and L5 signals for civil use will soon be launched in 2005, and the Galileo system will be fully operational in 2008. Since Galileo will be interoperable with GPS, receivers can be designed to simultaneously access both Galileo and GPS systems. Hence, the number of visible GNSS satellites will be significantly increased. Using the multi-frequency technique can eliminate the ionospheric effect because it is highly related to the carrier frequency of the signal. In addition, the new signals can also be regarded as a backup, and this will significantly increase the safety of navigation. Therefore, application of multi-frequency algorithms will improve the positioning accuracy, shorten the failure detection time, and reduce the incorrect exclusion rate (IER). Simulation results show that, in comparison with the conventional single frequency method, the proposed multi- frequency algorithms not only possess more accurate positioning results but also demonstrate higher performance in detecting and excluding failures. At the second part of this thesis, we propose an algorithm based on the autoregressive moving average to perform satellite failure detection and exclusion. ARMA filter is widely used in the field of quality control as a tool for fault diagnosis. It uses the historical data as well as the up-to-date information since failure may exist in past measurements before it is detected. The proposed algorithm includes fault detection and fault exclusion. For fault detection, the ARMA-filter is proposed to speed up the detection time by taking the average of the last several sums of the squares of the range residual errors. Speeding up of the failure detection can provide more time for pilots to prevent serious deviations of vehicles from their intended paths. In order to determine the detection threshold under a specified false alarm rate (FAR), the ARMA model is firstly transformed into the state-space model, and the threshold can then be approximated by a “discrete finite-state Markov chain”. Moreover, the alteration of the number of visible satellites will cause problems in data fusion. The probability integral transformation (PIT) method is adopted to solve it. As for fault exclusion, the multivariate ARMA-filter is proposed to reduce the IER by taking the average of the last several parity vectors. Simulation results show that, in comparison with the conventional fault detection methods, the ARMA-filter has higher performance in detecting small failures and however, in detecting large failures, their performances are similar. Moreover, simulation results also verify that the proposed method can reduce the IER in excluding the failed satellite. At the third part of this thesis, we propose an algorithm based on a parallel bank of Kalman filters to perform satellite positioning and FDE. Conventionally, the well known position- velocity-acceleration (PVA) model is adopted as the dynamic model of Kalman filter for navigation. However, as a moving vehicle accelerates or slows down furiously, or as the vehicle corners at faster speeds, the conventional PVA model without using extra sensors (such as inertial navigation sensors) can no longer be adequate for describing the motion of the vehicle. Therefore, the positioning result of the vehicle will become less accurate. Moreover, the normalized innovation squared (NIS) will deviate from the chi-square distribution and is no longer suitable as the test statistic for FDE. To overcome these problems, the delta range (DR) equation is proposed to accurately model the dynamic behavior of a maneuvering vehicle. Simulation results show that using the proposed DR to replace the PVA model can obtain better positioning and FDE results as the vehicle maneuvers. Furthermore, as a satellite fails at a specified time and if the range measurements associated to the failed one is not yet excluded, the positioning result of the vehicle will become inaccuracy and even unusable. To solve this, an algorithm based on multiple model (MM) approach is proposed. Simulation results also present that, compared to the original Kalman filter, the proposed MM can perform positioning well as the satellite is failed. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/39393 |
全文授權: | 有償授權 |
顯示於系所單位: | 電機工程學系 |
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