張帆人臺灣大學：電機工程學研究所李嘉政Lee, Chia-ChengChia-ChengLee2007-11-262018-07-062007-11-262018-07-062004http://ntur.lib.ntu.edu.tw//handle/246246/53313Abstract In this thesis, a new approach based on the bank of Kalman filters is proposed to reduce the fault detection time and the incorrect exclusion rate. The dynamic behavior of the failure vector can be described as P-V (position-velocity) model。By applying the bank of the Kalman filters, the updated fault value can be obtained. Furthermore, the test statistic can be constructed from the fault value. By hypothesis testing, the detection threshold under a given false alarm rate can be calculated directly. Simulation results show that in comparison with the parity-space method, the best improvement of percentage for average detection time is 84.3% and the best improvement of percentage for incorrect exclusion rate is 100% under the step-type failure Also the best improvement of percentage for average detection time is 45.6% and the best improvement of percentage for incorrect exclusion rate is 100% under the ramp-type failure.. The method of the bank of the Kalman filters is better than the method of the parity-space method both in average detection time and incorrect exclusion rate when the fault value is small. Both methods are almost the same in detection time when the fault value is big. Therefore by use of the bank of Kalman filters can monitor the small fault value to keep GPS working continuously. At the end of thesis the concept of the modified bank of Kalman filters is proposed to reduce the number of Kalman filters. From the observerbility analysis, the upper bound of the number of satellites to be monitored by one Kalman filter is obtained.目錄 摘要………………………………………………………………………I Abstract………………………………………………………………II 目錄……………………………………………………………………III 圖目錄…………………………………………………………………V 表目錄………………………………………………………………IX 第1章 緒論……………………………………………………………1 1.1 研究動機………………………………………………………………1 1.2文獻回顧……………………………………………………………………2 1.3論文架構……………………………………………………………………2 第2章 GPS定位演算法………………………………………………4 2.1 GPS定位原理 ………………………………………………………………4 2.1.1虛擬距離……………………………………………………………5 2.1.2載波相位……………………………………………………………5 2.2 GPS定位誤差分析…………………………………………………………6 2.2.1誤差來源與影響……………………………………………………6 2.3衛星幾何分佈………………………………………………………………8 2.4定位演算法…………………………………………………………………9 2.4.1虛擬距離觀測量表示式……………………………………………10 2.4.2 單頻接收機定位演算法……………………………………………10 2.4.3雙頻接收機定位演算法……………………………………………13 2.4.3.1 雙頻率數學模型…………………………………………14 2.4.3.2 多頻率數學模型…………………………………………16 第3章 SSE故障偵測與同位空間故障偵測與隔離演算法…………19 3.1衛星故障偵測演算法………………………………………………………20 3.1.1誤差平方和演算法…………………………………………………20 3.3.2 同位空間演算法……………………………………………………27 3.2衛星故障隔離演算法………………………………………………………29 3.2.1同位空間法…………………………………………………………29 3.2.2 同位向量與特性向量關係…………………………………………30 3.3 同位空間法故障偵測與隔離模擬………………………………………32 3.4 同位空間法故障隔離成功率提升………………………………………40 第4章 多組卡爾曼濾波器故障偵測與隔離演算法…………………45 4.1卡爾曼濾波器演算法………………………………………………………45 4.2故障偵測與隔離性能指標…………………………………………………50 4.3多組卡爾曼濾波器演算法…………………………………………………51 4.3.1量測方程式建立…………………………………………………51 4.3.2 動態方程式建立…………………………………………………52 4.3.3故障偵測與隔離原理………………………………………………53 4.4 多組卡爾曼濾波器模擬…………………………………………………55 4.5 故障偵測與隔離演算法比較……………………………………………70 4.5.1 模擬環境…………………………………………………………………70 4.5.2 模擬結果…………………………………………………………………73 4.5.3 分析與討論………………………………………………………………81 第5章 修改型多組卡爾曼濾波器…………………………………82 5.1 系統可觀察性……………………………………………………………...82 5.2 範例說明…………………………………………………………………...84 5.3 範例模擬…………………………………………………………………88 第6章結論與未來工作………………………………………………106 6.1結論………………………………………………………………………106 6.2未來工作…………………………………………………………………107 參考文獻…………………………………………………………108 附錄A PVA與PV模型介紹…………………………………………i921082 bytesapplication/pdfen-US卡爾曼濾波器Kalman Filterthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/53313/1/ntu-93-R91921004-1.pdf