臺灣博碩士論文加值系統

Abstract
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…………………………………………i

參考文獻
[1]Lee, Y.C., Analysis of Range and Position Comparison Methods as aMeans to Provide GPS Integrity in the User Receiver, Proceedings of theInstitute of Navigation Forty-second Annual Meeting, Seattle,Washington ,24-26 June 1986,pp.1-4.
[2] Parkinson , B. W. and Axelrad, P., “ Autonomous GPS Integrity MonitoringUsing the Pseudo-range Residual, Navigation Journal of Institute ofNavigation ,Vol. 35,No.2,Summer 1988,pp.255-274.
[3]Sturza, M. A., Navigation System Integrity Monitoring Using RedundantMeasurements, Navigation, Journal of Institute of Navigation, Vol.35 ,No.4,
Winter 1988-1989 pp.483-501.
[4]Brown,R.G.,”A Baseline GPS RAIM Scheme and Note on the equivalence ofThree RAIM Methods, Navigation Journal of the Institute of Navigation,Vol.39,No.3,Fall 1992,pp.301-316.
[5]B.W.Parkinson and J.J.Spilker Jr., Global Positioning System :Theory andApplication Vol I and II,AIAA, Washington DC,1996.
[6]E.R.Dougherty, Probability and Statistics for the Engineering , Computing and Physical Sciences , Prentice-Hall,1990.
[7]R.G.Brown and G.Y.Chin ,“ GPS RAIM: Calculation of Threshold andProtection Radius Using Chi-Square Methods A Geometric ApproachGlobal Positioning System ,Papers Published in Navigation,Volume V, theInstitute of Navigation,1997,pp.155-178.
[8]Brian D.O.Anderson,John B.Moore, Optimal Filtering, Prentice-Hall,Inc.,1979.
[9]Bar-Shalom,Y.and Fortaman ,T.E., Estimation and Tracking Principle,Techniqus and Software, Artech House ,Inc. ,Boston ,London,1993.
[10]B.D.Brumback and M.D.Srinth, A Chi-Square Test for Fault-Detection inKalman Filters, IEEE Trans.On Automatic Control,VOL.AC-32,No.6,June1987.
[11]Ren Da and Ching-Fan Lin ,Sensor Failure Detection With a Bank of Kalman Filters, Proceedings of The American Control Conference,June1995.
[12]Ren Da, A New Failure Detection Approach and Its Application to GPSAutonomous Integrity Monitoring, IEEE TRANSACTION ON AEROSPACE AND ELECTRONIC SYSTEMS VOL.31,NO.1,Janurary 1995.