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研究生:張文政
研究生(外文):Wen-Cheng Chang
論文名稱:卡爾曼濾波器於非白雜訊環境之GPS導航系統
論文名稱(外文):Kalman filtering approach for GPS navigation with non-white measurement noise
指導教授:卓大靖
指導教授(外文):Dah-Jing Jwo
學位類別:碩士
校院名稱:國立海洋大學
系所名稱:導航與通訊系碩士班
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:英文
論文頁數:67
中文關鍵詞:全球定位系統卡爾曼濾波器非白色雜訊奇異值分解
外文關鍵詞:GPSKalman filteringnon-white noisedecorrelation processsingular value decomposition
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在GPS進行導航定位模擬時,我們一般都是使用卡爾曼濾波器來進行估測與應用,雖然卡爾曼濾波器是一個最理想的濾波器,但是在使用方面有其一定的假設與限制。
在系統之動態模式包含了狀態方程式與測量方程式,其中狀態雜訊與量測雜訊需同時假設為一均值為零之白色雜訊並且彼此之間並無相關,但是在GPS接收機所收到的偽距當中,其雜訊並非都為白色雜訊,為了符合現實的應用,我們使用非白色雜訊來進行模擬,為了處理這類非白色雜訊,我們提出了兩個方法來解決這個問題。
我們先將量測雜訊定義成一階的高斯馬可夫過程[4],接下來便可用此二方法來解決此問題,第一,decorrelation process [3],利用可設定的參數來降低非白色雜訊的影響,使其近似成白色雜訊,如此一來卡爾曼濾波器便可以使用而得到不錯的結果,第二,奇異值分解(SVD)技術加上卡爾曼濾波器 [1][2],此方法不但有很好的數值穩定性,而且並不需要任何的轉換便可以處理此類的問題。
The Kalman filter is a popular estimation tool and can be applied to GPS Navigation design. Although the Kalman filter is the optimal filter but it has some assumptions and limits in use.
The Kalman filtering process contains the state equation and measurement equation. The process and measurement errors are assumed to be zero mean Gaussian white noise and independent each other in the derivation of Kalman filtering. In practice, the pseudorange error is not white. In order to obtain the better accuracy, the non-white noise model will be employed. Under the real error environment, Navigation accuracy based on the conventional Kalman filter can be severely degraded. To resolve the problem, two methods are proposed: (1) decorrelation process [3], (2) singular value decomposition (SVD) based Kalman filter [1][2].
It is assumed that the GPS error can be modeled as a first-order Morkov process [4]. Now we use the two methods to solve the problem. First, decorrelation process, we use preset (estimated) value to reduce the effect of the non-white noise and it would be white noise. The Kalman filter work well after decorrelation. Second, singular value decomposition (SVD) based Kalman filter. The algorithm has a good numerical stability and can handle the problem without any addition transformations.
致謝………………………………………………………………………i
摘要………………………………………………………………………ii
Abstract…………………………………………………………………iii
Contents…………………………………………………………………iv
Figure List……………………………………………………………vii
Table List………………………………………………………………ix
CHAPTER 1 INTRODUCTION...............................01
1.1 GENERAL..........................................01
1.2 BACKGROUND, MOTIVATION AND METHOD................03
1.3 THESIS OUTLINE...................................04
CHAPTER 2 GPS MEASUREMENTS AND ERROR SOURCES..........05
2.1 INTRODUCTION OF GPS...............................05
2.2 GPS MEASUREMENT...................................07
2.3 GPS ERROR SOURCES.................................08
2.3.1 SATELLITE CLOCK ERROR.....................09
2.3.2 RECEIVER CLOCK ERROR......................09
2.3.3 ATMOSPHERIC DELAY.........................10
2.3.4 RECEIVER NOISE............................14
2.3.5 EPHEMERIS ERRORS..........................14
2.3.6 MULTIPATH EFFECT..........................14
2.3.7 SELECTIVE AVAILABILITY....................16
CHAPTER 3 KALMAN FILTER...............................17
3.1 ABOUT KALMAN FILTER...............................17
3.2 THE DISCRETE KALMAN FILTER........................17
3.3 THE ECTENDED KALMAN FILTER........................23
3.4 EKF FOR PARAMETER ESTIMATION......................25
CHAPTER 4 CORRELATED NOISE AND DECORRELATION..........25
4.1 WHITE NOISE.......................................28
4.2 KALMAN FILTERING IN COLOR NOISE...................28
4.3 CORRELATD MEASUREMENT NOISE.......................29
4.4 DECORRELATION PROCESS.............................30
CHAPTER 5 SVD BASED KALMAN FILTER.....................32
5.1 SINGULAR VALUE DECOMPOSITION (SVD)................32
5.2 SVD-BASED KALMAN FILTER...........................34
5.2.1 TIME EXTRAPOLATION FORMULATION..................34
5.2.2 MEASUREMENT UPDATE FORMULATION .................35
5.3 ALGORITHMIC DETAILS ..............................38
CHAPTER 6 SIMULATION AND DISCUSSION...................40
6.1 SYSTEM DESCRIPTION FOR NAVIGATION.............40
6.2 ESTIMATION FOR THE FIRST-ORDER MARKOV
PROCESS...........................................43
6.3 NAVIGATION RESULTS................................47
6.3.1 DECORRELATION PROCESS...........................47
6.3.2 SVD BASED EKF...................................54
6.3.3 DECORRELATION PROCESS AND SVD BASED EKF...................................................61
6.4 DISCUSSION........................................64
CHAPTER 7 CONCLUSION............................................65
REFERENCE.............................................66
[1] Wang, L.; Libert, G.; Minneback,; P. , “A singular value decomposition based Kalman filter algorithm,” Industrial Electronics, Control, Instrumentation, and Automation, 1992. ''Power Electronics and Motion Control''., Proceedings of the 1992 International Conference on , 9-13 Nov 1992
Page(s): 1352 -1357 vol.3
[2] Youmin Zhang; Li, X.R.; , ‘’Fixed-interval smoothing algorithm based on singular value decomposition,’’ Control Applications, 1996., Proceedings of the 1996 IEEE International Conference on , 15-18 Sep 1996 Page(s): 916 -921
[3] Jiin-An Guu; Che-Ho Wei; , ‘’Maneuvering target tracking using IMM method at high measurement frequency,’’ Aerospace and Electronic Systems, IEEE Transactions on , Volume: 27 Issue: 3 , May 1991 Page(s): 514 -519
[4] Rogers, S. R. ,’’Alpha-beta filter with correlated measurement noise,’’ IEEE Trans. 1987, AES-23, pp 592-594
[5] Guu, J.-A.; Wei, C.-H.; , ‘’Tracking technique for manoeuvring target with correlated measurement noises and unknown parameters,’’ Radar and Signal Processing, IEE Proceedings F , Volume: 138 Issue: 3 , Jun 1991 Page(s): 278 -288
[6] Rogers, S.R. , ’’ Steady-state Kalman filter with correlated measurement noise-an analytical solution,’’ Aerospace and Electronics Conference, 1989. NAECON 1989., Proceedings of the IEEE 1989 National , 22-26 May 1989,Page(s): 218 -221 vol.1
[7] G. Minkler and J. Minkler, “Theory and Application of Kalman Filtering”, 1993
[8] 莊智清、黃國興,”電子導航”,全華科技圖書股份有限公司,2001年4月。
[9] 張大中,’高測頻下閃躲目標追蹤 ’,國立交通大學電信工程研究所碩士學位論文,中華民國81年6月。
[10] Jay Farrell, Matthew Barth, “The Global Positioning System and Inertial Navigation”, 1999
[11] A. H. Mohamed, K. P. Schwarz ; ‘’Adaptive Kalman Filtering for INS/GPS’’ Department of Geomatics Engineering , The University of Calgary , 2500 University Drive NW , Calgary , Alberta , Canada , T2N , 1N4 . Received: 14 September 1998 / Accepted : 21 December 1998 , Journal of Geodesy (1999) 73 : 193-203
[12] MOHINDER’S GREWAL , ANGUS P. ANDERWS ; ‘’Kalman Filtering : Theory and Practice Using MATLAB’’ Second Edition , page : 155-159
[13] Pratap Misra and Per Enge, ‘’GLOBAL POSITION SYSTEM Signals, Measurements, and Performance’’, 2001
[14] G.H Golub and C.Reinsch, ‘’Singular value decomposition and least squares solutions,’’ Numer . Math., vol. 14, pp. 403-420,
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