臺灣博碩士論文加值系統

在GPS量測中，時常會受到周圍環境的影響，多路徑效應造成接收端訊號之間的干擾，將會對量測結果造成不可預測的誤差影響，為了能夠在具有非高斯雜訊或重尾異常值的非線性環境下依然有良好的濾波表現，採用了基於中心誤差熵之擴展型卡爾曼濾波器演算法(Centered Error Entropy Extended Kalman Filter, CEE-EKF)。最小誤差熵(Minimum Error Entropy, MEE)準則能夠降低估測誤差分佈的隨機不確定性，但由於誤差熵的平移不變性，導致當誤差存在偏移時，即使最小化了誤差熵，仍然可能產生偏差導致誤差收斂效果不佳；而最大相關熵準則(Maximum Corentropy Criterion, MCC)藉由最大化相關熵使得誤差機率密度函數更加集中在接近零的位置，儘管誤差產生偏移，基於相關熵的特性使得熵值仍然會受影響而改變，因此能得到較好的誤差收斂結果。針對各自單一方法的優點以及不足之處，將兩種方法加權做結合，形成基於中心誤差熵之擴展型卡爾曼濾波器演算法。相較於使用單一演算法的MEE-EKF、MCC-EKF，CEE-EKF在較為複雜並具有非高斯雜訊的非線性GPS環境下進行實驗，結果顯示基於中心誤差熵之卡爾曼濾波器的雜訊抑制表現較佳。

In GPS navigation, the signal at the receiver is often affected by the surrounding environment. Multipath effects can cause interference between signals, leading to unpredictable errors in measurement results. To maintain good filtering performance in nonlinear environments with non-Gaussian noise or heavy-tailed outliers, a Centered Error Entropy Extended Kalman Filter (CEE-EKF) algorithm is used. The Minimum Error Entropy (MEE) criterion can reduce the random uncertainty of the error distribution. However, due to the translation invariance of error entropy, even if the error entropy is minimized, bias can still occur when errors are shifted, resulting in poor error convergence. On the other hand, the Maximum Correntropy Criterion (MCC) maximizes correntropy to bring the error probability density function (PDF) closer to zero. Despite error shifts, the properties of correntropy ensures that its value changes, leading to better error convergence. By combining the strengths and addressing the weaknesses of both methods, a weighted combination of the two forms the CEE-EKF algorithm. Compared to using single algorithms like MEE-EKF and MCC-EKF, experiments in more complex nonlinear GPS environments with non-Gaussian noise show that the CEE-EKF algorithm has better noise suppression performance.

誌謝 I
摘要 II
ABSTRACT III
目錄 IV
圖目次 VI
表目次 VII
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 1
1.3 文獻回顧 2
1.4 論文架構 3
第二章 全球定位系統 4
2.1 導航衛星系統簡述 4
2.2 GPS定位原理 5
2.3 GPS架構 6
2.4 參數估測方法 7
第三章 卡爾曼濾波器 10
3.1 卡爾曼濾波器簡述 10
3.2 離散型卡爾曼濾波器 11
3.3 擴展型卡爾曼濾波器 14
第四章 熵原理 17
4.1 熵的基礎理論 17
4.2 最小誤差熵準則 18
4.3 最大相關熵準則 19
4.4 中心誤差熵準則 20
第五章 基於中心誤差熵準則之卡爾曼濾波器演算法 21
5.1 基於最小誤差熵準則之擴展型卡爾曼濾波器 21
5.2 基於最大相關熵準則之擴展型卡爾曼濾波器 27
5.3 基於中心誤差熵準則之擴展型卡爾曼濾波器 31
第六章 實驗結果與分析 38
6.1 目標物於自由落體下之雷達追蹤測試 38
6.2 GPS導航衛星之狀態估測問題 46
第七章 結論與未來展望 57
7.1 結論 57
7.2 未來展望 57
7.2.1 自由參數之探討 57
參考文獻 59

[1]莊智清、黃國興，電子導航，全華科技圖書股份有限公司，2001年
[2]莊智清，衛星導航，全華科技圖書股份有限公司，2012年
[3]秦永元、張洪鉞、汪淑華，卡爾曼濾波與組合導航，西北工業大學出版社，2015年
[4]陳霸東、朱煜、胡金春、喬斯．C.普倫斯派，系統參數辨識的信息準則及算法，清華大學出版社，2014年
[5]R. G. Brown and P. Y. C. Hwang, Introduction to Random Signals and Applied Kalman Filtering. New York, NY, USA: John Wiley and Sons, 1997.
[6]J. C. Principe, Information Theoretic Learning, Renyi's Entropy and Kernel Perspectives. New York, NY, USA: Springer, 2010.
[7]D. J. Jwo, S. H. Wang, “Adaptive Fuzzy Strong Tracking Extended Kalman Filtering for GPS Navigation,” IEEE Sensors Journal, vol. 7, no. 5, pp. 778-789, 2007.
[8]D. J. Jwo, C. M. Huang, “An Adaptive Fuzzy Strong Tracking Kalman Filter for GPS/INS Navigation,” IECON 2007 - 33rd Annual Conference of the IEEE Industrial Electronics Society, 2007.
[9]D. J. Jwo, S. J. Chang, “Outlier Resistance Estimator for GPS Positioning,” 2006 IEEE International Conference on Systems, Man and Cybernetics, 2006.
[10]B. Chen, L. Dang, Y. Gu, N. Zheng and J. C. Principe, “Minimum error entropy Kalman filter,” IEEE Transactions on Systems, Man, and Cybernetics: Systems (Early Access), pp.1–11, 2019.
[11]G. Gang, B. Chen, X. Yang, B. Peng, Z. Feng, “Numerically stable minimum error entropy Kalman filter,” ScienceDirect Signal Processing, vol. 181, 2021.
[12]Z. Feng, G. Wang, B. Peng, J. He, K. Zhang, “Novel robust minimum error entropy wasserstein distribution kalman filter under model uncertainty and non-gaussian noise,” ScienceDirect Signal Processing, vol. 203, 2023
[13]M. Zhang, X. Song, “A novel robust minimum error entropy Kalman filter in the presence of measurement packet dropping,” ScienceDirect Signal Processing, vol. 206, 2023.
[14]B. Chen, X. Liu, H. Zhao and J. C. Principe, “Maximum correntropy Kalman filter,” Automatica, vol. 76, pp. 70–77, 2017.
[15]R. Izanloo, S. A. Fakoorian, H. S. Yazdi, D. Simon, “Kalman filtering based on the maximum correntropy criterion in the presence of non-Gaussian noise,” 2016 Annual Conference on Information Science and Systems (CISS), 2016.
[16]X. Liu, H. Qu, H. Zhao and B. Chen, “Extended Kalman filter under maximum correntropy criterion,” in Proc. IEEE International Joint Conference on Neural Networks (IJCNN), Vancouver, BC, Canada, pp. 1733–1737, 2016.
[17]X. Liu, Z. Ren, H. Lyu, Z. Jiang, P. Ren and B. Chen, “Linear and nonlinear regression-based maximum correntropy extended Kalman filtering,” IEEE transactions on systems, man, and cybernetics: Systems, vol. 51, no. 5, pp. 3093-3102, 2021.
[18]L. Cheng, M. F. Ren, G. Xie, “Multipath Estimation Based on Centered Error
Entropy Criterion for non-Gaussian Noise,” IEEE Access, vol. 4, pp. 9978-9986, 2016.
[19]B. Yang, L. Cao, D. Ran, B. Xiao, “Centered error entropy Kalman filter with application to satellite attitude determination,” Transactions of the Institute of Measurement and Control, vol. 43, 2021.
[20]B. Yang, L. Cao, L. Li, C. Jiang, D. Ran, B. Xiao, “A New Robust Centered Error Entropy Cubature Kalman Filter,” IEEE 7th International Conference on Control Science and Systems Engineering (ICCSSE), 2021.
[21]L. Dang, B. Chen, “Cubature Kalman Filter Under Minimum Error Entropy With Fiducial Points for INS/GPS Integration,” IEEE/CAA Journal of Automatica Sinica, vol. 9, no. 3, 2022.
[22]L. Dang, B. Chen, “Dual Extended Kalman Filter Under Minimum Error Entropy With Fiducial Points,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 12, pp. 7588-7599, 2022.
[23]B. Chen, Y. Xie, X, Wang, Z. Yuan, P. Ren, J. Qin, “Multikernel Correntropy for Robust Learning,” IEEE Transactions on Cybernetics, vol. 52, no. 12, 2022.