Cubature Kalman Filter Under Minimum Error Entropy With Fiducial Points for INS/GPS Integration

Lujuan Dang; Badong Chen; Yulong Huang; Yonggang Zhang; Haiquan Zhao

doi:10.1109/JAS.2021.1004350

Volume 9 Issue 3

Mar. 2022

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2022 > 9(3): 450-465

L. J. Dang, B. D. Chen, Y. L. Huang, Y. G. Zhang, and H. Q. Zhao, “Cubature Kalman filter under minimum error entropy with fiducial points for INS/GPS integration,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 3, pp. 450–465, Mar. 2022. doi: 10.1109/JAS.2021.1004350

Citation:

L. J. Dang, B. D. Chen, Y. L. Huang, Y. G. Zhang, and H. Q. Zhao, “Cubature Kalman filter under minimum error entropy with fiducial points for INS/GPS integration,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 3, pp. 450–465, Mar. 2022. doi: 10.1109/JAS.2021.1004350

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Cubature Kalman Filter Under Minimum Error Entropy With Fiducial Points for INS/GPS Integration

doi: 10.1109/JAS.2021.1004350

1.
Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, Xi’an 710049, China
2.
Department of Automation, Harbin Engineering University, Harbin 150001, China
3.
School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610000, China

Funds: This work was supported by the Fundamental Research Funds for the Central Universities (xzy022020045) and the National Natural Science Foundation of China (61976175)

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Author Bio:
Lujuan Dang received the B.S. degree in information science and technology from Northwest University, Xi’an, in 2015, and the M.S. degree in electronic and information engineering from Southwest University, Chongqing, China, in 2018. She is currently a Ph.D. candidate at the Institute of Artificial Intelligence and Robotics (IAIR), Xi’an Jiaotong University, Xi’an, China. Her current interests focus on state estimation and information theoretic learning

Badong Chen (Senior Member, IEEE) received the B.S. and M.S. degrees in control theory and engineering from Chongqing University, Chongqing, China, in 1997 and 2003, respectively, and the Ph.D. degree in computer science and technology from Tsinghua University, Beijing, China, in 2008. He was a Post-Doctoral Researcher with Tsinghua University from 2008 to 2010, and a Post-Doctoral Associate with the Computational NeuroEngineering Laboratory, University of Florida, Gainesville, FL, USA, from 2010 to 2012. He visited the Nanyang Technological University, Singapore, as a Visiting Research Scientist in 2015 for one month. He is currently a Professor with the Institute of Artificial Intelligence and Robotics (IAIR), Xi’an Jiaotong University, Xi’an, China. His current research interests include signal processing, information theory, machine learning and their applications to cognitive science and neural engineering. He has published two books, four chapters, and over 200 papers in various journals and conference proceedings. He is a Technical Committee Member of IEEE Signal Processing Society (SPS) Machine Learning for Signal Processing and IEEE Computational Intelligence Society (CIS) Cognitive and Developmental Systems, and an Associate Editor of the IEEE Transactions on Cognitive and Developmental Systems and the Neural Networks

Yulong Huang (Member, IEEE) received the B.S. degree in automation from the College of Automation, Harbin Engineering University, Harbin, China, in 2012, the Ph.D degree in control science and engineering from the College of Automation, Harbin Engineering University, Harbin, China, in 2018. From Nov. 2016 to Nov. 2017, he was a Visiting Graduate Researcher at the Electrical Engineering Department of Columbia University, New York, USA. Currently, he is an Associate Professor of navigation, guidance, and control at Harbin Engineering University (HEU) in China. From Dec. 2019 to Dec. 2021, he is associated with the Department of Mechanical Engineering, City University of Hong Kong, as a Hong Kong Scholar. His current research interests include state estimation, information fusion and their applications in navigation technology, such as inertial navigation, integrated navigation, and cooperative navigation. He was the recipient of excellent doctoral thesis from Chinese Association of Automation (CAA) in 2019, and the 11th China Youth Science and Technology Innovation Awards in 2018, and the Honorable Mention of 2017 Barry Carlton from IEEE Transactions on Aerospace and Electronic Systems, and the Outstanding Reviewer of 2020 for IEEE Transactions on Instrumentation and Measurement. He was selected into the sixth Young Elite Scientists Sponsorship Program by China Association for Science and Technology in 2020. He serves as an Associate Editor for the IEEE Transactions on Aerospace and Electronic Systems and the IEEE Sensors Journal

Yonggang Zhang (Senior Member, IEEE) received the B.S. and M.S. degrees from the College of Automation, Harbin Engineering University, Harbin, China, in 2002 and 2004, respectively, the Ph.D. degree in electronic engineering from Cardiff University, UK in 2007 and worked as a Post-Doctoral Fellow at Loughborough University, UK from 2007 to 2008 in the area of adaptive signal processing. Currently, he is a Professor of navigation, guidance, and control in Harbin Engineering University (HEU) in China. His current research interests include signal processing, information fusion and their applications in navigation technology, such as fiber optical gyroscope, inertial navigation and integrated navigation

Haiquan Zhao (Senior Member, IEEE) received the B.S. degree in applied mathematics, and the M.S. and Ph.D. degrees in signal and information processing from Southwest Jiaotong University, Chengdu, China, in 1998, 2005, and 2011, respectively. Since 2012, he has been a Professor with the School of Electrical Engineering, Southwest Jiaotong University. From 2015 to 2016, as a Visiting Scholar, he worked with the University of Florida, USA. His current research interests include nonlinear active noise control, information theoretic learning, neural networks, adaptive network, adaptive filtering algorithm, and power system frequency estimation. At present, he is the Author or Coauthor of more than 150 international journal papers (SCI indexed), and the Owner of 49 granted invention patents. He has served as an Active Reviewer for several IEEE transactions, institution of engineering and technology (IET) series, signal processing, and other international journals. At present, he is a Handling Editor of Signal Processing
Corresponding author: Badong Chen, e-mail: chenbd@mail.xjtu.edu.cn
Received Date: 2020-12-16
Revised Date: 2021-07-10
Accepted Date: 2021-08-16

Available Online: 2023-03-29

Abstract

Abstract

Traditional cubature Kalman filter (CKF) is a preferable tool for the inertial navigation system (INS)/global positioning system (GPS) integration under Gaussian noises. The CKF, however, may provide a significantly biased estimate when the INS/GPS system suffers from complex non-Gaussian disturbances. To address this issue, a robust nonlinear Kalman filter referred to as cubature Kalman filter under minimum error entropy with fiducial points (MEEF-CKF) is proposed. The MEEF-CKF behaves a strong robustness against complex non-Gaussian noises by operating several major steps, i.e., regression model construction, robust state estimation and free parameters optimization. More concretely, a regression model is constructed with the consideration of residual error caused by linearizing a nonlinear function at the first step. The MEEF-CKF is then developed by solving an optimization problem based on minimum error entropy with fiducial points (MEEF) under the framework of the regression model. In the MEEF-CKF, a novel optimization approach is provided for the purpose of determining free parameters adaptively. In addition, the computational complexity and convergence analyses of the MEEF-CKF are conducted for demonstrating the calculational burden and convergence characteristic. The enhanced robustness of the MEEF-CKF is demonstrated by Monte Carlo simulations on the application of a target tracking with INS/GPS integration under complex non-Gaussian noises.

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References

[1]	B. Parkinson, J. Spilker, P. Axelrad, and P. Enge, Global Positioning System: Theory and Applications. Norwood, MA, USA: Artech House, 2008.
[2]	L. Chang, J. Li, and K. Li, “Optimization-based alignment for strapdown inertial navigation system: Comparison and extension,” IEEE Trans. Aerosp. Electron. Syst., vol. 52, no. 4, pp. 1697–1713, Aug. 2016. doi: 10.1109/TAES.2016.130824
[3]	D. Titterton and J. Weston, Strapdown Inertial Navigation Technology. London, UK: Institution of Engineering and Technology, 2004.
[4]	P. D. Groves, Principles of GNSS, Inertial, and Multisensor Integrated Navigation Systems. Washington, USA: American Institute of Aeronautics and Astronautics, 1996.
[5]	M. Grewal, L. Weill, and A. Andrews, Global Positioning Systems, Inertial Navigation, and Integration. Hoboken, NJ: A John Wiley & Sons, 2007.
[6]	F. Zhao, C. Chen, W. He, and S. Sam Ge, “A filtering approach based on MMAE for a SINS / CNS integrated navigation system,” IEEE/CAA Journal of Automatica Sinica, vol. 5, no. 6, pp. 1113–1120, Nov. 2018. doi: 10.1109/JAS.2017.7510445
[7]	Y. Huang, Y. Zhang, and L. Chan, “A new fast in-motion coarse alignment method for GPS-aided low-cost SINS,” IEEE/ASME Trans. Mechatronics, vol. 23, no. 3, pp. 1303–1313, May 2018. doi: 10.1109/TMECH.2018.2835486
[8]	C. B. Medeiros and M. M. Wanderley, “Multiple-model linear Kalman filter framework for unpredictable signals,” IEEE Sensors J., vol. 14, no. 4, pp. 979–991, Apr. 2014. doi: 10.1109/JSEN.2013.2291683
[9]	A. Singh, “Major development under Gaussian filtering since unscented Kalman filter,” IEEE/CAA Journal of Automatica Sinica, vol. 7, no. 5, pp. 1308–1325, Sep. 2020.
[10]	S. Julier and J. Uhlmann, “A new extension of the Kalman filter to nonlinear systems,” in Proc. 11th Int. Symp. Aerospace/Defence Sens., Simul. Controls, 1997, pp. 182–193.
[11]	K. H. Kim, J. G. Lee, and C. G. Park, “Adaptive two-stage extended Kalman filter for a fault-tolerant INS/GPS loosely coupled system,” IEEE Trans. Aerosp. Electron. Syst., vol. 45, no. 1, pp. 125–137, Jan. 2009. doi: 10.1109/TAES.2009.4805268
[12]	D. Sun, M. G. Petovello, and M. E. Cannon, “Ultratight GPS/reducedIMU integration for land vehicle navigation,” IEEE Trans. Aerosp. Electron. Syst., vol. 49, no. 3, pp. 1781–1791, Jul. 2013. doi: 10.1109/TAES.2013.6558019
[13]	J. Wendel, J. Metzger, R. Moenikes, A. Maier, and G. F. Trommer, “A performance comparison of tightly coupled GPS/INS navigation systems based on extended and sigma point Kalman filters,” Navigation, vol. 53, no. 1, pp. 21–31, Aug. 2014.
[14]	J. Zhou, Y. Yang, J. Zhang, E. Edwan, and O. Loffeld, “Tightly coupled INS/GPS using quaternion-based unscented Kalman filter,” in Proc. AIAA Guid., Navigat., Control Conf., Portland, OR, USA, 2011, pp. 1–14.
[15]	L. Chang, K. Li, and B. Hu, “Huber’s M-estimation-based process uncertainty robust filter for integrated INS/GPS,” IEEE Sensors J., vol. 15, no. 6, pp. 3367–3374, Jun. 2015. doi: 10.1109/JSEN.2014.2384492
[16]	I. Arasaratnam and S. Haykin, “Cubature Kalman filters,” IEEE Trans. Autom. Control, vol. 54, pp. 1254–1269, Jun. 2009. doi: 10.1109/TAC.2009.2019800
[17]	B. Cui, X. Chen, and X. Tang, “Improved cubature Kalman filter for GNSS/INS based on transformation of posterior sigma-points error,” IEEE Trans. Signal Process., vol. 65, no. 11, pp. 2975–2987, Mar. 2017. doi: 10.1109/TSP.2017.2679685
[18]	Y. Zhao, “Performance evaluation of cubature Kalman filter in a GPS/IMU tightly-coupled navigation system,” Signal Process., vol. 119, pp. 67–79, Feb. 2016. doi: 10.1016/j.sigpro.2015.07.014
[19]	B. Cui, X. Chen, Y. Xu, H. Huang, and X. Liu, “Performance analysis of improved iterated cubature Kalman filter and its application to GNSS/INS,” ISA Trans., vol. 66, pp. 460–468, Jan. 2017. doi: 10.1016/j.isatra.2016.09.010
[20]	M. D. Pham, K. S. Low, S. T. Goh, and S. S. Chen, “Gain-scheduled extended Kalman filter for nanosatellite attitude determination system,” IEEE Trans. Aerosp. Electron. Syst., vol. 51, no. 2, pp. 1017–1028, Apr. 2015. doi: 10.1109/TAES.2014.130204
[21]	S. V. Bordonaro, P. W, Y. Bar-Shalom, and T. Luginbuhl, “Converted measurement sigma point Kalman filter for bistatic sonar and radar tracking,” IEEE Trans. Aerosp. Electron. Syst., vol. 55, no. 1, pp. 147–159, Feb. 2019. doi: 10.1109/TAES.2018.2849179
[22]	K. Feng, J. Li, X. Zhang, X. Zhang, C. Shen, H. Cao, Y. Yang, and J. Liu, “An improved strong tracking cubature Kalman filter for GPS/INS integrated navigation systems,” Sensors, vol. 18, no. 6, Article No. 1919, Jun. 2018. doi: 10.3390/s18061919
[23]	X. Chen, C. Shen, W. B. Zhang, M. Tomizuka, Y. Xu, and K. L. Chiu, “Novel hybrid of strong Kalman filter and wavelet neural network for GPS/INS during GPS outages,” Measurement, vol. 46, no. 10, pp. 3847–3854, Dec. 2013. doi: 10.1016/j.measurement.2013.07.016
[24]	M. S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking,” IEEE Trans. Signal Process., vol. 50, no. 2, pp. 174–188, Feb. 2002. doi: 10.1109/78.978374
[25]	X. Liu, H. Qu, J. Zhao, and P. Yue, “Maximum correntropy squareroot cubature Kalman filter with application to SINS/GPS integrated systems,” ISA Trans., vol. 80, pp. 195–202, May 2018. doi: 10.1016/j.isatra.2018.05.001
[26]	J. C. Príncipe, Information Theoretic Learning: Renyis Entropy and Kernel Perspectives, New York, NY, USA: Springer, 2010.
[27]	D. L. Alspach and H. Sorenson, “Nonlinear Bayesian estimation using Gaussian sum approximations,” IEEE Trans. Autom. Control, vol. 17, no. 4, pp. 439–448, Aug. 1972. doi: 10.1109/TAC.1972.1100034
[28]	Y. Huang and Y. Zhang, “A new process uncertainty robust Student’s t based Kalman filter for SINS/GPS integration,” IEEE Access, vol. 5, pp. 14391–14404, Jul. 2017. doi: 10.1109/ACCESS.2017.2726519
[29]	O. Straka and J. Duník, “Stochastic integration Student’s − t filter,” in Proc. 20th Int. Conf. Inf. Fusion, pp. 1–8, Jul. 2017.
[30]	Y. Huang and Y. Zhang, “Robust student’s t based stochastic cubature filter for nonlinear systems with heavy-tailed process and measurement noises,” IEEE Access, vol. 5, no. 5, pp. 7964–7974, May 2017.
[31]	F. Sun and L. Tang, “Cubature particle filter,” Syst. Eng. Electron., vol. 33, no. 11, pp. 2554–2557, Nov. 2011.
[32]	B. Cui, X. Chen, X. Tang, H. Huang, and X. Liu, “Robust cubature Kalman filter for GNSS/INS with missing observations and colored measurement noise,” ISA Trans., vol. 72, pp. 138–146, Jan. 2018. doi: 10.1016/j.isatra.2017.09.019
[33]	L. Mili, G. Steeno, F. Dobraca, and D. French, “A robust estimation method for topology error identification,” IEEE Trans. Power Syst., vol. 14, no. 4, pp. 1469–1476, Nov. 1999. doi: 10.1109/59.801932
[34]	L. Mili and C. W. Coakley, “Robust estimation in structured linear regression,” Ann. Statist., vol. 24, no. 6, pp. 2593–2607, Dec. 1996.
[35]	Y. S. Shmaliy, “An iterative Kalman-like algorithm ignoring noise and initial conditions,” IEEE Trans. Signal Process., vol. 59, no. 6, pp. 2465–2473, Jun. 2011. doi: 10.1109/TSP.2011.2129516
[36]	T. Chien-Hao, S. F. Lin, and J. Dah-Jing, “Robust Huber-based cubature Kalman filter for GPS navigation processing,” J. Navigat, vol. 229, no. 7, vol. 70, pp. 527–546, Otc. 2016.
[37]	K. Li, B. Hu, L. Chang, and Y. Li, “Robust square – Root cubature Kalman filter based on Huber’s mestimation methodology,” Proc. Inst. Mech. Eng. G-J. Aer., vol. 229, no. 7, pp. 1236–1245, Jun. 2015. doi: 10.1177/0954410014548698
[38]	A. Singh and J. C. Príncipe, “Using correntropy as a cost function in linear adaptive filters,” in Proc. Int. Joint Conf. Neural Netw (IJCNN), Jul. 2009, pp. 2950–2955.
[39]	B. Chen, J. Wang, H. Zhao, N. Zheng, and J. C. Príncipe, “Convergence of a fixed-point algorithm under maximum correntropy criterion,” IEEE Signal Process. Lett., vol. 22, no. 10, pp. 1723–1727, Otc. 2015. doi: 10.1109/LSP.2015.2428713
[40]	B. Chen, X. Liu, H. Zhao, and J. C. Príncipe, “Maximum correntropy Kalman filter,” Automatica, vol. 76, pp. 70–77, Feb. 2017. doi: 10.1016/j.automatica.2016.10.004
[41]	H. Wang, H. Li, J. Zuo, W. Zhang, and H. Wang, “Maximum correntropy derivative-free robust Kalman filter and smoother,” IEEE Access, vol. 6, pp. 70794–70807, Nov. 2018. doi: 10.1109/ACCESS.2018.2880618
[42]	S. Wang, C. Yin, G. Qian, Y. Feng, S. Kai, and L. Wang, “Maximum correntropy cubature Kalman filter based on statistical linear regression,” C.N. Patent, 106487358 A, Mar. 8, 2017. [Online]. Available: https://ieeexplore.ieee.org/document/9546666.
[43]	B. Chen, L. Xing, B. Xu, H. Zhao, and J. C. Príncipe, “Insights into the robustness of minimum error entropy estimation,” IEEE Trans. Neural Netw. Learn. Syst., vol. 29, no. 3, pp. 731–737, Mar. 2018. doi: 10.1109/TNNLS.2016.2636160
[44]	D. Erdogmus and J. C. Príncipe., “An error-entropy minimization for supervised training of nonlinear adaptive systems,” IEEE Trans. Signal Process., vol. 50, no. 7, pp. 1780–1786, Jul. 2002. doi: 10.1109/TSP.2002.1011217
[45]	Y. Zhang, B. Chen, X. Liu, Z. Yuan, and J. C. Príncipe, “Convergence of a fixed-point minimum error entropy algorithm,” Entropy, vol. 17, no. 8, pp. 5549–5560, Aug. 2015.
[46]	B. Chen, L. Dang, Y. Gu, N. Zheng, and J. C. Principe, “Minimum error entropy Kalman filter,” IEEE Trans. Syst.,Man,Cybern.,Syst., vol. 51, no. 9, pp. 5819–5829, Sep. 2021.
[47]	W. Liu, P. P. Pokharel, and J. C. Príncipe, “Error entropy, correntropy and M-estimation,” in Proc. 16th IEEE Workshop Machine Learn. Signal Process., 2006, pp. 179–184.
[48]	J. Zhao and L. Mili, “A robust generalized-maximum likelihood unscented Kalman filter for power system dynamic state estimation,” IEEE J. Sel. Topics Signal Process., vol. 12, no. 4, pp. 578–592, Aug. 2018. doi: 10.1109/JSTSP.2018.2827261
[49]	C. Andreou and V. Karathanassi, “Estimation of the number of endmembers using robust outlier detection method,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., vol. 7, no. 1, pp. 247–256, Jan. 2014. doi: 10.1109/JSTARS.2013.2260135
[50]	B. Chen, X. Wang, Y. Li, and J. C. Príncipe, “Maximum correntropy criterion with variable center,” IEEE Signal Process. Lett., vol. 26, no. 8, pp. 1212–1216, Aug. 2019. doi: 10.1109/LSP.2019.2925692
[51]	B. Chen, X. Wang, Z. Yuan, P. Ren, and J. Qin, “MultiKernel correntropy for robust learning,” [Online]. Available: https://ieeexplore.ieee.org/document/9546666. Accessed on: Oct. 15, 2021.
[52]	B. Ristic, S. Arulampalam, and N. Gordon, Beyond the Kalman Filter: Particle Filters for Tracking Applications. Norwood, MA, USA: Artech House, 2003.

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The MEEF-CKF is developed by applying the minimum error entropy with fiducial points (MEEF) to CKF, where the MEEF can automatically locate the peak of the error probability density function (PDF) at zero and is beneficial for robustness enhancement
A novel optimization approach is presented for determining the free parameters of MEEF-CKF adaptively
The complexity of MEEF-CKF is analyzed in detail, which indicates an acceptable burden in comparison with traditional Kalman filters. In addition, a sufficient condition is provided for ensuring the convergence of the fixed-point iteration in MEEF-CKF
The novel MEEF-CKF is applied for target tracking with the INS/GPS integration under different non-Gaussian noises. Simulation results have demonstrated the robustness of MEEF-CKF and the effectiveness of parameter optimization

Cubature Kalman Filter Under Minimum Error Entropy With Fiducial Points for INS/GPS Integration

doi: 10.1109/JAS.2021.1004350

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