Adaptive “Cubature and Sigma Points” Kalman Filtering Applied to MEMS IMU/GNSS Data Fusion during Measurement Outlier
Affiliation(s)
SET Laboratory (Systèmes Electriques et Télecommande) of Electronic Department of Saad Dahlab University of Blida, Soumaa, Algeria. International Institute for Advanced Aerospace Technologies of Saint-Petersburg State University of Aerospace Instrumentation, 67 Bolshaya Morskaya, Saint Petersburg, Russia.
SET Laboratory (Systèmes Electriques et Télecommande) of Electronic Department of Saad Dahlab University of Blida, Soumaa, Algeria. International Institute for Advanced Aerospace Technologies of Saint-Petersburg State University of Aerospace Instrumentation, 67 Bolshaya Morskaya, Saint Petersburg, Russia.
ABSTRACT
In this paper, adaptive sensor fusion INS/GNSS is proposed to solve specific problem of non linear time variant state space estimation with measurement outliers, different algorithms are used to solve this specific problem generally occurs in intentional and non-intentional interferences caused by other radio navigation sources, or by the GNSS receiver’s deterioration. Non linear approximation techniques such as Extended Kalman filter EKF, Sigma Point Kalman Filters such as UKF and CDKF are computed to estimate the navigation states for UAV flight control. Several comparisons are conduced and analyzed in order to compare the accuracy and the convergence of different approaches usually applied in navigation data fusion purposes. The last non linear filter algorithm developed is the Cubature Kalman Filter CKF which provides more accurate estimation with more stability in Tracking data fusion application. In this work, CKF is compared with SPKF and EKF in ideal conditions and during GNSS outliers supposed to occur during specific interval of time, innovation based adaptive approach is selected and used to modify the covariance calculation of the non linear filters performed in this paper. Interesting results are observed, discussed with real perspectives in navigation data fusion for real time applications. Three parallel modified algorithms are simulated and compared to non-adaptive forms according to Root Mean Square Error (RMSE) criteria.
In this paper, adaptive sensor fusion INS/GNSS is proposed to solve specific problem of non linear time variant state space estimation with measurement outliers, different algorithms are used to solve this specific problem generally occurs in intentional and non-intentional interferences caused by other radio navigation sources, or by the GNSS receiver’s deterioration. Non linear approximation techniques such as Extended Kalman filter EKF, Sigma Point Kalman Filters such as UKF and CDKF are computed to estimate the navigation states for UAV flight control. Several comparisons are conduced and analyzed in order to compare the accuracy and the convergence of different approaches usually applied in navigation data fusion purposes. The last non linear filter algorithm developed is the Cubature Kalman Filter CKF which provides more accurate estimation with more stability in Tracking data fusion application. In this work, CKF is compared with SPKF and EKF in ideal conditions and during GNSS outliers supposed to occur during specific interval of time, innovation based adaptive approach is selected and used to modify the covariance calculation of the non linear filters performed in this paper. Interesting results are observed, discussed with real perspectives in navigation data fusion for real time applications. Three parallel modified algorithms are simulated and compared to non-adaptive forms according to Root Mean Square Error (RMSE) criteria.
KEYWORDS
IMU; MEMS; GPS; GNSS; Kalman Filtering; Cubature Rule; Sigma Points; Unscented Kalman Filter
IMU; MEMS; GPS; GNSS; Kalman Filtering; Cubature Rule; Sigma Points; Unscented Kalman Filter
Cite this paper
H. Benzerrouk, H. Salhi and A. Nebylov, "Adaptive “Cubature and Sigma Points” Kalman Filtering Applied to MEMS IMU/GNSS Data Fusion during Measurement Outlier," Journal of Sensor Technology, Vol. 3 No. 4, 2013, pp. 115-125. doi: 10.4236/jst.2013.34018.
H. Benzerrouk, H. Salhi and A. Nebylov, "Adaptive “Cubature and Sigma Points” Kalman Filtering Applied to MEMS IMU/GNSS Data Fusion during Measurement Outlier," Journal of Sensor Technology, Vol. 3 No. 4, 2013, pp. 115-125. doi: 10.4236/jst.2013.34018.
References
[1] I. Arasaratnam and S. Haykin, “Cubature Kalman Filtering,” IEEE Transactions on Automatic Control, Vol. 54, No. 6, 2009, pp. 1254-1269. http://dx.doi.org/10.1109/TAC.2009.2019800 [2] A R. Runnalls, “A Kullback-Leibler Approach to Gaussia Mixture Reduction,” IEEE Transaction on Aerospace and Electronic System, 2006. [3] P. Tchikavsky, C. H. Muravchik and A. Nehorai, “Posterior Cramer Rao Bounds for Discrete Time Nonlinear Filtering,” IEEE Transactions on Signal Processing, Vol. 46, No. 5, 1998, pp. 1386-1396. [4] H. Benzerrouk and A. V. Nebylov, “Robust Nonlinear Filtering Applied to Integrated Navigation System under Non Gaussian Measurement Noise Effect,” Proceeding of IEEE AEROSPACE Conference 2012, Big Sky Montana. [5] D. Karlgaard Christopher and S. Henspeter, “Huber Divided Difference Fiters,” Vol. 30, No. 3, 2007, pp. 885-891. [6] P. Closas and C. Fernandez-Prades, “Bayesian Nonlinear Filters for Direct Position Estimation,” Proceedings of the IEEE Aerospace Conference, Big Sky, MT (USA), March 2010, pp. 1-12. [7] P. Closas and C. Fernandez-Prades and J. Vilà-Valls, “Multiple Quadrature Kalman Filtering,” IEEE Transactions on Signal Processing, Vol. 60, No. 12, 2012, pp. 6125-6137. [8] H. Benzerrouk, “Gaussian vs. Non-Gaussian Noise in Inertial/GNSS integration,” GNSS Solutions, Inside GNSS Magazine, November/December 2012, pp. 32-39.
[1] I. Arasaratnam and S. Haykin, “Cubature Kalman Filtering,” IEEE Transactions on Automatic Control, Vol. 54, No. 6, 2009, pp. 1254-1269. http://dx.doi.org/10.1109/TAC.2009.2019800 [2] A R. Runnalls, “A Kullback-Leibler Approach to Gaussia Mixture Reduction,” IEEE Transaction on Aerospace and Electronic System, 2006. [3] P. Tchikavsky, C. H. Muravchik and A. Nehorai, “Posterior Cramer Rao Bounds for Discrete Time Nonlinear Filtering,” IEEE Transactions on Signal Processing, Vol. 46, No. 5, 1998, pp. 1386-1396. [4] H. Benzerrouk and A. V. Nebylov, “Robust Nonlinear Filtering Applied to Integrated Navigation System under Non Gaussian Measurement Noise Effect,” Proceeding of IEEE AEROSPACE Conference 2012, Big Sky Montana. [5] D. Karlgaard Christopher and S. Henspeter, “Huber Divided Difference Fiters,” Vol. 30, No. 3, 2007, pp. 885-891. [6] P. Closas and C. Fernandez-Prades, “Bayesian Nonlinear Filters for Direct Position Estimation,” Proceedings of the IEEE Aerospace Conference, Big Sky, MT (USA), March 2010, pp. 1-12. [7] P. Closas and C. Fernandez-Prades and J. Vilà-Valls, “Multiple Quadrature Kalman Filtering,” IEEE Transactions on Signal Processing, Vol. 60, No. 12, 2012, pp. 6125-6137. [8] H. Benzerrouk, “Gaussian vs. Non-Gaussian Noise in Inertial/GNSS integration,” GNSS Solutions, Inside GNSS Magazine, November/December 2012, pp. 32-39.