Non-Gaussian Sensor Fusion Analysis with “Gaussian Mixture and Adaptive” Based Cubature Kalman Filtering for Unmanned Aerial Vehicle

Hamza Benzerrouk(1*), Hassen Salhi(2), Alexander Nebylov(3)

(1) SET Laboratory (Systèmes Electriques et Télecommande) of Electronic Department of Saad Dahlab University of Blida, 270, Soumaa, Algeria
(2) SET Laboratory (Systèmes Electriques et Télecommande) of Electronic Department of Saad Dahlab University of Blida, 270, Soumaa, Algeria
(3) 2International Institute for Advanced Aerospace technologies of Saint-Petersburg State University of Aerospace Instrumentation, 67 Bolshaya Morskaya, 190000, Saint Petersburg, Russian Federation
(*) Corresponding author

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In this paper, comparison of adaptive and robust non Gaussian sensor fusion INS/GNSS is proposed to solve specific problem of non linear non Gaussian time variant state space estimation with impulsive measurement noise, different algorithms are proposed based on the most recent approaches in non linear filtering during intentional and non intentional interferences caused by multiple sources, or by the GNSS receivers signal degradation. Non linear filters such as Extended Kalman filter EKF and the last developed Cubature based Kalman Filter are implemented to estimate the navigation flight states for UAV. A specific hypothesis assumes high non Gaussian scenario and low non Gaussian noise level. Especially, alpha stable impulsive noise is simulated and affects GNSS measurement. The modern non linear filter algorithm called Cubature Kalman Filter CKF which provides more accurate estimation with more stability in Tracking data fusion application is compared with conventional non linear filters under non Gaussian constraints as a first step, thus, additional hypothesis is introduced which consists on Gaussian measurement outliers of each non Gaussian densities. In our work, Gaussian sum filtering and adaptive fading algorithms are proposed to solve the problem of IMU/GNSS integration in denied environment. CKF is compared with EKF in ideal conditions and during GNSS impulsive interferences modeled as non Gaussian noises “Sum of Gaussian” supposed to occur during specific interval of time, during the same interval, we assume additional denied environment which consists on the vari\ation of the Gaussian sum noise covariance, then, innovation based adaptive fading approach is selected and used to modify the covariance calculation of the parallel non linear filters performed in this work. Two important results are carried out depending on the variation of the Gaussian mixture density modeled in this work. original results are observed, discussed with real perspectives in navigation data fusion for real time applications under multiple denied environment conditions.
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MEMS; GPS; GNSS; Kalman Filtering; CKF; Gaussian Sum; Alpha-Stable Noise; Adaptive Fading

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Rudolph van der Merwe and Eric A. Wan, Sigma-Point Kalman Filters for Nonlinear Estimation and Sensor-Fusion- Applications to Integrated Navigation - GNC American Institute of Aeronautics and Astronautics,2004.

D. Li, J. Wang, S. Babu, Enhancing the Performance of Ultra-Tight Integration of GPS/PL/INS: A Federated Filter Approach,Pub. Date: March 24, 2009.

Benzerrouk. H, Nebylov.A.V., “Robust Nonlinear Filtering Applied to Integrated Navigation System under non Gaussian measurement noise Effect”-in Proceeding of IEEE AEROSPACE Conference 2012, Big Sky Montana.

Gerasimos G. Rigatos , Nonlinear Kalman Filters and Particle Filters for integrated navigation of unmanned aerial vehicles Original Research Article, Robotics and Autonomous Systems, Volume 60, Issue 7, July 2012, Pages 978-995.

A R. Runnalls, “ A Kullback-Leibler Approach to Gaussian Mixture Reduction”, IEEE Transaction on Aerospace and Electronic System,2006.

H. Benzerrouk, « Gaussian vs. Non-Gaussian noise in inertial/GNSS integration », GNSS Solutions, Inside GNSS Magazine, november/december 2012, pp32-39.

I. Arasaratnam and S. Haykin,” Cubature Kalman Filtering”, IEEE Trans. Automatic Control, vol.54,no.6, pp.1254-1269,June 2009

Revo autopilot board, products/openpilot-revolution-platform/15th october2013

Francisco Martín, Vicente Matellán, Pablo Barrera, José M. Cañas , Localization of legged robots combining a fuzzy-Markov method and a population of extended Kalman filters, Original Research Article, Robotics and Autonomous Systems, Volume 55, Issue 12, 31 December 2007, Pages 870-880.

P. Closas and C. Fern´andez-Prades, “Bayesian Nonlinear Filters for Direct Position Estimation,” in Proceedings of the IEEE Aerospace conference, Big Sky, MT (USA), March 2010.

Emadeldeen Noureldaim, Mohamed Jedra, Multiple Tracking of Moving Objects with Kalman Filtering and PCA-GMM Method, Nouredine Zahid, PP. 42-47, Pub. Date: March 29, 2013.

Chingiz Hajiyev, Sıtkı Yenal Vural, LQR Controller with Kalman Estimator Applied to UAV Longitudinal Dynamics, PP. 36-41, Pub. Date: February 27, 2013.

Ienkaran Arasaratnam , Sensor Fusion with Square-Root Cubature Information FilteringPP. 11-17, Pub. Date: February 6, 2013, DOI: 10.4236 /ica.2013.41002.

P. Closas and C. Fern´andez-Prades,” The Marginalized Square Root Quadrature Kalman Filter” in Signal Processing Advanced in Wireless Communications (SPAWC), 2010 IEEE 11th International Workshop on.

P. Tchikavsky, CH. Muravchik and A. Nehorai, “ Posterior Cramer Rao Bounds for Discrete Time Nonlinear Filtering”, IEEE Trans. Signal Processing,vol.46,no.5, 1998.

Leong, P.H. ; Coll. of Eng. & Comput. Sci., Australian Nat. Univ., Canberra, ACT, Australia ; Arulampalam, S. ; Lamahewa, T.A. ; Abhayapala, T.D., A Gaussian-Sum Based Cubature Kalman Filter for Bearings-Only Tracking, ,2013 (Volume:49 , Issue: 2 ) 10.1109/TAES.2013.6494405.

Mounir DJEDDI, Messaoud BENIDIR, A Robust Estimator for Polynomial Phase Signals in Non Gaussian Noise Using Parallel Unscented Kalman Filters, 14th European Signal Processing Conference (EUSIPCO 2006), Florence, Italy, September 4-8, 2006.

Miroslav Simandl “Lecture notes on state estimation of nonlinear non-Gaussian stochastic systems”, • Department of Cybernetics, Faculty of Applied Sciences -University of West Bohemia in Pilsen, Pilsen 2006.

Karlgaard Christopher.D, SCHAUBT Henspeter, Huber Divided Difference filters 2007, vol. 30, no3, pp. 885-891.

Shesheng Gao, Yongmin Zhong, Xueyuan Zhang, Bijan Shirinzadeh ,Multi-sensor optimal data fusion for INS/GPS/SAR integrated navigation system Original Research Article, Aerospace Science and Technology, Volume 13, Issues 4–5, June–July 2009, Pages 232-237.

Shu Ting Goh, Ossama Abdelkhalik, Seyed A. (Reza) Zekavat, A Weighted Measurement Fusion Kalman Filter implementation for UAV navigation, Aerospace Science and Technology, Volume 28, Issue 1, July 2013, Pages 315-323.

Xiaolin Ning, Jiancheng Fang,An autonomous celestial navigation method for LEO satellite based on unscented Kalman filter and information fusion, Original Research Article, Aerospace Science and Technology, Volume 11, Issues 2–3, March–April 2007, Pages 222-228.

Xiaogang Wang, Naigang Cui, Jifeng Guo, INS/VisNav/GPS relative navigation system for UAV Original Research Article, Aerospace Science and Technology, Volume 28, Issue 1, July 2013, Pages 242-248.


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