Maximum Correntropy Unscented Kalman Filter for Spacecraft Relative State Estimation

A new algorithm called maximum correntropy unscented Kalman filter (MCUKF) is proposed and applied to relative state estimation in space communication networks. As is well known, the unscented Kalman filter (UKF) provides an efficient tool to solve the non-linear state estimate problem. However, the UKF usually plays well in Gaussian noises. Its performance may deteriorate substantially in the presence of non-Gaussian noises, especially when the measurements are disturbed by some heavy-tailed impulsive noises. By making use of the maximum correntropy criterion (MCC), the proposed algorithm can enhance the robustness of UKF against impulsive noises. In the MCUKF, the unscented transformation (UT) is applied to obtain a predicted state estimation and covariance matrix, and a nonlinear regression method with the MCC cost is then used to reformulate the measurement information. Finally, the UT is adopted to the measurement equation to obtain the filter state and covariance matrix. Illustrative examples demonstrate the superior performance of the new algorithm.

[1]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[2]  Nanning Zheng,et al.  Steady-State Mean-Square Error Analysis for Adaptive Filtering under the Maximum Correntropy Criterion , 2014, IEEE Signal Processing Letters.

[3]  V. Miranda,et al.  Entropy and Correntropy Against Minimum Square Error in Offline and Online Three-Day Ahead Wind Power Forecasting , 2009, IEEE Transactions on Power Systems.

[4]  S. Seereeram,et al.  Vision-based relative pose estimation for autonomous rendezvous and docking , 2006, 2006 IEEE Aerospace Conference.

[5]  Hyochoong Bang,et al.  Adaptive sparse grid quadrature filter for spacecraft relative navigation , 2013 .

[6]  Wentao Ma,et al.  Estimator with forgetting factor of correntropy and recursive algorithm for traffic network prediction , 2013, 2013 25th Chinese Control and Decision Conference (CCDC).

[7]  S. Haykin.  Kalman Filtering and Neural Networks , 2001 .

[8]  Ran He,et al.  Maximum Correntropy Criterion for Robust Face Recognition , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[10]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[11]  Badong Chen,et al.  Efficient and robust deep learning with Correntropy-induced loss function , 2015, Neural Computing and Applications.

[12]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[13]  Paul Honeine,et al.  Maximum correntropy unscented filter , 2016, Int. J. Syst. Sci..

[14]  Xi Liu,et al.  > Replace This Line with Your Paper Identification Number (double-click Here to Edit) < , 2022 .

[15]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[16]  Jian Zhang,et al.  Relative Navigation Method of Communication Supporting Spacecraft base-on Particle Filter ⋆ , 2013 .

[17]  Liang Wang,et al.  Robust Recognition via Information Theoretic Learning , 2014, SpringerBriefs in Computer Science.

[18]  Baiqing Hu,et al.  Huber-based novel robust unscented Kalman filter , 2012 .

[19]  Ran He,et al.  Robust Principal Component Analysis Based on Maximum Correntropy Criterion , 2011, IEEE Transactions on Image Processing.

[20]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[21]  Weifeng Liu,et al.  Correntropy: Properties and Applications in Non-Gaussian Signal Processing , 2007, IEEE Transactions on Signal Processing.

[22]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[23]  Michael Marszalek,et al.  Intersatellite Links and Relative Navigation: Pre-conditions for Formation Flights with Pico- and Nanosatellites , 2011 .

[24]  Yvonne Feierabend.  Estimation Theory And Applications , 2016 .

[25]  Hari B. Hablani,et al.  Guidance and Relative Navigation for Autonomous Rendezvous in a Circular Orbit , 2002 .

[26]  J. Junkins,et al.  Analytical Mechanics of Space Systems , 2003 .

[27]  Nanning Zheng,et al.  Generalized Correntropy for Robust Adaptive Filtering , 2015, IEEE Transactions on Signal Processing.

[28]  Jian Yang,et al.  Recursive robust least squares support vector regression based on maximum correntropy criterion , 2012, Neurocomputing.

[29]  Badong Chen,et al.  Maximum Correntropy Estimation Is a Smoothed MAP Estimation , 2012, IEEE Signal Processing Letters.

[30]  Liming Shi,et al.  Convex Combination of Adaptive Filters under the Maximum Correntropy Criterion in Impulsive Interference , 2014, IEEE Signal Processing Letters.

[31]  Nanning Zheng,et al.  Convergence of a Fixed-Point Algorithm under Maximum Correntropy Criterion , 2015, IEEE Signal Processing Letters.

[32]  S. Mitter,et al.  Robust Recursive Estimation in the Presence of Heavy-Tailed Observation Noise , 1994 .

[33]  Ferial El-Hawary,et al.  Robust regression-based EKF for tracking underwater targets , 1995 .

[34]  Falin Wu,et al.  Relative navigation for formation flying spacecrafts using X-ray pulsars , 2012, Proceedings of the 2012 IEEE/ION Position, Location and Navigation Symposium.

[35]  Jose C. Principe,et al.  Information Theoretic Learning - Renyi's Entropy and Kernel Perspectives , 2010, Information Theoretic Learning.

[36]  Wentao Ma,et al.  Maximum correntropy criterion based sparse adaptive filtering algorithms for robust channel estimation under non-Gaussian environments , 2015, J. Frankl. Inst..

[37]  Badong Chen,et al.  System Parameter Identification: Information Criteria and Algorithms , 2013 .