Maximum correntropy unscented filter

ABSTRACT The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilising a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimator leads to the well-known unscented Kalman filter (UKF). Although the UKF works very well in Gaussian noises, its performance may deteriorate significantly when the noises are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises. To improve the robustness of the UKF against impulsive noises, a new filter for non-linear systems is proposed in this work, namely the maximum correntropy unscented filter (MCUF). In MCUF, the UT is applied to obtain the prior estimates of the state and covariance matrix, and a robust statistical linearisation regression based on the maximum correntropy criterion is then used to obtain the posterior estimates of the state and covariance matrix. The satisfying performance of the new algorithm is confirmed by two illustrative examples.

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

[2]  José Carlos Príncipe,et al.  Using Correntropy as a cost function in linear adaptive filters , 2009, 2009 International Joint Conference on Neural Networks.

[3]  Petar M. Djuric,et al.  Gaussian particle filtering , 2003, IEEE Trans. Signal Process..

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

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

[6]  Nasser E. Nahi,et al.  Estimation Theory and Applications , 1969 .

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

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

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

[10]  H. Schaub,et al.  Huber-based divided difference filtering , 2007 .

[11]  Dan Li,et al.  Fault tolerant navigation method for satellite based on information fusion and unscented Kalman filter , 2010 .

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

[13]  Frederick R. Forst,et al.  On robust estimation of the location parameter , 1980 .

[14]  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..

[15]  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.

[16]  Yuanqing Xia,et al.  Unscented Kalman Filter Over Unreliable Communication Networks With Markovian Packet Dropouts , 2013, IEEE Transactions on Automatic Control.

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

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

[19]  José Carlos Príncipe,et al.  A closed form recursive solution for Maximum Correntropy training , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

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

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

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

[23]  Ying Wang,et al.  Robust Hyperspectral Unmixing With Correntropy-Based Metric , 2013, IEEE Transactions on Image Processing.

[24]  José Carlos Príncipe,et al.  A Pitch Detector Based on a Generalized Correlation Function , 2008, IEEE Transactions on Audio, Speech, and Language Processing.

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

[26]  Guangjun Liu,et al.  Adaptive unscented Kalman filter-based online slip ratio control of wheeled-mobile robot , 2014, Proceeding of the 11th World Congress on Intelligent Control and Automation.

[27]  Badong Chen,et al.  Kernel adaptive filtering with maximum correntropy criterion , 2011, The 2011 International Joint Conference on Neural Networks.

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

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

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

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

[32]  Y. Cho,et al.  Fixed Point Theory and Applications , 2000 .

[33]  Xiaogang Wang,et al.  Huber-based unscented filtering and its application to vision-based relative navigation , 2010 .

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

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

[36]  Bijaya Ketan Panigrahi,et al.  Adaptive complex unscented Kalman filter for frequency estimation of time-varying signals , 2010 .